The module discusses various techniques for evaluating the past performance of the well and shows how we can correctly predict the reservoir parameters as well as future performance
In addition to discussing conventional wells, the module also discusses unconventional wells’ performance
Old techniques such as Arp’s method are discussed, as well as modern techniques such as Blasingame and Agarwal’s methods
Arp’s Blasingame Agarwal’s
Why Take This Module?
Examples re-enforce the concepts presented
A section on unconventional reservoir discusses the analysis of production data
Understanding this module will provide the user with ability to apply appropriate techniques for evaluating the performance of various types of wells
Example Well
The user will also understand the limitations and the strengths of various techniques
Below are some very important assumptions which are made in a traditional rate transient analysis.
Past producing trends are reflective of future performance. If you observe the past rate then you can use that information to predict what's going to happen in the future.
Produced at or near capacity: Producing the well at the the maximum possible rate the well can be produced.
Constant drainage area: If the well starts producing with a certain amount of drainage area then the drainage area does not change significantly.
Constant bottomhole pressure. At later stages if the well is on a gas lift, ESP, or rod pump their assumption is reasonable.
Rate time analysis, at minimum, requires measured production rates as a function of time. In most instances, the measurements available would be monthly.
The following additional data can improve the rate transient analysis:
Fluid properties
Knowledge of if the well is producing under singles phase or multi-phase conditions
Bottom hole pressure data
Well operations (e.g., stimulation, installation of gas lift, etc.) and when they took place
The rate transient analysis can be applied under any flow regime conditions. However, the information gained is different under different flow regimes.
By evaluating the data under transient conditions, we canobtain reservoir parameters such as permeability, skin factor,hydraulic fracture characteristics
Data available under transient stateData available under transient state
By evaluating the data under pseudo-steady state or boundarydominated flow conditions, we can obtain the remainingreserves, EUR and future rate predictions as a function of time
Data available under pseudo-steady state or boundary dominated state
Data available under pseudo-steady state or boundary dominated state
See Reservoir Flow Properties Fundamentals for more information on this topic.
Dimensionless variables are used in rate time analysis. As the name indicates these variables are dimensionless and they are comprised of multiple reservoir parameters. The main advantage of using the dimensionless variables is that they allow evaluation of multiple variables very quickly. Rather than varying a single variable we can vary the dimensionless variable and that will allow us to evaluate multiple variables at the same time.
It is often convenient to use dimensionless variables in rate transient analysis
Dimensionless variables – as the name suggests – have no dimensions
Dimensionless variables are comprised of multiple reservoir parameters
This allows evaluating the effects of individual parameters on the reservoir performance much easier
The main advantage of using dimensionless variables is that they allow combining the effects of multiple variables on the reservoir performance
Dimensionless variables also allow rate transient analysis using type curves which are generated using dimensionless variable
By superposing actual production data on type curves, we can determine important reservoir parameters
Where qD and pD are defined previously and re and rw are drainage and wellbore radii respectively. The alternate definition for qDd comes directly from the rate equation for qi
based on Darcy’s law.
Where qD and pD are defined previously and re and rw are drainage and wellbore radii respectively. The alternate definition for qDd comes directly from the rate equation for qi
based on Darcy’s law.
Important Dimensionless Variables
Dimensionless time
3792ϕDimensionless Time (another version)
=
Dimensionless time
2.814 10 ϕDimensionless Time (another version)
=
Field UnitsField Units SI UnitsSI Units
k md
t hrs
fraction
cp
ct psi-1
re and rw ft
rwa Effective well bore radius or rwe-S where S is the skin factor
tDd Can be defined in terms of decline rate, Di and t.
k md
t hrs
fraction
Pa.s
ct kPa-1
re and rw m
rwa Effective well bore radius or rwe-S where S is the skin factor
tDd Can be defined in terms of decline rate, Di and t.
The dimensionless variables which are explained here are based on either simple geometry with circular reservoir or based on area if the reservoir is not circular.
The dimensionless variables explained here are based on either simple radial geometry with circular reservoir or based on area if the reservoir is non-circular.
The equations for oil are written in terms of pressure; whereas, the equation for gas are written in terms of pseudo-pressure.
The definition of dimensionless time is different for fractured reservoirs.
Many of these dimensionless variables are used in various forms in rate transient analysis as will be discussed in later sections.
Below there are certain implicit assumptions in Arps equation to be familiar with:
The well is producing at constant bottom hole pressure and at full capacity.
