Accuracy of Commercial Process Simulators for Hydrate Inhibition

Many materials may be added to water to depress both hydrate and freezing temperatures. For many practical reasons an alcohol or one of the glycols is injected as an inhibitor, usually methanol, diethylene glycol (DEG) or mono ethylene glycol (MEG). All may be recovered and recirculated, but economic of methanol recovery may not be favorable in many cases. Total injection rate is that needed to provide the necessary inhibitor concentration in the liquid water plus that inhibitor which enters the vapor and hydrocarbon liquid phases. Any inhibitor in the vapor phase or liquid hydrocarbon phase has little effect on hydrate formation conditions. Determination of the amount and concentration of inhibitors and their distribution in different phases are very important for practical purposes and industrial applications. Therefore, in order to determine the required amount and concentration of these inhibitors, several thermodynamic models for hand and rigorous calculations have been developed and incorporated into the computer software.

In this Tip of the Month, we will evaluate the accuracy of two commercial process simulators “A” and “B” against the experimental data. These softwares were used to predict hydrate formation condition in the presence of inhibitor. Pure gas component as well as multi component natural gas mixtures covering a wide pressure range of up to 100 MPa have been studied. These softwares may be used to simulate an integrated NGL (natural gas liquid) plant with inhibitor injection and regeneration process. The optimum concentration and circulation rate are determined using different softwares. The strength and limitation of these softwares are identified and recommendations for industrial applications have been made.

Table 1 presents the composition, inhibitor weight % range, pressure range, number of points, the reference of the experimental data for the gas mixtures studied in this work. The ability of the two softwares to predict the hydrate formation temperature for gas E is shown in Figure 1. The accuracy of these softwares for CH4, C2H6, C3H8, CO2, H2S and their mixtures as shown in Table 1 are presented in Figures 2 and 3; for methanol and MEG, respectively

The analysis of Figures 2 and 3 indicates that for methanol inhibition, the lower limits of hydrate formation temperatures are -75°F (-60°C) for Sim A (maximum of 70 wt% methanol) and -25°F (-32°C) for Sim B (Maximum of 50 wt% methanol). It should be pointed out that Sim B could not converge for cases of 85 wt% methanol. For MEG, both softwares give accurate results down to 25°F (-4°C) corresponding to 25 wt% MEG; however, for lower temperatures the accuracy drops while the Sim A gives better results. To learn more about inhibitor injection we suggest participating in our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Ng, Heng-Joo, and D.B. Robinson, Research Report RR-66, Gas Processors association, Tulsa, Oklahoma, 19832. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-106, Gas Processors association, Tulsa, Oklahoma, 19873. Blanc, C., and Tournier-Lasserve, J., World Oil, November, 1990.4. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-92, Gas Processors association, Tulsa, Oklahoma, 1985

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Accuracy of Three Shortcut Prediction Methods for Hydrate Inhibition

In the last “Tip of the Month”, we evaluated the accuracy of two commercial process simulators against the experimental data. In this “Tip of the Month”, we will evaluate the accuracy of three shortcut methods for prediction of depression of hydrate formation temperature in the presence of two common inhibitors, methanol (MeOH) or mono ethylene glycol (MEG). We have used the same set of experimental data from the previous “Tip of the Month” as the basis for our evaluation. These shortcut methods may be used to calculate the required concentration of inhibitor and the injection rate for dew point correction process, NGL (Natural Gas Liquid) recovery, or pipeline transportation of natural gas. The detail of the calculation procedure is presented in chapter 6 of Volume 1 of Gas Conditioning and Processing [1]. The three methods evaluated are the Hammerschmidt (HA) [2], Nielsen- Bucklin (NB) [3], and Moshfeghian-Maddox (MM) [4]. These methods were used to predict hydrate formation temperature in the presence of inhibitors. Pure compounds as well as multi component natural gas mixtures covering a wide pressure range of up to 14500 psia (100 MPa) have been studied. Even though the shortcut methods presented in reference [1] could have been used, the required hydrate formation temperatures in the absence of inhibitor (pure water) were predicted by Parish and Prausnitz (PP) [5] for all three methods. This assured the same basis and accurate results. The strength and limitation of these methods are identified and recommendations for industrial applications have been made.

Table 1 presents the composition, inhibitor weight % range, pressure range, number of points, the reference of the experimental data for the gas mixtures studied in this work. The ability of the three methods to predict the hydrate formation temperature for gas E is shown in Figure 1. The accuracy of these methods, for CH4, C2H6, C3H8, CO2, H2S and their mixtures as shown in Table 1, are presented in Figures 1 and 2 for MeOH and Figures 3 and 4 for MEG.

Figure 1 indicates that the PP method predicts the hydrate formation temperature for gas E in the presence of pure water (0 wt% MeOH) accurately. This method was used to add its perdition temperature to the depression temperature predicted by the three shortcut methods for the sake of easy comparison with the experimental data. Figure 1 also indicates that all three methods give good results for 20 wt% MeOH; however, for 40 wt% MeOH, the HA results deviate from the experimental data considerably.

The analysis of Figures 2 indicates that all three methods give accurate results for temperature as low as 20 °F (-6.7 °C) equivalent to maximum of 25 wt% MeOH, but at lower temperature (or higher MeOH concentration) the HA method deviates from the experimental data considerably. For lower temperatures, the MM gives better results than the NB method.

Figure 3 and 4 indicate that all three methods give accurate results for gas mixture F up to concentration of 50 wt% MEG (as low as 0 °F or -18 °C) for which experimental data were available but their prediction for some of the pure compounds below this temperature is questionable.

To learn more about inhibitor injection we suggest participating in our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Campbell, J. M., “Gas Conditioning and Processing, Vol. 1, the Equipment Modules, 8th Ed., J. M. Campbell and Company, Norman, Oklahoma, 2001

2. Hammerschmidt, E.G., ‘Formation of gas hydrates in natural gas transmission lines,” Ind & Eng. Chem, Vol. 26, p. 851, 19343. Nielsen, R. B. and R.W. Bucklin, “Why not use methanol for hydrate control,” Hydrocarbon Processing, Vol 62, No. 4, P 71, April 19834. Moshfeghian, M. and R. N. Maddox, “Method predicts hydrates for high- pressure gas streams,” Oil and Gas J., August 1993.5. Parrish, W. R. and J. M. Prausnitz. “Dissociation Pressures of Gas Hydrates Formed by Gas Mixtures”, Ind. Eng. Chem. Proc. Dev.,11, 1, 26-35,

(1972).6. Ng, Heng-Joo, and D.B. Robinson, Research Report RR-66, Gas Processors association, Tulsa, Oklahoma, 19837. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-106, Gas Processors Association, Tulsa, Oklahoma, 19878. Blanc, C., and Tournier-Lasserve, J., World Oil, November, 1990.9. Ng, Heng-Joo, C.J. Chen, and D.B. Robinson, research report RR-92, Gas Processors Association, Tulsa, Oklahoma, 1985

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Liquid Density

Liquid density is needed for process simulation and equipment design. For example, accurate predictions of liquid density are needed for calculation of pressure drop in a piping/pipeline and vessel sizing. Accurate liquid density is also essential for custody transfer.

Liquid density ranges from a few hundred above thousand to couple of 100 kg/m3. Table 1 presents typical range of liquid densities where as typical re-injection gas has a density in the range of 125 to 150 kg/m3 and pipeline gases at 7000kPa has a density in the order of 70 kg/m3.

Liquid densities are sometime expressed in terms of relative density (specific gravity) or API gravity. The relative density,? , is defined as:

and the API (American Petroleum Index) gravity is:

Depending on the applications, three different methods can be used to compute liquid density in addition to direct laboratory measurement. These methods are (a) charts and monographs, (b) correlations and (c) EoS or volume translated EoS, of which the correlations are usually the most accurate.

For the LNG density measurement and calculation, one of the standard procedures practiced in industry is ISO 6578: 1991 [1]. This procedure specifies the calculations to be made to adjust the volume of a liquid from the conditions at measurement to the equivalent volume of liquid or vapor at a standard temperature and pressure, or to the equivalent mass or energy (calorific content). Annexes A to H of this procedure form an integral part of this standard.

Generalized Charts

There are several generalized charts for prediction of liquid density of petroleum fluids and hydrocarbons [2].

The relative density of petroleum fluids are normally expressed in terms of two of three characteristics- API gravity at 15°C, the Watson characterization factor, KW, or the mean average boiling point. The Watson characterization factor is defined in terms of mean average boiling point, Tb, and the relative density at standard condition.

The charts normally present the relative density of paraffinic hydrocarbon mixtures at their boiling point or bubble point temperature and pressure. These charts apply to mixtures as well to pure components. Alignment points for paraffinic hydrocarbon mixtures and pure components are located according to their molecular weight. The accuracy of these charts is generally within 3 % of the measured values. However, the accuracy is somewhat less for mixtures having molecular weights less than 30 where temperature is low, and where the methane content is high or reduced temperatures above 0.9 [3].

EoS Methods and Volume Translation

The EoSs are used in commercial simulation softwares for predicting phase behavior and thermodynamic properties. Generally, EoSs need a few parameters (usually two or three) that are normally obtained from critical properties. The cubic equations of state (EOS) give accurate results for prediction of vapor-liquid equilibria, especially for non-polar or slightly polar systems. Furthermore, these equations could be used to accurately predict vapor densities, enthalpy and entropy. These advantages encourage the researchers to augment EoS ability more than before, especially, liquid density, although their accuracy for liquid density prediction is not as good as correlations. The popular EoSs such as SRK [4] and PR [5] predict liquid density with an average absolute error about 8%, much more than the correlations [6]. This large magnitude of error is not acceptable by industry; therefore; they are not used for this purpose. In order to overcome this deficiency, a volume translated method has been developed by Peneloux et al. [7]. The working equations are:

In the above equation, vSRK is calculated by SRK EoS and the correction term “c” as follows:

Correlations

In order to calculate liquid density reliably, several correlations such as COrresponding STAte Liquid Density (COSTALD) and modified Rackett equation by Spencer and Danner (RSD), have been developed.

COSTALD correlation: The COSTALD correlation, Hankinson and Thomson [8], requires two parameters, ?SRK, the optimized value of the acentric factor based on the SRK EoS and V*, the pure component characteristic volume.

The RSD correlation: Spencer and Danner [9] improved the liquid density correlation of Rackett [10]. The improved correlation for saturated liquid density calculation requires only ZRA, the improved compressibility factor.

In next “Tip of the Month” we will provide guidelines for use of these methods and present the results of a comparison study between these methods.

To learn more about liquid density and its impact on facilities calculation, design and surveillance, refer to JMC books and enroll in our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By Dr. Mahmood Moshfeghian

Guidelines for Liquid Density Prediction – Part 2: Process Simulators

In the last two “Tip of the Month” we briefly discussed the importance of liquid density for process simulation and equipment design. Three different methods were introduced to compute liquid density. The methods were (a) charts and monographs, (b) correlations and (c) EoS or volume translated EoS. We also presented a comparison between accuracy of different correlations and EoS methods and provided guidelines for using correlations.

In this “Tip of the Month”, we will present a comparison between accuracy of HYSYS [1] and ProMax [2] process simulation packages which normally use correlations for liquid density calculations. For HYSYS we used the “Smooth Liquid Density” option and in ProMax there are two options of COSTALD [3, 4] and Rackett [5] but we only used the COSTAD method for the reasons discussed in the last tip of the month. Both of these methods are discussed in Chapter 3 of JMC Volume 1 of Gas Conditioning and Processing Book [6]. The focus will be on the mixture of light hydrocarbons which have wider applications in gas industry. We will provide guidelines to use these process simulation programs effectively. In this study we have used the experimental data reported in GPA Research Report RR-147 [7].

We predicted the saturated liquid density of the ethane-propane mixture for the conditions reported in the GPA research report using the default option of HYSYS and ProMax. For the default option for each set of experimental conditions, we entered temperature, pressure, composition and total number of moles (100 moles was used for all cases). In Figure 1, the predicted results for 90 points are plotted as a function of the experimental values.

As can be seen in this figure, for several points the errors are very large. These large errors are due to the fact that for these points the process simulators predict partially vaporized systems and the reported densities are for a two phase mixture and not for the actual liquid mixture as reported experimentally. Therefore, we performed a flash calculation for each experimental point, separated the gas from the feed and predicted the density for the resulting liquid stream and re-plotted the results in Figure 2. This causes some changes in composition but Figure 2 indicates that considerable improvement in accuracy is obtained by degassing the feed stream.

Since the reported experimental data were at saturated liquid conditions, a second option is to predict the liquid density using the bubble point option. For this option, we entered temperature, vapor fraction of zero, composition of components, and 100 moles for total feed. By performing bubble point calculation, the liquid density and bubble point pressure were calculated. Figures 3 and 4 show the accuracy of HYSYS and ProMax in predicting the liquid densities and bubble point pressures, respectively. Again, quite an improvement is obtained by performing bubble point calculation to obtain the liquid density.

