[Society of Petroleum Engineers SPE Annual Technical Conference and Exhibition -...

SPE 124197

Injectivity and Gravity Segregation in WAG and SWAG Enhanced Oil Recovery A. Faisal, K. Bisdom, B. Zhumabek, A. Mojaddam Zadeh, and W. R. Rossen Department of Geotechnology, Delft University of Technology

Copyright 2009, Society of Petroleum Engineers This paper was prepared for presentation at the 2009 SPE Annual Technical Conference and Exhibition held in New Orleans, Louisiana, USA, 4–7 October 2009. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract Gas-injection enhanced oil recovery can recover nearly all residual oil where the gas sweeps. Sweep efficiency in these processes is often poor, in large part because of gravity override of gas. Stone and Jenkins presented a model for gravity override in homogeneous reservoirs, showing that the distance gas and water travel before segregation depends directly on injection rate. In cases where injection pressure is limiting, injectivity is key to overcoming gravity override.

Stone assumed continuous co-injection of gas and water as a model for WAG, contending that this is valid as long as slugs mix near the well. This model for co-injection can be extended to relate segregation distance for co-injection processes directly to injection pressure. Injectivity depends on saturations very near the well, however. Therefore, where injection pressure is limiting, this model is pessimistic because injectivity in WAG is greater than in co-injection.

We investigate the increase in injectivity possible with WAG compared to co-injection in 1D and 2D, and the implications for gravity override in 2D, using a range of models for gas and water relative permeabilities. We confirm that the greater injectivity of WAG improves vertical sweep compared to Stone's model when injection pressure is limiting. The greatest improvements occur when slugs violate Stone's assumption: that is, they are too large to mix fully near the well. The increase in injectivity over co-injection is greater for foam than for WAG without foam, because foam has much lower mobility when gas and water flow together.

A similar benefit occurs for "simultaneous water and gas" (SWAG) injection from a single vertical well with water injected higher in the formation than gas. There is a modest benefit to injectivity of injecting water above gas, but far smaller for water-gas flow than that estimated for foam in a previous study.

Introduction Injection of gas (CO2, hydrocarbon gases, or steam) can be nearly 100% efficient in displacing oil from regions swept by gas (Lake, 1989). Unfortunately, sweep efficiency is often poor, because of reservoir heterogeneity, the large mobility of gas, and density differences between gas, oil and water. The most common way to improve gas sweep efficiency is water-alternating-gas (WAG) injection; injected water reduces the mobility of the gas and helps stabilize the displacement front. At fixed injection rate, reducing gas mobility also helps alleviate gravity segregation (Stone, 1982; Jenkins, 1984). Christensen, Stenby and Skauge (1989) reviewed 60 field applications of WAG. Generally it is applied at the later stages of water flooding and it can give higher oil recovery compared to waterflooding alone. WAG application is effective because of a combination of two recovery processes: the advantage of microscopic displacement efficiency of the gas flooding and the improved macroscopic sweep created by the injection of water.

In a WAG enhanced-oil-recovery (EOR) process, gas and water are injected sequentially through the same well. Average volumes per slug are small (in the range of 1 to 5% of the pattern pore volume (PV)) (Sanchez, 1999). For foam injection, it has been suggested to inject much larger slug sizes in order to improve injectivity and increase the distance before complete gas and water segregation takes place (Shan and Rossen, 2004; Kloet et al., 2009).

A useful model for gravity segregation in horizontal gas-water flow in homogeneous reservoirs was introduced by Stone (1982) and Jenkins (1984). Stone contended that his model for gravity segregation of injected gas and water, based on continuous co-injection, approximates WAG as long as the injection cycles are kept short enough, because then the slugs mix near the well; in other words, most of the swept zone would experience only steady gas-liquid flow. WAG and co-injection are also expected to perform similarly in terms of development of miscibility between oil by gas (LaForce and Orr, 2009). Stone and Jenkins' theory predicts the distance gas and water travel before complete segregation at steady state. By jumping to steady

2 A. Faisal, K. Bisdom, B. Zhumabek, A. Mojaddam Zadeh, and W. R. Rossen SPE 124197

state, after all mobile oil has been displaced from the region of interest, the model seeks to avoid the complications of three-phase miscible or immiscible flow during the displacement of the oil, and come immediately to the final state that would be attained after a sufficient period of injection.