Prior production is an indication of future trend in the production. If you make a change in the performance of the well, the prior decline may not be indicative of what's going to happen in the future.
The well is producing under boundary dominated flow or pseudo-steady state conditions.
Here is the graph shown in terms of dimensionless properties, qDd, which we have already defined in the previous section as a function of dimensionless time, tDd, and you can see that when qDd is equal to one that's when the rate is equal to initial rate and then it slowly declines. For B equal to zero corresponds to a faster decline and B equal to one corresponds to a slower decline.
Knowing the current and abandonment rates, we can calculate the remaining reserves by substituting into the previous equation.
12 20.12365
30,417
The units of decline rate and the production rate must be consistent. Since rate is bbl/day, the decline rate must be per day.
EUR = Cumulative production so far + Remaining reserves = 150,417 bbls
A well has already produced 120,000 barrels of oil. The current rate of the well is 12 bbl/day and the abandonment rate is expected to be 2 bbl/day. If the decline rate is 0.12/year, what is the EUR for this well?
Exponential decline provides the most conservative estimation of EUR compared to other types of decline
We can obtain the decline rate by either plotting log of rate versus time and calculating the slope, or by plotting cumulative production versus rate and calculating the slope
Exponential decline allows prediction of future rate performance by using an assumption of constant decline rate
Hyperbolic Decline
For values of b between 0 and 1, we can use hyperbolic decline
Unlike exponential decline, the decline rate decreases with time for hyperbolic decline. We can calculate the decline rate after certain time.
1
The cumulative production, at the time of abandonment, can be calculated. 1
Knowing the current and abandonment rates, we can calculate the remaining reserves as:
12
0.063365 1 0.5
1212
.
82,281
* The units of decline rate and the production rate must be consistent. Since rate is bbl/day, the decline rate must be per day.
EUR = Cumulative production so far + Remaining reserves = 202,281 bbls
Compared to exponential decline, the remaining reserves are a lot greater in the case of hyperbolic decline because the decline rate is a lot smaller compared to what we assume for exponential decline.
A well has produced 120,000 barrels of oil after 15 years. The current rate of the well is 12 bbl/day and the abandonment rate is expected to be 2 bbl/day. If the initial decline rate is 0.12/year and the ‘b’ value is 0.5, what is the EUR for this well?
Knowing the current and abandonment rates, we can calculate the remaining reserves as:
12
0.043365
122
183,118
* The units of decline rate and the production rate must be consistent. Since rate is bbl/day, the decline rate must be per day.
EUR = Cumulative production so far + Remaining reserves = 303,118 bbls
A significant increase in the EUR for harmonic decline compared to hyperbolic decline and that's of course greater than exponential decline so again this just reconfirms the fact that the exponential decline is the most conservative method why we can predict the future performance.
A well has produced 120,000 barrels of oil after 15 years. The current rate of the well is 12 bbl/day and the abandonment rate is expected to be 2 bbl/day. If the initial decline rate is 0.12/year and the production is under harmonic decline, what is the EUR for this well?
Certain observations of exponential decline depends on only two parameters qI and D.
The evaluation of exponential decline depends on two parameters: qi and D; the evaluation of hyperbolic decline depends on three parameters: qi, Di and b; and the evaluation of harmonic decline depends on two parameters qi and Di.
It is possible to determine the parameters for exponential decline using simple plots. This is also true for harmonic decline (a plot of 1/q vs. t will provide the two parameter values). However, to determine 3 parameters for hyperbolic decline, we will need more sophisticated technique such as “type curve” analysis. We plot the actual rate vs. time data on dimensionless graph and by matching one of the stems, we can determine qi, Di and b values.
The exponential decline provides the most conservative estimate of remaining reserves; whereas, the harmonic decline provides the most optimistic estimate of remaining reserves. Except for exponential decline, the decline rate decreases faster as the value of ‘b’ increases.
The following are extensions of Arps curves for transient state.
Original Arps equation was restricted to pseudo-steady state (or boundary dominated state) conditions. It allowed the calculation of EUR or remaining reserves as long as the well-produced is under existing conditions.
Fetkovich, in 1980, extended Arps equation by combining it with transient state solution.
Fetkovich generated a type curve which can be used to evaluate wells which can be either producing in transient or pseudo-steady state conditions.
Below are some changes in the 1990's which resulted in this modern-day time analysis.