We repeated similar calculations for propane-normal butane and normal butane-normal pentane mixtures and have summarized in Table 1 the error analysis for different options using the simulation softwares.

Table 1 indicates that if the default option of HYSYS and ProMax are used, the calculated liquid density may contain a large error. On the other hand, when the mixture was flashed and the vapor was removed the calculated density was more accurate. Finally, calculating the liquid density using bubble point calculation yields more accurate density; however, the pressure may deviate slightly from the specified system pressure. The deviation of pressure does not cause a major concern because the pressure effect on liquid properties is not that much and more often it is ignored.

To learn more about liquid density and its impact on facilities calculation, design and surveillance, refer to JMC books and enroll in our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By Dr. Mahmood Moshfeghian

Reference:

1. HYSYS, version 2004.2, Aspen Technology Inc., Cambridge, Massachusetts, 2005.2. ProMax, version 1.2, Bryan Research & Engineering Inc, Bryan, Texas, 2005.3. Hankinson, R. W.; Thomson, G. H. A new correlation for saturated densities of liquids and their mixtures. AIChE J. 1979, 25, 653.4. Thomson, G. H.; Brobst, K. R.; Hankinson, R. W. An improved correlation for densities of compressed liquids and liquid mixtures. AIChE J., 28, 671,

19825. Rackett, H. G. Equation of state for saturated liquids. J. Chem. Eng. Data, 15, 514, 19706. Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.7. Holcomb, C.D., Magee, J.W., and W.M. Haynes, “Density Measurements on Natural Gas Liquids,” Gas Processor Associations, RR-147, Tulsa,

1995.

Why do I care about phase diagrams?

In facilities operations the understanding of where the process is on a phase diagram can often help the engineer and operator avoid extremely embarrassing design and operating mistakes. The oil and gas industry is full of many “war stories” about “phase diagram disasters.” Most instances are never related back to the phase diagram misunderstanding. In one well-documented but poorly published case a “dry gas” pipeline that was pigged flooded miles of sandy beach. In another case thousands of kilowatts of compression power were installed to maintain the pressure of a reservoir above the dew point when in fact the reservoir was at a temperature above the cricondentherm. In many cases equipment manufacturers and purchasers of gas have specifications of “superheat” or dew point that have not been met and led to upset customers and/or millions of dollars of lawsuits.

One of the first issues to be resolved by a facilities engineer working in a gas plant or gas production facility is where is the process operating with respect to the phase diagram. A general knowledge, if not a detailed knowledge, will allow the design engineer and the facilities operator to make intelligent decisions that have significant impact on the profitability of a gas production facility.

The following figure is a “generic hydrocarbon mixture” phase diagram for a lean gas. The area to the left of the Bubble Point line is the sub-cooled liquid region.

The area to the right of the Dew Point line is the super-heated gas region. Between these two lines the mixture is two-phase. Other areas of interest are the retrograde region and the supercritical region. Each of these regions provides advantages and disadvantages for operations.

This month we will start to define the points of interest so that we may choose proper operating points for various types of processes. The first point to define is the cricondentherm. The definition of this point is the highest temperature at which twophases (liquid and vapor for most processes) can coexist. In Figure 1, this is point M. Point M has considerable theoretical and practical importance. For example, if the cricondentherm for a sales gas (point M) is 0 ºC (32 ºF) cooling the gas to 4 ºC (40 ºF) at any pressure will not result in condensation of liquids. This type of operation is typically the type used for cross-country transportation of gas in pipelines. Operation with this type of system will not require “slug catchers” at the end of the pipeline and will significantly decrease pressure drop in the pipeline.

If the gas were processed in a cold separator such that point B (a dew point) was 0 ºC (32 ºF) problems could occur in the same conditions as the pipeline mentioned above. If the pressure of the pipeline was between the pressure of point B and F and the pipeline cooled to 4 ºC (40 ºF) there could be significant quantities of liquid in the pipeline. If the operations people were not familiar with the phase diagram they might increase the operating pressure of the cold separator and still keep the temperature at 0 ºC (32 ºF). This action would result in increased liquids in the pipeline, not decreased. However, if the cold separator was operated at the pressure of point M, at a temperature of 0 ºC (32 ºF), in theory there would be no liquids in the pipeline again. (More about the difference between theory and practice in future tips).

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special) and G7 (Process Simulation in Gas Conditioning and Processing) courses.

Dr. Larry L. Lilly

Consequence of Liquid Carry Over in a Simple Dew Point Control Plant

Problems in meeting sales-gas dew point specifications are not unusual. A facility engineer often suspects separator carryover when trouble-shooting such a plant. Proper sizing of equipment for vapor-liquid separation is essential to almost all processes. The fundamentals of a simple separator design may be extended to several other processes such as fractionation towers, two-phase flow, slug catcher design etc. Many facility operating problems are related to improperly designed or under-sized gas-liquid separators.

Let’s consider the process flow diagram shown in Figure 1 for a simple gas plant. The feed composition and conditions are shown in Table 1. In one of our past Tip of the Months (TOTM) we demonstrated the impact of liquid carry over on the “sales gas dew point” and we experienced that for even a small liquid carry over (1 %), the dew point offset was about 6°F [3.3 °C]. In this Tip of the Month, we will demonstrate the consequences of liquid carry over on the other equipment while maintaining the “spec dew point”.

It is desired to process this feed gas to produce a sales gas with a dew point of 20 °F (-6.7 °C) at 540 psig (3.723 MPa) The feed gas is mixed with recycle gas from a stabilizer, compressed and cooled to 110°F (43.3°C) and 555 psig (3.827 MPa), then cooled in the gas-gas exchanger, gas-liquid exchanger and finally in the chiller to 20°F (-6.7°C) before entering the separator at 540 psig (3.723 MPa). In real equipment, there would be some liquid carry over. The commercial simulators will assume a perfect gas-liquid separation unless the users manually force some carryover. In order to show the impact of liquid carry over, in simulation we withdraw a small portion of liquid stream from separator and remixed it with the vapor stream. The solid curve in Figure 2 shows how the dew point of sales gas goes off spec as a function of the liquid carry over.

In order to bring back the sales gas dew point to spec, we re-adjusted (lowered) the stream 7 temperature. The required degree of re-adjustment is shown by the dashed line in the same figure. As a consequence of re-adjusting of the stream 7 temperature, the conditions of other equipment and streams changed. Figure 3 shows the variation of compressor power and the heat exchanger duties as a function of liquid carry over. As can be seen in this figure, a-one percent liquid carry over can cause considerable change. For this case, the percent changes ranged from 15 to 55 percent. The changes in the reboiler duty, sales gas and LPG flow rates were negligible. Please note that we assumed variable area of the heat exchangers. If this analysis is done prior to building a new plant, the largest heat exchangers needed could be purchased. However, in an existing plant the heat exchanger areas are fixed. An interesting “surprise” can be seen in Figure 3, the duty of chiller went down as the liquid carryover increased. This is due to the fact that the enthalpy of stream 6 decreases more than the required change in the enthalpy (temperature) of the cold separator. Therefore the process gas duty across the chiller decreases as the liquid carry over increases (see Table 2). In other words, liquid carry-over from the LTS makes the gas/gas heat exchanger into a “chiller” as the liquids vaporizes in that heat exchanger, lowering actual chiller duty, but still increasing the sales gas dewpoint temperature.

Not included in this analysis is an examination of the affect of lowering the chiller outlet temperature on the refrigeration system. In an existing plant, to lower the refrigerant temperature, the chiller would have to operate at a lower pressure so that the power required for the refrigerant compressor would increase. The overall effect of liquid carry over is the increase in the operating cost, as expected.

To learn more about similar cases and how to minimize operational problems such as liquid carry over, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

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Posted on July 1, 2007 at 10:12 pm

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Consequence of Liquid Carry Over – Part 2: Fixed Heat Exchanger Area

Many facility operating problems are related to improperly designed or under-sized gas-liquid separators. Due to the importance of separators, in the July Tip of the Month (TOTM), we studied the effect of liquid carry over in a simple dew point control plant. In that study, assuming variable area of the heat exchangers, we found that one percent liquid carry over can cause considerable change in compressor power requirement and heat exchanger duty. This assumption is valid if we are designing a new plant and the equipment is being sized for construction. However, for an existing plant, the heat exchanger areas are fixed. In the continuation of our previous study, we will revisit the same case study and investigate the consequence of liquid carry over but we will use the same heat exchangers (i.e. keeping UA constant; U=overall heat transfer coefficient and A=area).

Let’s consider the same process flow diagram as shown in Figure 1 for a simple gas plant. The feed composition and conditions are shown in Table 1. We have already shown the impact of liquid carry over on the “sales gas dew point” and we experienced that for even a small liquid carry over (1 %), the dew point offset was about 6°F [3.3 °C]. We will demonstrate the consequences of liquid carry over on the other equipment while maintaining the “spec dew point”.

Figure 1. Process flow diagram for simple dew point correction gas plant

It is desired to process this feed gas to produce a sales gas with a dew point of 20°F [-6.7 °C] at 540 psig [3.723 MPa] The feed gas is mixed with recycle gas from a stabilizer, compressed and cooled to 110°F [43.3°C] and 555 psig [3.827 MPa], then cooled in the gas-gas exchanger, gas-liquid exchanger and finally in the chiller to 20°F [-6.7°C] before entering the separator at 540 psig [3.723 MPa]. In real equipment, there would be some liquid carry over. In order to show the impact of liquid carry over, in the simulation we withdraw a small portion of liquid stream from the separator and remixed it with the vapor stream.  The solid curve in Figure 2 shows how the dew point of sales gas goes off spec as a function of the liquid carry over.

In order to bring back the sales gas dew point to spec, we re-adjusted (lowered) the stream 7 temperature. The required degree of re-adjustment is shown by the dashed line in the same figure. As a consequence of re-adjusting of the stream 7 temperature, the conditions of other equipment and streams changed. Figure 3 shows the variation of compressor power and the heat exchanger duties as a function of liquid carry over. As can be seen in this figure, one percent liquid carry over can cause considerable change. For this case, the percent changes ranged from 0 to 27 percent. The changes in the reboiler duty, sales gas and LPG flow rates were negligible. Contrary to the findings of the July TOTM, here we see that the chiller duty increases as we expected.

Not included in this analysis is an examination of the affect of lowering the chiller outlet temperature on the refrigeration system.  In an existing plant, to lower the refrigerant temperature, the chiller would have to operate at a lower pressure so that the power required for the refrigerant compressor would increase. The overall effect of liquid carry over is the increase in the operating cost, as expected.

To learn more about similar cases and how to minimize operational problems such as liquid carry over, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

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Posted on September 1, 2007 at 10:27 pm

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Water-Sweet Natural Gas Phase Behavior

In the past Tips of the Month, we discussed the phase behavior of water-free natural gas mixtures. In this tip, we will demonstrate the water-sweet natural gas phase behavior. In future tip, we will address wet sour gas.

Water is produced with oil and gas. A question that comes to mind is: “why water is important?” The presence of water may cause corrosion, freezing and hydrate formation. Hydrates can even form at warm temperatures in the presence of water. Once hydrates are formed, they are hard to remove. For design and operation of a plant it is important to know:

1. Where water is in the process?2. How much water is present?3. What form/phase water is in at operating conditions, during start-up, during shut-down and during upsets?

A phase envelope with hydrate and water dew point curves is an excellent tool to answer the above questions. The water content of a gas depends on the system temperature, pressure and composition of the water containing gas. There are several methods of calculating of water content. The details of these methods can be found in Chapter 6 of Volume 1 and Chapter 9 of Volume 3 of “Gas Conditioning and Processing” [1, 2]. In this work we will use Figure 6.1 of Volume 1 and the modified Soave-Redlich-Kwong (SRK EoS) reported in GPA RR-42 by Erbar et al. [3]. This version of SRK is tailor fitted for water-hydrocarbon systems. The compositions of natural gases studied in this work are shown in Table 1.

Figure 1 presents the phase behavior for mixture 1. This figure includes from right to left: the water dew point, hydrocarbon dew point, retrograde, hydrate formation, 25 weight percent methanol (MeOH) inhibited hydrate formation, and the bubble point curves, respectively. The blue-triangular-symbol water dew point curve is predicted by use of Figure 6.1 of Volume 1 and the red curve represents the water dew point predicted by rigorous calculations using the modified SRK. It is interesting to see that both methods agree quite well with each other. However, the results obtained by Figure 6.1 are somewhat more conservative. The region to the right of water dew point curve is gas phase and to the left the liquid water is present.

Figure 2 presents the phase behavior for mixture 2 which contains heavier compounds including nC9H20. However, the water content is the same as in mixture 1. Note the position of the water dew points did not change but, the hydrocarbon dew point curve has moved to the right, as expected, due to presence of heavier compounds. At lower pressures, the water dew point curves coincide with the hydrocarbon dew point curve. This is merely by coincidence.

Figure 3 presents similar phase diagram for mixture 3 which is essentially the same as mixture 1 except nC6H14 has been replaced with nC9H20. Again, the hydrocarbon dew point curve shifts to the right due to presence of nC9H20.

It is interesting to note that the dry hydrocarbon dew points and the wet hydrocarbon dew points predicted by SRK coincide very closely with each other; the difference is practically negligible. Also note that at a specified pressure, the higher of the two dew points (hydrocarbon and water) have been calculated by the SRK EoS. So, below about 1400 psia [9653 kPa], the wet hydrocarbon dew point is predicted while for pressures above 1400 psia [9653 kPa], the water dew point (the higher one) is predicted.

Finally, mixture 2 has been passed through a separator at 100 °F [38 °C] and 1000 psia [6895 kPa] and the resulting vapor compositions from a three-phase flash calculation based on the SRK EoS is shown in the last column of Table 1 as mixture 4. Due to the removal of free water and heavy hydrocarbons from mixture 2, the phase envelope and the water dew point curve have moved to the left, as expected. At this condition, the water content by SRK EoS is 0.0012 mole fraction equivalent of 57 lbm/MMSCF or 914 kg/106 std. m3. Figure 4 indicates that the hydrocarbon dew point and water dew point curves intersect at 100 °F [38 °C] and 1000 psia [6895 kPa] which are the conditions of the separator.

Due to the fact that hydrate formation is controlled mostly by lighter components, there are only small variations of the hydrate formation curve and its inhibition by 25 weight percent methanol in all four mixtures.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

Reference:

1. Campbell, J.M., “Gas conditioning and Processing, Vol 1: The Basic Principles”, 8th Edition, Edited by R.A. Hubbard, John M. Campbell & Company, Norman, USA, 2001.

2. Maddox, R.N., “Gas conditioning and Processing, Vol 3: Computer Applications and Production/Processing Facilities”, John M. Campbell & Company, Norman, USA, 1982.

3. Erbar, J.H., Jagota, A.K., Muthswamy, S. and Moshfeghian, M., “Predicting Synthetic Gas and Natural Gas Thermodynamic Properties Using a Modified Soave Redlich Kwong Equation of State,” Gas Processor Research Report, GPA RR-42, Tulsa, USA, 1980.

Water-Sour Natural Gas Phase Behavior

In the last Tip of the Month, we discussed the phase behavior of water-sweet natural gas mixtures. In this tip, we will demonstrate the water-sour natural gas phase behavior. In a future tip, we will address water content of acid gases.

Water is produced with oil and gas. A question that comes to mind is: “Why is water important?” The presence of water may cause corrosion, freezing and hydrate formation. All of these problems are enhanced by the presence of acid gases such as H2S and CO2.

A phase envelope with hydrate and water dew point curves is an excellent tool to find out what form/phase water is in at operating conditions, during start-up, during shut-down and during upsets. The water content of a gas depends on the system temperature, pressure and composition of the water containing gas. There are several methods of calculating of water content of sour gases. The details of these methods can be found in Chapter 6 of Volume 1 [1] and Chapter 9 of Volume 3 [2] of “Gas Conditioning and Processing”. In this work we will use Maddox et al. [3] (Figures 6.1, 2, 3 and Equation 6.2 of Volume 1) and the modified Soave-Redlich-Kwong (SRK EoS) reported in GPA RR-42 by Erbar et al. [4]. This version of SRK is tailor-fitted to handle water-hydrocarbon systems containing hydrogen sulfide and carbon dioxide.

The compositions of several sour gases studied in this study along with their measured and predicted water contents are shown in Table 1. The Maddox et al. (referred to as Chart) results were generated using GCAP software and the modified SRK EOS results were generated by performing rigorous three-phase (gas-liquid hydrocarbons-aqueous) flash calculations. A trial version of GCAP can be downloaded here, at the bottom of the page.

Table 1 indicates that as long as the total acid gas concentrations is less than 60 mole percent, Maddox et al. and the modified SRK methods produce results within the accuracy of experimental data. However, for higher concentrations of acid gases, the modified SRK provides a better prediction.  The water content of acid gas systems will be discussed further in the next Tip of the Month.

The composition, experimental, and predicted water content by Maddox et al. and the modified SRK for two natural gas mixtures are presented in Table 2. The upper part of columns 1, 2, 4, 5 report the measured mole percent. Based on the feed compositions shown in columns 1 and 4, three-phase flash calculations using the modified SRK were performed and the resulting vapor stream compositions are shown in columns 3 and 6, respectively. Notice that the measured and predicted vapor compositions are not identical.  Inaccuracies in predicting the vapor composition can result in errors in predicting the water saturation.

For each vapor stream, the saturated water content was predicted by both methods and is presented in the lower portion of this table. As can be seen from this table, both methods predict saturated water content reasonably well. Not surprisingly, the accuracy of both methods is improved slightly when the experimental vapor composition is used rather than the predicted vapor composition.

Figure 1 represents the phase behavior for mixture A. This figure includes from right to left: the water dew point, hydrate formation, 25 weight percent methanol (MeOH) inhibited hydrate formation, hydrocarbon dew point, retrograde, and the bubble point curves, respectively. The blue-triangular-symbol water dew point curve is predicted by use of Figures 6.1, 6.22 and 6.3 with Equation 6.2 of Volume 1 (Maddox et al. method). The red curve represents the water dew point predicted by rigorous calculations using the modified SRK. It is interesting to see that both methods agree quite well with each other. The region to the right of the water dew point curve is gas phase and to the left, liquid water is present.

Figure 2 presents the phase behavior of sour gas mixture B. With exception of low pressure region, both methods agree quite well.

Figure 3 demonstrates the effect of acid gases on phase behavior of mixture B. As shown in this figure, the presence of acid gases shifts all of the curves to the right. In other words, the presence of acid gases increases the hydrate formation temperature considerably. It also increases the water dew point temperature. It should be noted that the water dew point curves have been generated for a fixed amount of water content predicted at specified separator condition. In this case the separator temperature and pressure were 120 °F [48.9 °C] and 1500 psia [10,342 kPa], respectively.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), RF-61 Refinery Gas Treating, Sour Water, Sulfur and Tail Gas and G7 (Process Simulation in Gas Conditioning and Processing) courses.

Dr. Mahmood Moshfeghian

Reference:

1. Campbell, J.M., “Gas Conditioning and Processing, Vol 1: The Basic Principles”, 8th Edition, Edited by R.A. Hubbard, John M. Campbell & Company, Norman, USA, 2001.

2. Maddox, R.N., L.L. Lilly, “Gas conditioning and Processing, Vol 3: Computer Applications and Production/Processing Facilities”, John M. Campbell & Company, Norman, USA, 1982.

3. Maddox, R.N., L.L. Lilly, M. Moshfeghian, and E. Elizondo, “Estimating Water Content of Sour Natural Gas Mixtures”, Laurance Reid Gas Conditioning Conference, Norman, OK, Mar., 1988.

4. Erbar, J.H., A.K. Jagota, S. Muthswamy, and M. Moshfeghian, “Predicting Synthetic Gas and Natural Gas Thermodynamic Properties Using a Modified Soave Redlich-Kwong Equation of State,” Gas Processor Research Report, GPA RR-42, Tulsa, USA, 1980.

5. Huang, S.S.-S., A.-D. Leu, H.-J. Ng, and D.B. Robinson, “The Phase Behavior of Two Mixtures of Methane, Carbon Dioxide, Hydrogen Sulfide, and Water” luid Phase Equil. 19, 21-32, 1985.

6. Ng, H.-J., C.-J. Chen, and H. Schroeder, “Water Content of Natural Gas Systems Containing Acid Gas”, Research Report RR-174, Gas Processors Association, Tulsa, OK, 2001.

Acid Gas-Water Phase Behavior

In the last Tips of the Month, we discussed the phase behavior of water-sweet natural gas and water-sour natural gas mixtures. In this tip, we will demonstrate the acid gas–water phase behavior.

The water content of a gas depends on the system temperature, pressure and composition of the gas. The phase equilibria in the system H2S + water and CO2 + water are key to the discussion of the water content of an acid gas system. Figure 1 presents the water content of hydrogen sulfide predicted by ProMax [1] as a function of pressure and temperature.  A limited number of experimental data points at 100°F [37.8°C] by Gillespie and Wilson [2] are also shown on this diagram. The behavior shown on this plot is quite complicated and explained by Carroll [3] thoroughly: “At low pressure the hydrogen sulfide + water mixture is in the gas phase. At low pressure the water content tends to decrease with increasing pressure, which is as expected. Eventually a pressure is reached where the H2S is liquefied. On this plot this is represented by the discontinuity in the curve and a broken line joins the phase transition. There is a step change in the water content when there is a transition from vapor to liquid. In the case of hydrogen sulfide the water content of the H2S liquid is greater than the coexisting vapor. This is contrary to the behavior for light hydrocarbons where the water content in the hydrocarbon liquid is less than the coexisting vapor.”

Figure 1. Water content of pure H2S predicted by ProMax, experimental data [2]

In general the phase behavior of the system CO2 + water is as complex as that of the H2S + water system. The CO2-rich liquid phase only occurs for temperatures less than about 90°F [32.2°C]. As shown in Figure 2 reported by Maddox and Lilly [4], the water content of CO2 exhibits a minimum.

Figure 2. Predicted saturated water contents at 100°F [38°C] for CO2, CH4 and mixture of both [4]

There are several methods available that can be used to predict the water content of acid gases. All of these methods are based on equation of state and rigorous thermodynamic models. As described above, the phase behavior is complicated and extra care should be taken to assure a correct prediction. In the remaining section of this tip, we will demonstrate the capabilities of some of these methods.

Figure 3 compares the water content calculation results for an acid gas stream by several methods in HYSYS [5] and ProMax [1]. The composition of the acid gas stream is shown in the inset of diagram. Even though at low pressures, all methods give close results, as can be seen from this figure, there are large differences at higher pressures.

Figure 3. Comparison of water content prediction by different methods at 59 °F [15°C]

Table 1 gives another comparison of available methods for prediction of acid gas water content.

Table 1. Comparison of ProMax and modified SRK EOS results with the experimental water content [6] of several acid gas mixtures:

The experimental composition and predicted water content by HYSYS, ProMax and the modified SRK for eight acid gas mixtures are presented in Table 2. The upper part of this table reports the measured mole percent of the feed stream and the lower part shows the experimental vapor stream compositions in mole percent. Based on the feed compositions, three-phase flash calculations were performed and the resulting vapor stream water content (mole %) are shown in the last three columns (upper part).

For each vapor stream, the saturated water content was predicted by the above methods and is presented in the lower portion of this table. As can be seen from this table, ProMax predict saturated water content reasonably well. The red figures in Table 2 indicate that the methods predict a non-aqueous liquid phase instead of the vapor phase. Based on a dry basis phase envelope, the conditions for these mixtures were dense phase/compressed liquid.

Table 2. Conditions and compositions of 8 acid gases and their saturated water contents

Figure 4 also compares the accuracy of the above methods graphically. This figure clearly indicates that ProMax gives the most accurate results. The Erbar et al. [7] SRK method also gives reasonable results.

To learn more about similar cases and how to minimize operational problems, we suggest attending

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), G-6 Gas Treating and Sulfur Recovery, RF-61 Refinery Gas Treating, Sour Water, Sulfur and Tail Gas and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By Wes Wright and M .Moshfeghian

Reference:

1. ProMax 2.0, Bryan Research and Engineering, Inc., Bryan, Texas, U.S.A., 20072. Gillespie, P.C. and G.M. Wilson, “Vapor-Liquid Equilibrium Data on Water-Substitute Gas Components: N2-H2O, H2-H2O, CO-H2O, H2-CO-H2O, and

H2S-H2O” Research Report RR-41, GPA, Tulsa, OK, 1980.3. Carroll, J.J., “The water content of acid gas and sour gas from 100 to 220 °F and pressures to 10,000 Psia,” Presented at the 81st Annual GPA

Convention, Dallas, Texas, USA, March 11-13, 2002.4. Maddox, R.N., L.L. Lilly, “Gas conditioning and Processing, Vol 3: Computer Applications and Production/Processing Facilities”, John M. Campbell &

Company, Norman, USA, 1982.5. ASPENone, Engineering Suite, HYSYS Version 2006, Aspen Technology, Inc., Cambridge, Massachusetts U.S.A., 2006.6. Huang, S.S.-S., A.-D. Leu, H.-J. Ng, and D.B. Robinson, “The Phase Behavior of Two Mixtures of Methane, Carbon Dioxide, Hydrogen Sulfide, and

Water” Fluid Phase Equil. 19, 21-32, 1985.7. Erbar, J.H., A.K. Jagota, S. Muthswamy, and M. Moshfeghian, “Predicting Synthetic Gas and Natural Gas Thermodynamic Properties Using a

Modified Soave Redlich-Kwong Equation of State,” Gas Processor Research Report, GPA RR-42, Tulsa, USA, 1980.8. Ng, H.-J., C.-J. Chen, and H. Schroeder, “Water Content of Natural Gas Systems Containing Acid Gas”,Research Report RR-174, Gas Processors

Association, Tulsa, OK, 2001.