The original Arps equation was based on an assumption that bottom hole pressure is unknown in most cases and hence assumed to be constant.
In the 1990s SCADA units became popular and with the advent of computers and remote sensing, it was possible for the operator to measure both the well head pressure and the rate data more frequently.
With the knowledge of well head pressure, bottom hole pressure could be estimated knowing the tubing/well bore configuration.
Hence operators had the information about both the rate and bottom hole pressure data.
The original Arps curves needed to be refined to add the possibility of additional data.
Here's an example of the type of data which we could obtain from a single well. We can see that on the left-hand side we have the oil flow rate scale and on the right hand you have a wellbore flowing pressure data. Both pieces of information are available and more important they are not constant. Oil flow is declining and so is the bottom hole pressure. We must incorporate that information to come up with a better methodology
Blasingame used the normalized rate plot to account for both variablerate and variable pressure
Instead of using rate (as in the case of Arps), we plot:
Blasingame Approach
After Palacio and Blasingame, SPE 25409 (1993)
∆on the y axis for oil wells
∆on the y axis for gas wells
Instead of plotting the actual time on x axis, Blasingame recommendedmaterial balance time, which is defined as:
The numerator represents cumulative production and the q in thedenominator represents the rate at the time Np or Gp hydrocarbons areproduced
for oil wells for gas wells
Blasingame Plot
The graph does show clear distinction between transient and boundarydominated flow
There is only single stem in boundary dominated flow (unlike multiple onesfor Arps equation); the slope is -1 in boundary dominated flow whichcorresponds to harmonic decline
This plot representsdimensionless normalizedrate versus dimensionlessmaterial balance time; thedefinitions of dimensionlessrate and time are alreadydefined, except that thedimensionless time iscalculated using materialbalance time
Blasingame also created integral and differential plots to improve the diagnostic power of the plot
The integral function provides more smoother data compared to raw data
The derivative of integral function provides a better signature to identify transition between transient and boundary dominated flow
When all three curves are plotted and fitted to the type curve, we can obtain reservoir parameters in transient region and EUR in boundary dominated region
Example – Blasingame Method
This plot shows all threecurves
Integral function issmoother but thederivative function hasmore character; thederivative of integralfunction is smoother thanthe derivative of raw data
By fitting the data, wecan identify the data inboth transient andboundary dominatedregions
In addition to predicting the reservoir parameters and EUR for oil and gas wells, Agarwal et al. also proposed a method to calculate initial oil or gas in place using different graphical procedure.
They demonstrated that during boundary dominated flow, if an inverse of dimensionless pressure (or dimensionless normalized rate) is plotted as a function of dimensionless cumulative production, the straight line intersection on the x axis will provide the initial gas or oil in place.
Both the dimensionless rate and dimensionless cumulative production are already defined for both oil and gas wells.
Normalized rate is /∆ and normalized cumulative production is ( )/∆ ;using the graph, we can calculate maximum recovery based on theintersection on x axis if we know the bottom hole pressure
To calculate oil in place, we need to assume different value of A (area) suchthat the intersection point on dimensionless graph goes through 1 on x axis;through trial and error we can calculate the value of A and hence oil in place ifother reservoir parameters are known
The graph shows trial and error procedure of adjusting the initial gas in place till a reasonable straight line is obtained.
Many commercial programs are available in the market place to generate this graph so that gas in place can be calculated relatively easily.
Main Contributions of Modern RTA:
Both Blasingame and Agarwal et al. methods allow us to incorporate variable rate and variable pressure.
Unlike Arps method, the boundary dominated flow is indicated by single stem, but for transient flow various stems exist depending on the type of well from which either oil and gas is produced. This includes both standard as well as fractured wells producing from various geometries of reservoir shape.
Both methods will allow us to predict the reservoir parameters if data are available in transient region.
In addition, Agarwal et al. method will allow us to predict initial oil or gas in place using flowing material balance time.
A typical horizontal well is drilled inthe direction of minimum stress
Multi-stage fractures are createdwhich are perpendicular to the well
Although each fracture may havedifferent length and height, forsimplicity in the model, we assumethat all the fractures are uniformand have the same length andheight
The space between the fracturesis also assumed to have somestimulation and hence alteration ofpermeability
Fractures are transverse (perpendicular) to well direction
Relationship between Normalized Rate (or Pressure) versus Time
For linear flow from stimulated region into fracture, depending on whether the well is producing at constant rate or pressure, we can write
the equation in terms of dimensionless form:
For constant rate: where tD is defined in terms of half fracture length.