Two Phase Gas-Liquid Pipeline Simulation

Translation: Español

As gas moves through a pipeline its pressure and temperature change due to the frictional loss, elevation change, acceleration, Joule-Thompson effect, and heat transfer from the surroundings. Due to pressure and temperature change, liquid and solid (hydrate) may also form in the line which in turn affects the pressure profile. Modeling and simulation of multiphase system, even under steady-state condition, is complex. There are a few tools designed specifically for modeling and analysis of complex multiphase systems such as PipePhase, PipeSim, OLGA, etc [1]. This Tip of the Month illustrates how general-purpose process simulation programs can be used to simulate wet pipelines.

In order to perform computer simulation, let’s consider the gas shown in Table 1. The gas enters a pipeline with an inside diameter of 18.81 inches (47.8 cm) at rate of 180 MMSCFD equivalent to 19800 lbmole/hr (8989 kgmole/h). The pipeline length and elevation profile are shown in Figure 1. The ambient temperature is assumed to be 60 °F (15.6 °C). The gas enters the line at 1165 psia (8032 kPa) and 95 °F (35 °C). The pipeline is buried under ground; with an approximate overall heat transfer coefficient of 1 Btu/hr-ft2-°F (5.68 W/m2-°C) was assumed. Due to the high content of H2S and CO2 (25.6 and 9.9 mole %, respectively) and to prevent corrosion and hydrate formation, the gas has been dehydrated before entering the pipeline.

The calculation algorithms for computer simulation are discussed in the Gas Conditioning & Processing, Vol 3, Computer Applications for Production/Processing Facilities [2]. The pipeline was divided into 14 segments according to the number of up-hills and down-hills in the line. In addition, each segment was divided into 10 equal increments to achieve higher calculation accuracy. The pipeline was simulated by HYSYS [3], ProMax [4] and EzThermo [5] programs. For pressure drop calculation, the Beggs and Brill method with the original liquid hold up correlation was chosen in all three programs. The SRK equation of state (EOS) was chosen in the ProMax and EzThermo but PR EOS was chosen for HYSYS.

Figures 2 through 4 present the pressure, temperature, and liquid formation profiles along the pipeline. Figure 2 indicates that the pressure profiles predicted by the three programs follow the same pattern and ProMax and EzThermo results are very close to each other. The main difference in the calculated outlet pressure is due to the different amount of liquid formation predicted from phase behavior.

Figure 3 indicates that the temperature profiles predicted by the three programs fall on top of each other. It seems that the small amount of liquid condensation in the line has a smaller effect on the temperature profile than on the pressure profile. The liquid formation profiles predicted by the three programs are shown in Figure 4. As shown in this figure, the amount of liquid formation in the line predicted by ProMax is relatively higher than the other 2 programs. This can be explained by viewing the dew point curves predicted by these programs on Figure 5. Note that the cricondentherm predicted by ProMax is higher than the other two. As we have shown in an earlier tip of the month and publication [6], the characterization of heavy ends has a strong effect on the dew point curve and consequently on the liquid condensation in transmission lines [7]. In this study, the same normal boiling point, relative density, and molecular weight for C6+, as shown in Table 1, are used in all three programs. However, the critical properties predicted by these programs were not quite the same. In addition, the binary interaction parameters between different components and C6+ are not the same.  Pipe surface roughness also play an important role for friction pressure drop in gas pipeline. It is interesting to see that the line pressure-temperature profiles by the three programs are practically the same despite the differences in the phase envelope.

The fractional hold-up along the pipeline calculated by the three programs are shown in Figure 6. Even though all three programs demonstrate the same trends, those predicted by HYSYS and EzThermo follow each other more closely.

In line with our earlier tip of the month and in order to see the impact of the overall heat transfer coefficient on the pipeline behavior, the overall heat transfer coefficient of 1 Btu/hr-ft2-°F (5.68 W/m2-°C) was changed to 0.25 Btu/hr-ft2-°F (1.42 W/m2-°C). The simulation results indicate that the overall heat transfer coefficient can affect the line behavior considerably. The effect of the overall heat transfer coefficient on the temperature profile predicted by the three programs is presented in Figure 7.

The work reported here clearly shows the importance of simulation tools and how general-purpose process simulation programs can be used to model and analyze the behavior of a gas transmission pipeline. However, care must be taken to utilize these programs properly. Improper use of the overall heat transfer coefficient or heavy end characterization can lead to completely erroneous conclusions about the presence or absence of liquid, even to indicate as far as a pipeline will be handling dry gas when in reality the line will be in two phase gas – liquid flow.

Note: The Liquid-Gas ratio at the pipeline outlet in bbl/MMSCF [m3/106 std m3] are: 3.676 [20.95], 5.479 [31.23], and 7.352 [41.92] for HYSYS, EzThermo, and ProMax, respectively.

Proper use of the simulation programs combined with correct input of design parameters will lead to more accurate and reliable forecasts of gas pipeline behavior. The overall heat transfer between the line and its surroundings has an impact on liquid formation in the line and, consequently, on the line pressure profile.

Similar cases of fluid flow are discussed in our Fundamentals of Onshore and Offshore Pipeline Systems – PL-4, Onshore Pipeline Facilities – Design, Construction and Operations – PL-42, Flow Assurance for Pipeline Systems – PL-61, Process Simulation in Gas Conditioning and Processing – G-7 courses.

By: Dr. Mahmood Moshfeghian

References:

1. Ellul, I. R., Saether, G. and Shippen, M. E., “The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial,” The Proceeding of Pipeline Simulation Interest Group, Paper PSIG 0403, Palm Spring, California, 2004.

2. Maddox, R. N. and L. L. Lilly, Gas Conditioning and Processing, Vol. 3 (2nd Edition), Campbell Petroleum Series, Norman, Oklahoma, 1990.3. Aspen HYSYS, Version 2006, Engineering Suit, Aspen Technology, Inc., Cambridge, Massachusetts, 2006.4. ProMax Version 2.0, Process Simulation Software by Bryan Research & Engineering, Inc., Bryan, Texas, 2008.5. EzThermo, Moshfeghian, M. and Maddox, R. N., 2008.6. Moshfeghian, M., Lilly, L., Maddox, R. N. and Nasrifar, Kh., “Study Compares C6+ Characterization Methods for Natural Gas Phase Envelopes,” Oil

& Gas Journal, 60-64, November 21, 2005.7. Dustman, T, Drenker, J., Bergman, D. F.; Bullin, J. A., “An Analysis and Prediction of Hydrocarbon Dew Points and Liquids in Gas Transmission

Lines,”  Proceeding of the 85th Gas processors Association, San Antonio, Texas, 2006

How good is Flanigan Correlation for Two Phase Gas-Liquid Pipeline Calculations?

Translation: Español

There are a few computer tools designed specifically for modeling and analysis of complex multiphase systems such as PipePhase, PipeSim, OLGA, and etc [1]. Modeling and simulation of multiphase system, even under steady-state condition, is complex. In the June Tip of the Month (TOTM), we illustrated how the process simulation programs can be used to simulate a natural gas transmission pipeline. These programs are based on mechanistic models and laboratory developed correlations and rely on complex iterative algorithms to perform the tedious calculations.

However, for hand calculation, the Flanigan correlation (which is based on field data for gas dominated transmission pipelines) has been developed and can be used in relatively straight manual calculations. This correlation has proven useful even though it is relatively simple. The relationship between gas flow rate, diameter and pressure drop is represented by Panhandle A gas flow equation (which is based on the Basic Gas Flow Equation modified with field data). The basic equation is single phase flow for gas as is the Panhandle A Equation. The basic equation is derived from basic principles, while the Panhandle A and Flanagan Equation are best fits to a range of field data. Two corrections are made in the Flanagan Equation for two-phase flow:

1. The value of outlet pressure is adjusted for the pressure loss due to uphill and downhill flow of two phases, including the effect of liquid holdup.2. The efficiency term is correlated to reflect measured system performance based on gas velocity and liquid-gas ratio.

For the detail of the Panhandle A equation and the Flanigan correlation, refer to chapter 10 of Gas Conditioning & Processing, Vol 1 [2]. The algorithms for computer simulation are discussed in the Gas Conditioning & Processing, Vol 3, [3].

In this TOTM (which is a continuation of the June TOTM), we will demonstrate the accuracy and application of the Flanigan correlation.

Let’s consider the same case study as was used in the June TOTM. The composition and conditions of the natural gas are shown in Table 1. The gas enters a 20 inch diameter pipeline with an inside diameter of 18.81 inches (47.8 cm) at rate of 180 MMSCFD, equivalent to 19800 lbmole/hr (8989 kgmole/h). The pipeline length and elevation profile are shown in Figure 1. The ambient temperature was assumed to be 60 °F (15.6 °C). The gas enters the line at 1165 psia (8032 kPa) and 95 °F (35 °C). The pipeline is buried under ground with an overall heat transfer coefficient of 1 Btu/hr-ft2-°F (5.68 W/m2-°C). Due to the high content of H2S and CO2 (25.6 and 9.9 mole %, respectively) and to prevent corrosion and hydrate formation, the gas has been dehydrated before entering the pipeline.

Three methods used in this analysis include the basic gas flow equation [2], the Flanigan correlation, and the computer models using the Beggs-Brill correlation with the original liquid hold-up correlation. The SRK equation of state (EOS) was used to perform the phase behavior calculations in the computer based analyses.

The pipeline is divided into 14 segments to match with the number of up-hill and down-hill sections in the line. In addition, each segment is divided into 10 equal increments to achieve higher calculation accuracy. This division is not required for the Flanigan correlation and is done for the sake of comparison with other methods.

Figures 2 through 5 present the pressure, temperature, and liquid formation profiles along the pipeline. Figure 2 indicates that the pressure profiles predicted by the Flanigan matches very well with the results obtained by the more rigorous computer analyses using Beggs-Brill method. However, as expected, due to presence of liquid formation in the line, the basic gas equation results deviate from the two phase flow correlations.

Figure 3 indicates that the temperature profiles predicted by the three correlations fall on top of each other. The small amount of liquid condensation in the line has smaller effect on the temperature profile than on the pressure profile. The liquid formation profiles predicted by the three correlations are shown in Figure 4. As shown in this figure, the amounts of liquid formation predicted by the Flanigan and Beggs-Brill correlations match very well, but the liquid formation predicted by the basic gas equation is different from the two-phase correlations. This can be explained by the fact the pressure drop and consequently the temperature change predicted by the basic equation are different from those predicted by the other two methods.

In this study, the same normal boiling point, relative density, and molecular weight for C6+, as shown in Table 1, are used for all three correlations. Therefore, the same predicted critical properties and acentric factor are used. These properties and the binary interaction parameters are needed to perform the phase behavior calculations by a cubic EOS such as SRK. In addition, the same binary interaction parameters between different components and C6+ are used.

The work reported here clearly shows the value of simple Flanigan correlation and how it can used to model and analyze the behavior of a gas transmission pipeline. However, care must be taken to utilize this correlation properly. Even though the Flanigan correlation is simple, its results match very well with the more rigorous method of Beggs-Brill. However, we expect the agreement between these two correlations deteriorate as the amount of liquid formation in the line increases. As expected the basic gas equation predicted smaller pressure drop in the line due to the fact the liquid formation in the line is ignored. Although the Flanagan Equation results are not sensitive to the elevation correction term, it is important to include the elevation term with a reasonable estimate of the total upward and downward elevation changes. The results are also relatively insensitive to the efficiency factor, therefore average values for liquid and gas ratios can be used for each segment.

Similar cases of fluid flow are discussed in our Fundamentals of Onshore and Offshore Pipeline Systems – PL-4; Onshore Pipeline Facilities – Design, Construction and Operations – PL-42; Flow Assurance for Pipeline Systems – PL-61; Process Simulation in Gas Conditioning and Processing – G-7 courses.

By: Dr. Mahmood Moshfeghian

References:

1. Ellul, I. R., Saether, G. and Shippen, M. E., “The Modeling of Multiphase Systems under Steady-State and Transient Conditions – A Tutorial,” The Proceeding of Pipeline Simulation Interest Group, Paper PSIG 0403, Palm Spring, California, 2004.

2. Campbell, J. M., and Hubbard, R. A., Gas Conditioning and Processing, Vol. 1 (8th Edition, 2nd Printing), Campbell Petroleum Series, Norman, Oklahoma, 2001.

3. Maddox, R. N. and L. L. Lilly, Gas Conditioning and Processing, Vol. 3 (2nd Edition), Campbell Petroleum Series, Norman, Oklahoma, 1990.

How good are the shortcut methods for sour gas density calculations?

Translation: Español

Gas density is needed for process simulation and equipment design. For example, accurate predictions of gas density are needed for calculation of pressure drop

in piping/pipeline and for vessel sizing. Accurate gas density is also essential for custody transfer metering. Gas density, , is calculated by:

(1)

Where:

&Gas density, kg/m3 (lbm/ft3)Absolute temperature, K (ºR)Pressure, kPa (psia)MW Molecular weight kg/kmole (lbm/lbmole)Gas compressibility factorUniversal gas constant, 8.314 (kPa)(m3)/(kmole)(K) or 10.73 (psia)(ft3)/(lbmole)(ºR)

In equation 1, “z” represents gas compressibility factor. For ideal gases, “z” is equal to 1. Gas densities are sometime expressed in terms of relative density

(specific gravity), , and is defined as:

 

(2)

 

Substituting Equation 1 for gas and air into Equation 2 and assuming ideal gas behavior at standard conditions, Equation 2 will be transformed to:

At the standard condition and for simplicity, Equation 3 can be written as

In Equation 1, the key parameter is the compressibility factor “z”, which is a function of pressure, temperature and gas composition. Compressibility factor is a dimensionless surrogate of non-ideal gas density. In general, equations of state are probably the most widely used for calculation of z. They are not necessarily the most accurate. Empirical correlations developed for a specific mixture or a narrow range of mixtures provide better accuracy, but may be less general. An example would be the Katz chart which is quite good when applied to “sweet” pipeline quality gases, but less reliable for gases containing H2S, CO2 and/or N2. Figure 3.2 in Chapter 3 of Gas Conditioning and Processing [1] shows the Katz chart for sweet natural gases as prepared by Standing and Katz [2]. The chart was developed by using experimental data on methane binary mixtures with ethane, propane, butane and other natural gases over a wide range of composition with a maximum molecular weight of 40.

For fiscal metering of natural gas, an accurate experimental database has been developed and compressibility factor correlations, with uncertainties generally within ±0.2%, have been published in the industry standards, AGA Report No. 8 and ISO 12213. A summary of some common “z” correlations and their effect on gas measurement accuracy can be found in reference [3]. Since many people use the Katz compressibility factor chart, the question is often asked how it may be extended to gases containing H2S and CO2. There are two methods available for this application.

 

1. The approach proposed by Robinson et al. [4]2. The approach proposed by Wichert and Aziz [5]

In this Tip of the Month (TOTM) we will demonstrate the accuracy of the second approach. The details of this method are presented in Chapter 3 of Gas Conditioning and Processing [1].Let’s consider the gas mixture shown in Table 1 with total acid gas (H2S and CO2) of 14.68 mole percent. At 13.94 MPa (2021 psia) and 58 ºC (136 ºF), the

compressibility factors are 0.797 (120.1 kg/m3) and 0.832 (114.8 kg/m3), using Katz chart and Wichert-Aziz method respectively. The percent deviation between two answers from each other is 4.4%.

In order to show the effect of acid gas on compressibility factor determined from Katz chart and Wichert-Aziz methods, we varied the acid gas content of the gas in Table 1 from 0 to 37 mole percent. This was accomplished by diluting the non-acid gas components with a 50:50 mixture of CO2 and H2S. Figure 1 presents the percentage difference between the two methods as a function of acid gas content. The graph shows that as the H2S and CO2 content increases, the deviation of Katz chart from Wichert-Aziz method increases almost linearly. This graph also indicates that the percentage difference between the two methods is greater for the case of diluting gas with only H2S than only CO2.

Next, we used the experimental data reported in the GPA RR-138 [6] and GPA RR 68 [7] to evaluate the accuracy of Katz, Wichert-Aziz and SRK equation of state (EOS) for binary mixtures of CO2 and CH4. The results of this evaluation are shown in Figures 2 through 6, for CO2 content of 9.83 to 100 mole percent. The figures indicate that the Katz correlation accuracy decreases as the mole percent of CO2 increases. However; Figure 5 indicates that as the gas becomes very rich in CO2, the accuracy of the Katz correlation and the Wichert-Aziz method are practically identical. Figure 6 shows that the Katz correlation best predicts the density of pure CO2, and also when the gas approaches pure CH4. The experimental data for pure CO2 in Figure 6 is from GPA RR 68 [7]. Figure 2 through 6 also indicate that the SRK EOS has low accuracy. In this study, a binary interaction parameter of 0.12 between CH4 and CO2 which had been determined from experimental vapor-liquid-equilibrium (VLE) data was used.

 

Based on the work done in this study, the following can be concluded:

1. Katz correlation gives accurate results for pipeline quality gases (lean sweet gases)2. For pure CO2, Katz correlation is the most accurate in comparison to Wichert-Aziz method or the SRK EOS.3. For binary mixture of CH4 and CO2, Wichert-Aziz method gives the most accurate result for CO2 content of between 10 and 90 mole percent.4. As H2S and CO2 content increases, the accuracy of the Katz correlation decreases, but its accuracy increases as the mixture approaches a single

(pure) component.5. The percentage difference between the Katz and Wichert-Aziz methods for gas mixtures containing acid gases is greater for H2S than CO2.6. Binary interaction parameters which have been optimized to predict VLE behavior, may not provide the best density prediction.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), G6 (Gas Treating and Sulfur Recovery), RF61 (RefineryGas Treating, Sour Water, Sulfur and Tail Gas), PF-81 (CO2 Surface Facilities), G7 (Process Simulation in Gas Conditioning and Processing) and G40 (Process/Facility Fundamentals) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Campbell, J. M., and Hubbard, R. A., Gas Conditioning and Processing, Vol. 1 (8th Edition, 2nd Printing), Campbell Petroleum Series, Norman, Oklahoma, (2001).

2. Standing, M.B. and Katz, D.L.; “Density of Natural gas gases,” AIME Trans., 146, 140-49 (1942)3. Hannisdal, N.E., “Gas Compression Equations Evaluated,” Oil and Gas J., p. 38-41 (May 4, 1987)4. Robinson, D. F. et al. Trans. AIME, Vol 219, P. 54, (1960).5. Wichert, E. and Aziz, K., Hydr. Proc., p. 119 (May 1972).6. Hwang, C-A., Duarte-Garza, H., Eubank, P. T., Holste, J. C. Hall, K. R., Gammon, B. E., March, K. N., “Thermodynamic Properties of CO2 + CH4

Mixtures,” GPA RR-138, Gas Processors Association, Tulsa, OK, June 19957. Hall, K. R., Eubank, P. T., Holste, J., Marsh, K.N., “Properties of C02-Rich Mixtures Literature Search and Pure C02 Data, Phase I,” GPA RR-68, A

Joint Research Report by Gas Processor Association and the Gas Research Institute, Gas Processors Association, Tulsa, OK, June 1985

How good are the detailed methods for sour gas density calculations?

Translation: Español

Gas density estimates are of fundamental importance for process simulation, equipment design, and process safety engineering.  In the previous Tip of the Month (TOTM), two shortcut methods for predicting sour and acid gas density were evaluated.  We showed that Katz correlation gives accurate results for lean sweet gases and it is the most accurate in comparison to Wichert-Aziz method or the SRK EOS. For binary mixtures of CH4 and CO2, Wichert-Aziz method gives the most accurate result for CO2 content of between 10 and 90 mole percent. As H2S and CO2 content increased, the accuracy of the Katz correlation decreased, but its accuracy increased as the mixture approached a single component. The percentage difference between the Katz and Wichert-Aziz [1] methods for gas mixtures containing acid gases was greater for H2S than CO2.

Process simulation software often use the Benedict-Webb-Rubin-Starling (BWRS), Soave-Redlich-Kwong (SRK) and/or Peng-Robinson (PR) equations of state for gas density calculations. Other sources of gas density calculation are NIST REFPROP (Reference Fluid Thermodynamic and Transport Properties) program and GERG-2004 [2, 3], a reference equation of state for natural gases.

Due to the importance of CO2 injection for enhanced oil recovery and the increasing interest in CO2 capture and sequestration, this study was undertaken to evaluate the accuracy of density calculations for gases containing nil to 100% CO2. An experimental data base was used for the basis of comparison. The study reviews all of the above mentioned methods and will report their accuracies. Table 1 presents the summary of the temperature, pressure, and CO2 mole percent ranges for the data used in this study. The sources of experimental data were reference [4, 5]. This table also presents the average absolute average percent error and the overall average percent error.

Table1 – Summary of error analysis and comparison of accuracy of sour gas and acid gas density prediction by several methods:

Table 1 provides the overall accuracy of the various methods.  It should be noted that the relative accuracy of each method varies depending on the CO2-CH4 proportion, the temperature and pressure.  The AGA 8 did not return values for many of the low temperature cases where two phases were present.  These points were ignored in the analysis.

Next, we plotted the experimental data reported in the GPA RR-138 [3] and GPA RR 68 [4] to evaluate the accuracy of Katz, Wichert-Aziz and the best four of the detailed methods. The results of this evaluation for the T=350°K and 320°K cases are shown in Figures 1 through 5, for CO2 content of 9.83 to 100 mole percent.  In Figure 1, Katz method is the most accurate and the accuracy of the other methods are almost the same.

In Figure 2, Katz method has the least accuracy and even though the accuracy of the other methods look the same, GERG 2004 is slightly better than the others.

In Figure 3, Katz method again has the least accuracy and even though the accuracy of the other methods look the same, AGA8 provided slightly better estimates than the others.

In Figure 4, Wichert-Aziz method has the least accuracy and even though the accuracies of the other methods look the same, AGA8, GERG-2004 and REFPROP are slightly more accurate than the PR EOS.

In Figure 5, Wichert-Aziz method has the least accuracy and REFPROP, GERG 2004 and AGA 8 equally have the best accuracy.

Based on the work done in this study and in the previous TOTM, the following can be concluded:

1. Katz correlation gives accurate results for pipeline quality gases (lean sweet gases)2. For pure CO2, AGA 8, REFPROP, and GERG 2004 methods equally are the most accurate method3. For binary mixtures of CH4 and CO2, REFPROP and GERG 2004 methods equally give the most accurate result for CO2 content of between 10 and

90 mole percent.4. As CO2 content increases, the accuracy of the Katz correlation decreases, but its accuracy increases as the mixture approaches a single (pure)

component.5. The Peng-Robinson EOS provides a better density estimate than the SRK EOS.6. Results from either the PR or the SRK EOS in ProMax are slightly more accurate than the comparable results from HYSYS.7. Binary interaction parameters which have been optimized to predict VLE behavior may not provide the best density prediction.8. At several low temperatures, AGA8 did not provide density estimates.  The average errors reported here ignored these missing data.  Note that

AGA8 is not valid for liquid nor for the extended region near the critical point.9. Table 1 indicates that REFPROP and GERG 2004 give equally the best results.

To learn more about similar cases and how to minimize operational problems, we suggest attending our G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), G6 (Gas Treating and Sulfur Recovery), RF61 (RefineryGas Treating, Sour Water, Sulfur and Tail Gas), PF-81 (CO2 Surface Facilities), G7 (Process Simulation in Gas Conditioning and Processing) and G40 (Process/Facility Fundamentals) courses.

By: Wes Wright and Dr. Mahmood Moshfeghian

References:

1. Wichert, E. and Aziz, K., Hydr. Proc., p. 119 (May 1972).2. Lemmon, E.W., Huber, M.L., McLinden, M.O.  NIST Standard Reference Database 23:  Reference Fluid Thermodynamic and Transport Properties-

REFPROP, Version 8.0, National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2007.3. Kunz, O., Klimeck, R., Wagner, W., and Jaeschke, M.  “The GERG-2004 Wide-Range Equation of State for Natural Gases and Other Mixtures,”

GERG Technical Monograph 15 (2007)4. Hwang, C-A., Duarte-Garza, H., Eubank, P. T., Holste, J. C. Hall, K. R., Gammon, B. E.,  March, K. N., “Thermodynamic Properties of CO2 + CH4

Mixtures,” GPA RR-138, Gas Processors Association, Tulsa, OK, June 19955. Hall, K. R., Eubank, P. T., Holste, J., Marsh, K.N., “Properties of C02-Rich Mixtures Literature Search and Pure C02 Data, Phase I,” GPA RR-68, A

Joint Research Report by Gas Processor Association and the Gas Research Institute, Gas Processors Association, Tulsa, OK, June 1985

Effect of gas molecular weight on centrifugal compressor performance

Translation: Español

In this tip of the month (TOTM) we will present the results of several case studies showing the effect of gas molecular weight on the performance and efficiencies of centrifugal compressors. We have considered several “what if” scenarios such as variation of compressor speed as a function of molecular weight, while maintaining the same suction and discharge pressures and mass flow rate. Variation of polytropic head and efficiencies as a function of gas molecular weight for a given compression ratio, and compressor speed has also been studied. In addition, the impact of thermodynamic properties package has been studied.Compressors can be generally classified in two categories:

1. Positive displacement; this type of compressor includes reciprocating, rotary screw, sliding vane, liquid ring and rotary lobe. The compression principle is volumetric displacement – reducing the gas volume increases pressure.

2. Kinetic or Dynamic: this type of compressor includes centrifugal and axial compressors. The compression principle is acceleration and deceleration of the gas – kinetic energy is converted to pressure rise.