For constant pressure: where tD is defined in terms of half fracture.
If both pressure and rate are varying (as is more common), use the equation corresponding to constant rate but instead of using time, use superposition time.
Depending on the flow regime, a distinct relationship existsbetween normalized pressure (or rate) and time
Superposition time is a way by which we can apply the constant rate equation to variable rate problem. That is, if the well is producing at three different rates, what would be equivalent time the well has to produce at the last rate so that the bottom hole pressure would be the same?
Plot normalized pressure versus superposition time on log-log graph.
Determine different flow regimes present in the reservoir.
Determine the transition from linear flow in stimulated region to fracture interference (boundary dominated) flow. Note the time at which transition happens (teLF).
Plot normalized pressure versus square root of time and determine the slope of the straight line. From the slope (m) calculate xF√k.
From the knowledge of teLF and based on simple rectangular geometry, determine the initial oil or gas in place within the rectangle.
Consider a simple example here to illustrate how we go about evaluating a gas or oil well when it is producing from horizontal multistage fracture well. On the Y axis is a plot of ∆m(p) over q as a function of time, and you see that there is a half slope which has developed corresponding to the linear flow and one slope which has developed during the boundary dominated flow or the fracture interference period. The time; which is about 3200 days at which the linear flow ends and the interface dominated period begins, is the intersection point between the two lines on the graph.
Then take the data corresponding to the linear flow regime and plot again the normalized pressure versus the square root of time to calculate the slope of the line corresponding to the linear flow. That slope will be used to calculate the half fracture length times square root of permeability.
Evaluation of a gas or oil well producing from unconventional reservoirs based on flow regimes is much more rigorous and more informative.
Alternately, the wells can also be analyzed using traditional decline curve analysis such as Arps method.
The main difficulty in using Arps method is the key assumption that a well is producing under boundary dominated flow is violated.
When early production data from unconventional well is fitted, the value of ‘b’ is much greater than 1 (close to 2 for linear flow) for transient flow regime and as the well becomes boundary dominated, the value of ‘b’ gets smaller.
The common practice is to use two different values of ‘b’ to fit the data. The early production data are fitted using higher ‘b’ value and when the decline rate reaches certain value, assume exponential decline (‘b’ = 0).
Here is the prediction. You plot the rate and you can see what happens is that after 3,200 days we switch to exponential decline which is much more conservative and make a prediction. It is possible to use Arps equations for horizontal wells which are producing from unconventional reservoirs and the traditional approach is to use two different values of b, the earlier transient period is fitted with higher value of b and the later period which is mostly boundary dominated flow or fracture interference dominated flow we use a value of b which is equal to zero. By using the combinations of the two we can come up with a prediction which is relatively conservative and provides us the information which is consistent with the transition from transient flow into boundary dominated or fracture interference dominated region.
For wells producing from unconventional reservoirs, the two most common flow regimes are linear flow in stimulated region and fracture interference dominated (boundary dominated) flow.
These regimes can be identified using log-log graphs of normalized pressure versus superposition time.
We can obtain half fracture length (if permeability of stimulated region is known) and original hydrocarbons in place if we observe both flow regimes.
Traditional decline curve analysis can be used for unconventional reservoirs except that the value of ‘b’ will exceed one in early part of the production data.
To prevent excessively aggressive predictions of EUR, normally, the value of ‘b’ is changed to zero when the decline rate reaches a pre-determined value.
The main limitation of material balance technique is that it is not related to time.
Material balance is used to predict the initial hydrocarbons in place, but it does not tell us about how the well is going to be produced in the future.
By combining material balance equation with Darcy’s law, it is possible to predict the future rate of a well if certain simplifying assumptions are made.
The calculation requires the knowledge of current average pressure and it assumes that material balance technique can be applied to a single well.
The Reservoir Material Balance Fundamentals module providedinformation on:
• How the material balance technique works
• Oil, gas and water rates, change in the reservoir pressure as afunction of time and fluid properties as a function of pressure
• Important mechanisms which influence the production
• Using the known mechanisms and the provided data, determine theinitial oil or gas in place depending on the type of the reservoir
To predict the rate from a well, work backwards and assume thatthe initial oil or gas in place is known and determine the rate atwhich the well will produce as a function of time
See Reservoir Material Balance Fundamentals for more information on this topic.