Reciprocating and centrifugal compressors are the most popular compressors used in E & P applications. Rotary screw compressors are gaining in popularity in low to moderate pressure gas boosting service, refrigeration systems and fuel gas compression for gas turbines. Further detail may be found in reference [1].From a calculation viewpoint alone, the power calculation is particularly sensitive to the specification of flow rate, inlet temperature and pressure, and outlet pressure. Gas composition is important but a small error here is less important providing it does not involve the erroneous exclusion of corrosive components. A compressor is going to operate under varying values of the variables affecting its performance. Thus the most difficult part of a compressor calculation is specification of a reasonable range for each variable and not the calculation itself. Maddox and Lilly [2] emphasize that using a single value for each variable is not the correct way to evaluate a compression system.Normally, the thermodynamic calculations are performed for an ideal (reversible process). The results of a reversible process are then adapted to the real world through the use of an efficiency. In the compression process there are three ideal processes that can be visualized: 1) an isothermal process, 2) an isentropic process and 3) a polytropic process. Any one of these processes can be suitably used as a basis for evaluating compression power requirement by either hand or computer calculation. The isothermal process, however, is seldom used as a basis because the normal industrial compression process is not even approximately carried out at constant temperature.Due to practical limitation the compression ratio per stage is often in the range between 2 and 6. For large overall compression ratio applications multistage compressors are used. The choice of the interstage pressure is an economic decision and can be estimated by equal compression ratios for each section but may be adjusted to minimize total power requirement.In order to study the effect of feed gas molecular weight on the performance of centrifugal compressors, several computer simulations using HYSYS [3] were performed. The gas mixtures with the composition shown in Table 1 with molecular weights ranging from 18.2 to 23.17, corresponding to relative density of 0.63 to 0.80, respectively, were used in this study. The characteristics curves for the centrifugal compressors used in this study are shown in Figures 1 and 2. These performance curves were supplied to the simulation software and used in the course of simulations.

Case 1: Effect of Molecular Weight on Flow Rate for Fixed ?P (Constant Speed)

For a fixed inlet pressure of 700 kPa, 35 °C, and 15000 RPM, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In order to maintain the outlet pressure, the feed flow rate has to vary. We are essentially fixing P1 and P2 and wanting to see the effect on the compressor of varying molecular weight feed. The set up shown in Figure 3 was used to generate the simulation results. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figure 4. The PR EOS [4] is used for thermodynamic properties calculations.

Figure 4 indicates that as the relative density decreased, the flow rate must decrease. Note, for the case of compression ratio of 2.5, no convergence could be achieved for relative density of 0.63 and 0.65 due to the fact the surge limit had been reached. For the same case, the required power as a function of relative density is shown in Figure 5. Since, the flow rate decreased with decreasing relative density, the required power decreased.

Finally, the variation of polytropic head as a function of inlet actual volumetric flow rate is shown in Figure 6. Note that the relative densities are identified on this diagram to show their influence on the performance of the compressor.

Case 2: Variable SpeedAs in the case 1, for a fixed inlet pressure of 700 kPa, 35 °C, and mass flow rate of 1000 kmol/hr, the feed gas relative density was varied from 0.63 to 0.80 with an increment of 0.05. In this case, the compressor is varying speed to maintain flow rate at the P speed imposed on it. The schematic setup to generate simulation results is shown in Figure 7. The simulation results for compression ratios of 2.0 and 2.5 are shown in Figures 8 and 9. In addition to the results by the PR EOS, the results obtained by BWRS are shown on these diagrams. The difference between the results of these two EOS for these cases is negligible.

As shown in Figure 8, as the relative density increases, the compressor speed dropped. However, as relative density or molecular weight increased, the required power increased, see Figure 9.

As shown in Figures 10 and 11, the polytropic efficiency and head decrease with relative density.  More detail of simulation results can be found in Reference [5].

ConclusionsThe impact of relative density (molecular weight) on the performance of a centrifugal compressor was studied by performing a series of computer simulations. Based on the simulation results, it is found that:

1. For the same feed condition, compression ratio, compressor speed, the flow rates must decrease as the relative density decreases, and will eventually approach a surge condition.

2. For the same feed condition, compression ratio, compressor speed, as the relative density increases, the flow rate increases which results in more power consumption.

3. For the same feed condition and rate, and compression ratio, the compressor speed decreases with molecular weight but as expected, the power requirement increases.

4. The PR EOS and BWRS EOS produced the same simulation results

To learn more about similar cases and how to minimize operational problems, we suggest attending our ME44 (Overview of Pumps and Compressors in Oil and Gas Facilities), ME46 (Compressor Systems – Mechanical Design and Specification), G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

Reference:

Campbell, J. M., “Gas Conditioning and Processing, Vol. 2, the Equipment Modules, 8th Ed., Campbell Petroleum Series, Norman, Oklahoma, 2001

Maddox, R. N. and L. L. Lilly, “Gas conditioning and processing, Volume 3: Advanced Techniques and Applications,” John M. Campbell and Company, 2nd Ed., Norman, Oklahoma, USA, 1990.

ASPENone, Engineering Suite, HYSYS Version 2006, Aspen Technology, Inc., Cambridge, Massachusetts U.S.A., 2006.

Peng, Y. D., Robinson, D. B., “A New Two-Constant Equation of State,” Ind. Eng. Chem. Fund., 15, 59, 1976

Moshfeghian, M., Bothamley, M., and Lilly, L.L., “Feed gas molecular weight affects performance of centrifugal efficiency,” Oil and Gas J., May 10, 2008

How to Tune the EOS in your Process Simulation Software?

Translation: Español

Process simulation computer programs are excellent tools for designing or evaluating gas processing plants, chemical plants, oil refineries or pipelines. In these simulation programs, most of the thermodynamic properties are calculated by an equation of state (EOS). The cubic equations of state can be regarded as the heart of these programs for generating the required properties. However, none of the equations of state is perfect and often some sort of tuning must be done prior to their applications. Some tuning is already done by researchers and has been embedded in the data base of these simulation programs. In dealing with non-standard or complex systems, the user should check the validity and accuracy of the selected thermodynamic package (i.e. EOS) in the simulation programs prior to attempting to run the desired simulation. Often the users find that tuning is required. This can be done by performing a series of vapor liquid equilibria (VLE) calculations such as dew point, bubble point or flash calculations and comparing the results with the field data or experimental data. If the accuracy is not within acceptable range, then the EOS should be tuned to improve its accuracy. The tuning can be done in several ways but the one most often used is adjusting/regressing the binary interaction parameters between binary pairs in the mixture using the experimental PVT or VLE data.

In this tip of the month (TOTM), we will demonstrate how the binary interaction parameters are tuned in a simulation program to improve the accuracy of a selected EOS. For this purpose, we will demonstrate how the accuracy of the bubble point pressure prediction of a ternary system of carbon dioxide, pentadecane, and hexadecane can be improved. We will use the Peng-Robinson (PR) [1] equation of state in ProMax [2] and the experimental VLE data published in the literature [3]. The same procedure can be used with any EOS in other simulation programs.

The PR EOSThe PR EOS [2] in terms of pressure (P), volume (v) and temperature (T) is defined as:

The values of the parameters a and b must be determined in a special way for mixtures. Any equation, or series of equations, used to obtain mixture parameters is called a combination rule or mixing rule. The calculation, regardless of its exact form, is based on the premise that the properties of a mixture are some kind of weighted average summation of the properties of the individual molecules comprising that mixture.The mixing rules used in cubic equations of state (i.e., Peng-Robinson, Soave-Redlich-Kwong, and van der Waals) are:

Where: a and b = the interaction energy and molecular size parameters for the mixtureai, bi = a and b parameters for component i in the mixturexi = composition (mol fraction) for component i in the mixturekij = binary interaction parametern = number of component in the mixtureR = Universal gas constantThe ai and bi for each component in the mixture are calculated in terms of critical temperature (Tci), pressure (Pci), and  acentric factor (?i) as presented in equations 4 and 5.

Once a and b have been determined, the equation of state computations proceed as though a and b were for a pure component. With cubic equations of state the mixing rules sum the properties based on binary pairs.

The binary interaction parameter, kij, has no theoretical basis. It is empirical and is used to overcome deficiencies in the corresponding states theory or the basic model (equation of state). Binary interaction parameters are regressed from experimental data for a specific model and should be applied in that model only. In addition, kij’s can be determined from regression of PVT data or VLE data. This will result in different kij’s for the same binary mixture.

The Effect of kij on Bubble Point Pressure PredictionTo study the effect of the kij, the bubble point pressure for a binary mixture of CO2 (1) and pentadecane (2) at 40 °C for a series of CO2 mole % in the liquid phase were predicted using the PR EOS in ProMax. First, the default value of the binary interaction in the data base (DB) of ProMax in which k12=0.0 was used.  The predicted results were compared with the experimental values and the average absolute percent deviation (AAPD) for eight data points calculated to be 41.06%. This AAPD was reduced to 1.64% when the binary interaction parameter of k12=0.112 was used. Figure 1 presents the effect of k12 on the predicted bubble point pressure of CO2 and pentadecane mixture. This figure demonstrates clearly the role of kij in improving the accuracy for bubble point pressure calculations. The improvement is substantial and the accuracy now is as good as the experimental data.

Similar improvement is observed when the binary interaction parameter, k12, was changed from zero, and the default value in data base (k12=DB) of ProMax, to 0.112 for the binary mixture of CO2 (1) and hexadecane (2) at 40 °C. For this case the AAPDs were 40.65%, 3.64% and 1.26% for k12=0.0, k12=DB, and k12=0.112; respectively.

For these two systems the liquid densities were also predicted and compared with the experimental values. For CO2and pentadecane binary system, the calculated AAPD for liquid densities were 6.10% and 6.36% for k12=0.0 and k12=0.112; respectively. Similar AAPD changes were observed for CO2 and hexadecane binary mixture.

Normally, the binary interaction parameters obtained from regressing binary mixture VLE data work well in multicomponent systems. This is demonstrated by using the same obtained kijs in a ternary mixture. The obtained binary interaction parameters of CO2 + pentadecane and CO2 + hexadecane were used without any further change to predict the bubble point pressure of the ternary mixtures of CO2 (1) + pentadecane (2) + hexadecane (3). Figure 3 indicates these binary interaction parameters obtained from the individual binary mixtures improve the accuracy of EOS considerably. Similar to the case of binary mixtures, when the binary interaction parameters, k12, k13, were changed from zero, and the default value of ProMax data base (kijs=DB), to 0.112 for the ternary mixture of CO2 (1) + pentadecane (2) + hexadecane (3) at 40 °C, the AAPDs were reduced from 40.99%  and 25.16% to 1.75%, respectively.

Discussion and ConclusionsIt was shown that the binary interaction parameters of an EOS can be adjusted/tuned/regressed to improve the accuracy of VLE calculations considerably. It was also shown that when the regressed binary interaction parameters based on the binary experimental VLE data used without further changes in a multicomponent system considerable improvement in accuracy may be obtained.

It is a sound practice to check the accuracy of a selected thermodynamic package prior to running any simulation. However, experimental or field data are required to fulfill this task.

To learn more about similar cases and how to run process simulations, we suggest attending our G40(Process/Facility Fundamentals), G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing) courses.

By: Dr. Mahmood Moshfeghian

References:

1. Peng, D.Y. and Robinson, D.B., “A New Two-Constant Equation of State,” Ind. Eng. Chem., Fundam., Vol. 15, No. 1, P. 59, 1976.2. ProMax, V. 3.0, Bryan, Tex.: Bryan Research & Engineering Inc, 2009.3. Tanaka, H., Yamaki, Y. and Kato, M., “Solubility of Carbon Dioxide in Pentadecane, Hexadecane, and Pentadecane + Hexadecane,” J. Chem. Eng.

Data,38, 386-388,1993.

The parameters affecting a phase envelope in the dense phase region

Translation: Español

Because phase envelope generation and its impact on design and performance of gas processing plants is so important it has been the topic of several Tips Of The Month (TOTM). As emphasized by Rusten et al. [1], there are several challenges that have to be addressed in order to succeed with the phase envelope modeling of real natural gases. The most important are:

1. Sampling procedures2. Sample preparations3. Chromatographic gas analysis. A detailed composition is required for satisfactory input to thermodynamic models4. Thermodynamic models that correctly predict the phase envelope

In this TOTM we will demonstrate the impact of thermodynamic modeling for rich gases in the dense phase region. For a discussion on the dense phase, please see the January 2010 TOTM. The value of the dense phase viscosity is very similar to gas phase viscosity. The dense phase density is closer to the liquid phase density. Therefore, it has become attractive to transport rich natural gas in the dense phase region. In October 2005 we discussed several methods of C7+ (heavy ends) characterization and checked the accuracy of several methods and presented tips to improve the accuracy of each method. These methods are presented briefly below. For more detail, please refer to Gas Conditioning and Processing, Volume 3, Advanced Techniques and Applications [2].

Method A: The C7+ is treated as a single hypothetical component based on its molecular weight (MW) and specific gravity (SG). The normal boiling point is predicted; the critical temperature, critical pressure, and acentric factor are also predicted using correlations similar to the ones by Riazi and Duabert [3].