A reservoir contains 21,000,000 STB [3,338,981 Sm3] of oil. The initial reservoir pressure is 6,325 psia [43,609 kPa] and the bubble point pressure is 3,472 psia [23,938 kPa]. The reservoir permeability is 10 md and thickness is 50 ft [15.2 m]. The drainage radius is 1,500 ft [457.2 m] and well bore radius is 0.4 ft [0.12 m]. The formation compressibility is 10x10-6 psi-1 [1.45x10-6 kPa-1] and water compressibility is 2.5x10-6 psi-1 [3.63x10-7 kPa-1]. The viscosity of oil is 0.84 cp [0.00084 Pa.s]. The initial oil saturation is 0.7. A single well is drilled in the formation. Predict the rate profile of the well as a function of time till the reservoir reaches a bubble point pressure. Assume that bottom hole pressure is 2,000 psia [13,790 kPa], Swi is 0.3.
Data Table
Here are the basic calculations. You could see that the pressure has declined from 6,325 psia [43,609 kPa] to 3,472 psia [23,938 kPa].
1. To calculate the value of E0 and EFW of the stated pressures, it requires knowledge of the fluid properties. The oil produced can be calculated using the value of E0 and EFW and by knowing the initial oil in place.
2. The rates in the next column are calculated using Darcy's law equation.
3. The delta NP represents simply the incremental oil which is produced as the pressure drops from the previous value to the next value.
4. The average rate during that time period is calculated by taking the previous rate and the next rate and using the logarithmic averaging and then delta T represents the delta NP divided by Q average.
5. By summing those delta T in an accumulative fashion, you can calculate the time.
Accounts for both the oil compressibility and formationcompressibility
Although the rate profile is predicted using pseudo-steadystate assumption, it can also be predicted using transientstate equation except that it will involve trial and errorprocedure since rate will change with time for transient state
Rate Profile
The figureshows the rateprofile as afunction of time
Similar to previous example, we can assume pressure decrement andcalculate Rp using prior pressure
Using material balance, we can calculate the produced oil and calculate the oil rate. To calculate the oil rate at a new pressure, we also need to account for oil saturation changes; hence the change in the rate. The oil rate is calculated as:
For black oil model, oil saturation can be calculated as a function of pressure:
Once saturation is calculated, we can calculate the producing gas oil ratio as:
FieldUnits
SIUnits
)
/703 10 ̅
0.75
/7.633 10 ̅
0.75
Gas Reservoirs
A similar procedure can also be applied for gas reservoirs
The rate at any given pressure is calculated using Darcy’s law:
Assume a simple case where the only mechanism by which gas is produced is by gas expansion only. The material balance equation can be written as:
If we assume the initial gas in place is known, we can calculate the amount of gas produced at a given pressure as:
A reservoir contains 7 BCF [0.184 BSm3] of gas. The initial reservoir pressure is 5,800 psia [39,940 kPa]. m( ̅) = 1.084x109 psi2/cp [5.151x1013 kPa2/pa.s]The reservoir permeability is 1 md and thickness is 50 ft [15.2 m]. The drainage radius is 1,500 ft [457.2 m] and well bore radius is 0.4 ft [0.12 m]. A single well is drilled in the formation. Predict the rate profile of the well as a function of time till the reservoir reaches 2,046 psia [14,106 kPa]. Assume that bottom hole pressure is 942 psia [6,493 kPa], Temperature is 650 °R [361 °K] and m(pwf) is 6.67x107 psi2/cp [3.17x1012 kPa2/Pa.s].
Fluid Properties and Pseudo Real Pressure
The table below contains the fluid properties and the pseudo real pressure.
1. Consider a pressure decrement from the initial pressure. Calculate EG by subtracting BGI from BG.
2. Calculate the cumulative gas produced using the standard material balance equation as the pressure declines.
3. Calculate the rate at the beginning and at every other average reservoir pressure.
4. Calculate the incremental gas produced.
5. Calculate the average rate.
6. Calculate the incremental time and by summing the incremental time you can calculate the cumulative time.
7. Using that information, the rate profile as a function of time can be estimated. The rate is shown as a function of time. Like oil wells, you can apply this for gas producing under transient conditions, however, it will require a trial and error procedure since the rate is dependent on time as well. You will not be able to calculate the incremental time till we assume a certain rate at a given time then iterate over that rate.
Similar to oil wells, we can apply it for gas wells producing undertransient conditions; however, it would require a trial and errorprocedure since the rate is dependent on time as well