Adjusting MW (or Tc) in Method A: By adjusting the molecular weight of the C7+ fraction we can closely match the measured dew point. The critical temperature (Tc) can also be adjusted to make the phase envelope curve pass through the measured dew point. The Tc adjustment is preferred because less work is involved to match the calculated and experimental values.

Method B: The C7+ is broken into Single Carbon Numbers (SCN) ranging from SCN 7 to SCN 17+ using the exponential decay procedure presented by Katz [4] and applied by others [5-7].

Method C: The large number of SCN components of Method B may be lumped into 4 cuts. The properties of the lumped cuts are estimated from the individual SCN components.

Method D: This method is similar to Method B except that 12 normal parafins (alkanes) are used to represent the C7+instead of SCN components. The advantage of this method is that n-alkane components are readily available in many commercial software packages but the SCNs may not be.

Tuning MW in Method D: The distribution (i.e. mole %) of the alkane part of the C7+ depends on the assumed value of the C7+ MW.

Tuning the binary interaction parameters, kij, in Methods B and C: A common correlation to estimate the binary interaction parameter is:

In the above equation, νci and νcj represent the critical volumes of components i and j, respectively. The default value of exponent n is normally set to 1.2 but it can be used as a tuning parameter to match the experimentally measured dew point.

In this TOTM we will generate the dew point curve for the rich gas shown in Table 1 using the C7+ characterization methods described above. The dew point curve portion of the phase envelope for this gas was generated using both HYSYS [8] and ProMax [9] simulation software by the Soave-Redlich-Kwong (SRK) [10] (Figure 1) and Peng-Robinson (PR) [11] (Figure 2). The experimentally measured dew point pressure [12] is also show in these two figures as a red triangle.

Figures 1 and 2 were generated using a single C7+ cut with the relative density and molecular weight shown in Table 1. Other required properities were estimated using the default options of the simulation software. As can be seen in these figures using the PR Equation of State with ProMax gives the closest prediction of the experimentally measured dew point. As decribed above the MW can be adjusted to match experimantal and calculated data.

The single carbon number (SCN) analysis as described in Method B above was used for further tuning of the thermodynamic model, The predidicted dew point pressures for the different cases studied here are shown in Table 2. Figure 3 demonstrates the same information graphically.

Using Method B, the experimental dew point is most closely represented using four SCNs with a combined molecular weight of 118.2. The properties and mole percent distribution of these four SCN components for the optimum case are given in Table 3.

Table 4 shows the improvement made in the dew point prediction by using four SCNs with a modified molecular weight of 118.2 instead of a single C7+ cut. The ProMax PR EOS is used for both cases. The predicted dew point curves for these two cases can be seen in Figure 4.

As can be seen in Figure 4, proper characterization of the heavy components (see Tables 3 and 4) can improve the quality of the phase envelope and match the experimentally measured dew point in the dense phase region. For a detailed discussion of this topic, the readers may refer to the Rusten et al. paper [1].

To learn more about similar cases and how to minimize operational problems, we suggest attending the John M. Campbell courses; G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing – Special), and G7 (Process Simulation in Gas Conditioning and Processing).

JMC Consulting can provide thermodynamic expertise for gas processing projects to ensure that the developed process model and phase envelopes are as accurate as possible. With the most sought after consultants in the world-wide energy industry, John M. Campbell Consulting provides first choice consulting services to select clients. For more information about services offered by Campbell, visit our website at Campbell Consulting.

By: Dr. Mahmood Moshfeghian

Reference:

1. Rusten, B.H., Gjertsen, L.H., Solbraa, E.,  Kirkerød, T., Haugum, T. and Puntervold, s., “Determination of the phase envelope – crucial for process design and problem solving,” presented at the 87th GPA National Convention, Grapevine, 2008

2. Maddox, R. N. and L. Lilly, “Gas Conditioning and Processing, Computer Applications for Production/Processing Facilities,” John M. Campbell and Company, Norman, Oklahoma, 1995.

3. Riazi, M.R. and T.E. Daubert, Hydr. Proc. P. 115, (March) 1980

4. Katz, D. J. Petrol. Technol., 1205-1214, (June) 1983.5. Whitson, C. H. SPE J., 683-694, (August) 19836. Starling, K. E. Presented at the American Gas Association Operations Conference, Orlando, FL, April 27-30, 20037. Moshfeghian, M., Maddox, R.N., and A.H. Johannes, “Application of Exponential Decay Distribution of C6+ Cut for Lean Natural Gas Phase

Envelope,” J. of Chem. Engr. Japan, Vol  39, No 4, pp.375-382, 20068. ASPENone, Engineering Suite, HYSYS Version 7.0, Aspen Technology, Inc., Cambridge, Massachusetts U.S.A., 2009.9. ProMax®, Bryan Research & Engineering Inc, Version 3.2, Bryan, Texas, 200910. Soave, G., Chem. Eng. Sci. 27, 1197-1203, 1972.11. Peng, D.,Y. and D. B. Robinson, Ind. Eng. Chem. Fundam. 15, 59-64, 1976.12. Sage, B.H, and R.H. Olds, AIME 170, 156–173, 1947.

Should the TEG Dehydration Unit Design Be Based on the Water Dew Point or Hydrate Formation Temperature?

Translation: Español

Glycol dehydration is the most common dehydration process used to meet pipeline sales specifications and field requirements (gas lift, fuel, etc.). Triethylene glycol (TEG) is the most common glycol used in absorption systems. Chapter 18, Gas Conditioning and Processing [1] presents the process flow diagram and basics of glycol units. A key parameter in sizing the TEG dehydration unit is the water dew point temperature of dry gas leaving the contactor tower. Once the dry gas water dew point temperature and contactor pressure are specified, water content charts similar to Figure 1 in reference [2] can be used to estimate the water content of lean sweet dry gas. The required lean TEG concentration is thermodynamically related to the dry gas water content which influences the operating (OPEX) and capital (CAPEX) costs. The lower dry gas water content requires a higher lean TEG concentration. This parameter sets the lean TEG concentration entering the top of contactor and the required number of trays (or height of packing) in the contactor tower.

The rich TEG solution is normally regenerated at low pressure and high temperature. Maximum concentrations achievable in an atmospheric regenerator operating at a decomposition temperature of 404 °F (206°C) is 98.7 weight %. The corresponding dry gas water dew point temperature for this lean TEG weight % and contactor temperature of 100°F (38°C) is 18°F  (-8°C).

If the lean glycol concentration required at the absorber to meet the dew point specification is higher than the above maximum concentrations, then some method of further increasing the glycol concentration at the regenerator must be incorporated in the unit. Virtually all of these methods involve lowering the partial pressure of the glycol solution either by pulling a vacuum on the regenerator or by introducing stripping gas into the regenerator.

For water saturated gases, the water dew point temperature is either above or at the hydrate formation temperature. However, if the gas is water under-saturated, the hydrate formation temperature will be higher than water dew point. This means at a given specified water dew point temperature, there are two water content values; the lower value will be at the hydrate formation temperature and the higher value will be at the water dew point temperature. Therefore, the designer has to choose one of these two values. Which value should be chosen? The answer to this question is “It depends”! The lower value of water content means higher lean TEG concentration and consequently higher CAPEX and OPEX.

In this TOTM we will attempt to answer the question by studying a case in which the specified water dew point temperature is below the hydrate formation temperature. For this purpose, we will discuss the water content of natural gas in equilibrium with hydrate and when the condensed water phase is liquid.

The water content chart of Figure 6.1 in reference [2] is based on the assumption that the condensed water phase is a liquid. However, at temperatures below the hydrate temperature of the gas, the “condensed” phase will be a solid (hydrate). The water content of a gas in equilibrium with a hydrate will be lower than equilibrium with a metastable liquid.

Hydrate formation is a time dependent process. The rate at which hydrate crystals form depends upon several factors including gas composition, presence of crystal nucleation sites in the liquid phase, degree of agitation, etc. During this transient “hydrate formation period” the liquid water present is termed “metastable liquid.” Metastable water is liquid water which, at equilibrium, will exist as a hydrate.

Reference [3] presents experimental data showing equilibrium water contents of gases above hydrates. Data from Reference [3] are presented in Figure 6.5 of reference [2] and plotted here as rotated square in Figure 1 at 1000 Psia (6,897 kPa). For comparative purposes, the “metastable” water content of the gas (dashed line) as well as the hydrate formation temperature (solid line) calculated by ProMax [4] using the Peng-Robinson [5] equation of state are also shown. The water content of gases in the hydrate region is a strong function of composition. Figure 1 should not be applied to other gas compositions.

Figure 1. Water content of 94.69 mole % methane and 5.31 mole % propane – gas in equilibrium with hydrate at 1000 Psia (6,897 kPa)

Case Study:

To demonstrate, the effect of water content of a dried gas in equilibrium with hydrate on the required lean TEG concentration, let’s consider the gas mixture presented in Figure 1. This gas enters a contactor tower at 1000 Psia (6,897 kPa) and 100 °F (37.8°C) with a rate of 144 MMSCFD (4.077 106 Sm3/d). At this condition, the water content of the wet gas is 57.6 lb/MMSCF (922.4 kg/106 Sm3). It is desired to dehydrate the gas to a water dew point temperature of 5°F (-15°C) using a TEG dehydration unit.

Results and Discussion:

According to Figure 1, at a temperature of 5°F (-15°C) the water content is 1.2 lb/MMSCF (19.2 kg/106 Sm3) and 1.97 lb/MMSCF (31.5 kg/106 Sm3) in equilibrium with metastable water and hydrate phase, respectively. ProMax was used to simulate this TEG dehydration unit for the case of three theoretical trays in the contactor tower.  The simulation results for these two water content cases are shown in Table 1. This table clearly indicates that the required lean TEG concentrations are not the same and consequently will impact the regeneration requirements of the rich TEG solution. The difference between the lean TEG concentrations will be even more at a lower dry gas water dew point specification.

The simulation results clearly indicate that the choice of water content for a specified dry gas water dew point as the basis for design affects the required lean TEG concentration and consequently the rich TEG solution regeneration requirements.

Table 1. Comparison of simulation results for two different water content specifications

Simulation Results Using ProMaxBased on Water Dew Point Temperature of 5 °F (-15°C)

Based on Hydrate Formation Temperature of 5 °F (-15°C)

Water Dew Point Temperature , °F (°C) 5.0 (-15.0) -6.2 (-21.2)

Hydrate Formation Temperature, °F (°C) 14.7 (-9.6) 5.0 (-15.0)

Water Content, lb/MMSCF (kg/106 Sm3) 1.97 (31.5) 1.20 (19.2)

Gallon/lb of Water Removed (liter/kg of Water Removed) 3.95 (32.9) 3.90 (32.4)

Lean TEG Weight % 99.45 99.72

Conclusions:

When designing dehydration systems, particularly TEG systems to meet extremely low water dew point specifications, it is necessary to determine the water content of the dried gas in equilibrium with a hydrate using a correlation like that presented in Figure 1. If a metastable correlation is used, one will overestimate

the saturated water content of the gas at the dew point specification. This, in turn, may result in a dehydration design which is unable to meet the required water removal. Where experimental data is unavailable, utilization of an EOS-based correlation which has been tuned to empirical data can provide an estimate of water content in equilibrium with hydrates.

To meet pipeline sales specifications, it is normally acceptable to use the water content in equilibrium with the metastable phase (the dashed line in Figure 1) because the difference in the water contents is not that high. However, for extremely low water dew point specifications where there is a cryogenic process downstream, it is recommended to use the water content in equilibrium with hydrate (the solid line in Figure 1).

To learn more about similar cases and how to minimize operational problems, we suggest attending the John M. Campbell courses: G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing-Special), and G7 (Process Simulation in Gas Conditioning and Processing).

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. With the most sought after consultants in the oil and gas industry, JMCC provides first choice consulting services to select clients. For more information about services offered by Campbell, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Reference:

1. Campbell, J. M., “Gas Conditioning and Processing”, Vol. 2, The Equipment Module, 8th Ed., Second Printing, J. M. Campbell and Company, Norman, Oklahoma, 2002

2. Campbell, J. M., “Gas Conditioning and Processing”, Vol. 1, The Basic Principles, 8th Ed., Second Printing, J. M. Campbell and Company, Norman, Oklahoma, 2002

3. Song, K.Y. and Kobayashi, R, “Measurement & Interpretation of the Water Content of a Methane-5.31 Mol% Propane Mixture in the Gaseous State in Equilibrium With Hydrate,” Research Report RR-50, Gas Processors Association, Tula, Oklahoma, 1982

4. ProMax 3.1, Bryan Research and Engineering, Inc, Bryan, Texas, 2010.5. Peng, D. Y. and Robinson, D. B., I. and E. C. Fund, Vol. 15, p. 59, 1976.

What is the Impact of Water Content on the Dew Point and Hydrate Phase Behavior?

Translation: Español

In a past Tip Of The Month (TOTM), we have shown that one of the first issues to be resolved by a facilities engineer working in a gas plant or gas production facility is where the process is operating with respect to the phase diagram.  A general knowledge, if not a detailed knowledge, will allow the design engineer and the facilities operator to make intelligent decisions that have significant impact on the profitability of a gas production facility.

The best way to prevent hydrate formation (and corrosion) is to keep the pipelines, tubing and equipment dry of liquid water. In this TOTM we will demonstrate how the water dew point and hydrate formation curves are shifted along a conventional phase envelope as natural gas is dehydrated.

Case Study:

In order to demonstrate the phase behavior of natural gases containing water and the impact of water content on the water dew point and hydrate formation temperatures, let’s consider the natural gas shown in Table 1. To generate the diagrams in this TOTM, we used ProMax [1] based on the Peng-Robinson equation of state (PR EOS) [2].

Table 1. Dry gas composition

Component Mole %C1 80.0C2 10.0C3 4.0iC4 3.0nC4 3.0Sum 100.0

Results and Discussion:

Figure 1 presents the phase envelope, hydrate formation and water dew point curves of this gas with a water content of 0.06 mole percent, equivalent to 28.5 lbm/MMSCF (456 kg/106 Sm3). Notice that up to a pressure of about 414 psia (2854 kPa), the water dew point curve is slightly to the left of the hydrate formation curve. This indicates that the gas is under-saturated with water at pressures below this point. This also means that it is thermodynamically unstable and will not form a free aqueous phase. All the water is converted to hydrate and this state is referred to as “meta-stable” equilibrium. For more detail on this meta-stable state, see December 2010 TOTM. Similar behavior is demonstrated in Figure 2 for which the water content was reduced to 0.0427 mole percent, equivalent to 20.3 lbm/MMSCF (324.6 kg/106 Sm3). In this case the water dew point and hydrate formation curves intersect at a higher pressure of 1000 psia (6895 kPa). Below this pressure, the gas is under-saturated and has a meta-stable equilibrium state. Therefore, the water dew point curve is to the left of the hydrate formation curve, but above the intersection pressure it moves to the right of the hydrate formation curve where the water content is above saturation.

Figure 3 presents the superimposition of Figures 1 and 2 having water dew point and hydrate formation curves for two different water contents (0.06 and 0.0427 mole%). Notice the hydrate formation curves for both cases coincide with each other for pressures of 1000 psia (6895 kPa) and higher.

Figure 4 presents the phase envelope along with the water dew point and hydrate formation curves for the same gas as the water content was reduced to 0.0427, 0.03, 0.0148, and 0.00422 mole % corresponding to 20.3, 14.2, 7, 2 lbm/MMSCF (324.6, 228, 112, 32 kg/106 Sm3), respectively. Notice for all the cases where the gas is under-saturated with water, the water dew point curves are located to the left of the corresponding hydrate formation curves. Under these conditions the equilibrium state is thermodynamically unstable (meta-stable) and will not form a free aqueous phase. However, if the water content is above saturation point, then the water dew point will position to the right of the corresponding hydrate formation curve and free water will form under stable condition.

Conclusions:

We have demonstrated the impact of the water content on the phase behavior of a natural gas. The emphasis was placed on the interaction of the water dew point and hydrate formation curves. It was shown that the relative location of the water dew point and hydrate curves with respect to each other is a strong function of

the water content. It was also shown for the cases where water content is above saturation point, the water dew point curve locates to the right of the hydrate curve. Under this condition free water forms and then hydrates may form if conditions are right. This is what is normally expected and shown in text books. However, if the water content is under-saturated, the water dew point curve will be located to the left of the hydrate formation curve and the equilibrium state is thermodynamically unstable (meta-stable) and will not form a free aqueous phase.

As discussed in last month’s TOTM, facility engineers have to determine how this behavior affects their operations.  These phase envelopes suggest that, at low water concentrations, hydrates may form even though free water is not present.  Indeed, this phenomenon has been observed.  At cryogenic conditions, when the water is removed by molecular sieves, the amount of metastable water is so small it should not cause operational issues.

To learn more about similar cases and how to minimize operational problems, we suggest attending the John M. Campbell courses; G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing-Special), and G7 (Process Simulation in Gas Conditioning and Processing).

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. With the most sought after consultants in the oil and gas industry, JMCC provides first choice consulting services to select clients. For more information about services offered by Campbell, visit our website at www.jmcampbellconsulting.com.

By: Dr. Mahmood Moshfeghian

Reference:

1. ProMax 3.2, Bryan Research and Engineering, Inc, Bryan, Texas, 2010.2. Peng, D. Y. and Robinson, D. B., I. and E. C. Fund, Vol. 15, p. 59, 1976.

Liquid Density by Volume Translated Method – Part 1: Pure Compound

Translation: Español

Liquid density is needed for process simulation and equipment design. For example, accurate predictions of liquid density are needed for calculating the pressure drop in piping/pipeline and vessel sizing. Accurate liquid density is also essential for custody transfer.

In November 2006, December 2006 and January 2007 tips of the month (TOTM), we presented an overview of different methods and tools for predicting liquid densities. The methods for liquid density prediction include but are not limited to the following.

Generalized Charts

There are several generalized charts for predicting the liquid density of petroleum fluids and hydrocarbons [1]. The charts normally present the relative density of paraffinic hydrocarbon mixtures at their boiling point or bubble point temperature and pressure. These charts apply to mixtures as well as pure components. Alignment points for paraffinic hydrocarbon mixtures and pure components are located according to their molecular weight. The accuracy of these charts is generally within 3 % of the measured values. However, the accuracy is somewhat less for mixtures with molecular weights less than 30 where temperature is low, and where the methane content is high or pseudo-reduced temperatures are above 0.9 [2].

Correlations

In order to calculate liquid density reliably, several correlations such as: COrresponding STAte Liquid Density (COSTALD), modified Rackett equation by Spencer and Danner (RSD), and Nasrifar-Moshfeghian (NM) have been developed.

COSTALD: The COSTALD correlation by Hankinson and Thomson [3] requires two parameters: wSRK, the optimized value of the acentric factor based on the SRK equation of state (EoS) and; V*, the pure component characteristic volume.

RSD: Spencer and Danner [4] improved the liquid density correlation of Rackett [5]. The improved correlation for saturated liquid density calculation requires only ZRA, the improved compressibility factor.

NM: Nasrifar and Moshfeghian [6] presented an equation and a set of mixing rules for predicting the liquid density of pure refrigerants and liquefied natural gas.

EoS Methods and Volume Translated

The equations of state are used in commercial simulation software for predicting phase behavior and thermodynamic properties. Generally, EoSs need a few parameters (usually two or three) that are normally obtained from critical properties. The cubic equations of state (EoS) give relatively accurate results for predicting vapor-liquid equilibria, especially for non-polar or slightly polar systems. Furthermore, these equations could be used to accurately predict vapor densities, enthalpy and entropy. These advantages encourage the researchers to augment EoS ability more than before, especially liquid density, although their accuracy for liquid density prediction is generally not as good as the correlations listed above. The popular EoSs such as SRK [7] and PR [8] predict liquid density with an average absolute error of about 8%, much higher than the correlations [9]. This large magnitude of error is not acceptable by industry; therefore they are not used for this purpose. In order to overcome this deficiency, a volume translated method has been developed by Peneloux et al. [10].

In this TOTM, we will present the method of volume translation for liquid density prediction and then demonstrate its application for liquid hydrocarbons such as pure methane, n-pentane, decane, pentadecane and carbon dioxide. In a future TOTM we will extend this procedure to multicomponent mixtures.

In order to improve the accuracy of EoSs for predicting liquid density, Peneloux et al. [10] proposed the following correction.

(1)

In the above equation, is the corrected liquid specific volume,  is the liquid specific volume calculated by SRK or PR EoS, MW is the molecular weight, ρL is the liquid density, and the correction term or volume shift factor “c” is determined from experimentally measured liquid density. It is normally regressed against several data points. In the absence of experimentally regressed value, it can be estimated as follows:

(2)

where ZRA, is the Rackett [10] parameter, R is the gas constant and TC and PC are the critical temperature and pressure, respectively.

In this work, we determined the value of “c” by minimizing the absolute error between experimentally measured liquid densities [11] and the corresponding predicted values using MathCad software. To achieve this, the following equation was defined.

(3)

where NP is the number of data points, ρexp is the experimental liquid density. The value of “c” was determined by minimizing  f(c). In MathCad nomenclature the appropriate command is:

(4)

Results and Discussion:

We applied the preceding procedure to several pure compounds shown in Table 1. The temperature and pressure ranges, and the optimized values of “c” for both PR and SRK EoS as well ZRA for the RSD correlation are shown in Table 1. Figures 1 and 2 present graphical comparisons between the predicted and experimental liquid density values of pentadecane. Similar trends were observed for the other compounds. Table 2 presents the summary of error analysis for different methods for the pure compounds shown in Table 1.

Table 1. Optimized volume translated parameter, c, for different compounds

Component Temperature Range, °C Pressure Range, kPa NPSRK            c x 106 m3/mol SRK (c/b)

PR            c x 106 m3/mol PR (c/b) ZRA

Methane -182 to -90 12 to 3464 55 -0.3506 -0.012 4.059 0.151 0.2891n-Pentane -121 to 124 0.0003 to 2548 21 -11.36 -0.113 2.04 0.023 0.2686Decane -13 to 344 0.006 to 2097 18 -41.44 -0.197 -13.99 -0.074 0.2522Pentadecane 12 to 432 0.0002 to 1421 29 -92.89 -0.270 -48.25 -0.156 0.2385CO2 -56 to 18 531 to 5463 63 -4.534 -0.153 0.955 0.036 0.2719

Figure 1. Comparison of predicted liquid density of C15H32 by PR and volume translated PR (VTPR) against experimental data [11]

Figure 1. Comparison of predicted liquid density of C15H32 by SRK and volume translated SRK (VTSRK) against experimental data [11]

Table 2 indicates that considerable improvements are obtained by applying volume translated correction to liquid specific volume (or liquid density) predicted by PR and SRK. However, the accuracy of the COSTALD, RSD and NM correlations are still by far much better than the volume translation applied to these two EoSs. The accuracy of EoS and its volume translated correction deteriorate as the critical point is approached.

Table 2. Summary of error analysis for different methods studied

ComponentAverage absolute Error %PR VTPR SRK VTSRK RSD NM COSTALD

Methane 9.65 2.13 3.96 3.68 0.12 0.20 0.12n-Pentane 2.64 2.14 11.03 3.07 0.14 0.15 0.11Decane 7.62 3.09 18.16 4.43 1.04 0.70 0.95Pentadecane 14.08 3.63 23.71 4.61 0.20 1.13 0.25Carbon Dioxide 2.68 2.24 11.25 3.48 0.28 0.12 0.31Overall Average 7.33 2.65 13.62 3.85 0.36 0.46 0.35

To learn more about similar cases and how to minimize operational problems, we suggest attending the John M. Campbell courses; G4 (Gas Conditioning and Processing), G5 (Gas Conditioning and Processing-Special), and G7 (Process Simulation in Gas Conditioning and Processing).

John M. Campbell Consulting (JMCC) can provide thermodynamic expertise for gas processing projects to ensure that the developed process model is as accurate as possible. With the most sought after consultants in the oil and gas industry, JMCC provides first choice consulting services to select clients. For more information about services offered by Campbell, visit our website at www.jmcampbellconsulting.com.

By Dr. Mahmood Moshfeghian

Reference:

Campbell, J. M. “Gas conditioning and processing, Volume 1: Fundamentals,” John M. Campbell and Company, Norman, Oklahoma, USA, 2001.

Engineering Data Book, 12th Editions, Gas Processors and Suppliers Association Data Book, Tulsa, Oklahoma, 2004.

Hankinson, R. W., Thomson, G. H., AIChE J., Vol. 25, no. 4, pp. 653-663, 1979.

Spancer, C. F., and Danner, R. P., J. Chem. Eng. Data, vol. 17, no. 2, pp. 236-241, 1972.

Rackett, H. G., J. Chem. Eng. Data, vol. 15, No. 4, pp. 514-517, 1970.

Nasrifar, Kh. and Moshfeghian, M., Fluid Phase equilibria Vol. 153, 231-242, 1998.

Soave, G., Chem. Eng. Sci., Vol. 27, pp. 1197-1203, 1972.

Peng, D. Y., and Robinson, D. B., Ind. Eng. Chem. Fundam., Vol. 15, p. 59, 1976.

Nasrifar, Kh. and M. Moshfeghian, J. of Fluid Phase Equilibria, Vol. 158-160, pp. 437-445, 1998.

Peneloux, A. E., Rauzy, E., and Freze, R., Fluid Phase Equilib., Vol. 8, pp. 7-23, 1982

Vargaftik, N.B., Handbook of Physical Properties of Liquids and Gases (Pure Substances and Mixtures), 2nd ed., English Translation, Hemisphere Publication, 1975.