Stone and Jenkins assumed that at steady state the reservoir model consists of three zones (Fig. 1): • An override zone, in which only gas is mobile • A mixed zone with both gas and water flowing • An underride zone, where only water is mobile.

Due to the high gas mobility at residual water in the override zone, the override zone occupies a much smaller fraction of the vertical cross section than the underride zone. Only the mixed zone and a thin override zone is flooded by gas, while the underride zone is waterflooded. The assumption that a WAG process can be represented as a continuous-injection process is illustrated in Fig. 2. Details of the model are discussed by Rossen and van Duijn (2004), Rossen et al. (2006) and Jamshidnezhad et al. (2009).

With these assumptions Stone and Jenkins derived equations for the distance Lg or Rg (for rectangular and cylindrical flow, respectively) that the injected water-gas mixture travels before complete segregation:

gQL

mk gWz w g rtρ ρ λ=

⎛ ⎞−⎜ ⎟⎝ ⎠

.....................................................................................................................................................(1)

gQR

mk gz w g rtπ ρ ρ λ=

⎛ ⎞−⎜ ⎟⎝ ⎠

...................................................................................................................................................(2)

where Q is total volumetric injection rate of gas and water, kz vertical permeability, ρw and ρg densities of water and gas, respectively, g gravitational acceleration, W the thickness of the rectangular reservoir perpendicular to flow, and λrt

m the total relative mobility in the mixed zone. Eqs. 1 and 2 imply that distance to the point of segregation scales directly with volumetric injection rate Q. This means that, holding other parameters fixed, by increasing Q one can increase distance to the point of segregation and the volume of the reservoir swept by gas.

By applying only standard assumptions of fractional flow theory (see, e.g. Lake, 1989), Rossen and van Duijn (2004) showed that Eqs. 1 and 2 are rigorous for the distance to the point of segregation (for co-injection of gas and water) and also confirmed Jenkins’s assertion that, short of this distance, the loss of gas and water from the mixed zone is proportional to x or r2 in linear or radial flow, respectively. Rossen and Shen (2007) and Rossen et al. (2009) showed a direct link between injection pressure and distance to the point of segregation. For cylindrical flow, the relationship is

2

2 1( ) ( ) ln 12 2

g ww g g

h w g

k g Rz w g Rp R p R R

Hk R R

ρ ρ⎛ ⎞− ⎡ ⎤⎜ ⎟ ⎛ ⎞⎛ ⎞⎛ ⎞⎝ ⎠ ⎢ ⎥⎜ ⎟− = − − ⎜ ⎟⎜ ⎟ ⎜ ⎟⎢ ⎥⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠⎣ ⎦.........................................................................................(3)

where p is pressure, Rw wellbore radius, and the second term in brackets disappears depending on the assumption made about the shape of the mixed zone. If injection pressure is limited, Eq. 3 suggests limits on the distance the mixed zone can travel before segregation. For instance, for kh / kz = 0.1, Rw = 0.1 m (4 in.), h = 6.1 m (20 ft), and (ρw - ρg) = 963 kg/m3, to place Rg at 1024 or 2048 ft (312 or 624 m) from the well would require an injection pressure 765 and 3310 psi (52 and 225 bar, or 5.2 and 22.5 MPa) above reservoir pressure, respectively.

Eq. 3 assumes uniform mobility in the mixed zone. Most injection pressure is dissipated near the well, while most segregation occurs far from the well. Fig. 3 illustrates this difference for a case where Rg = 500 m. An injection strategy that increases mobility near the well while keeping mobility low further from the well could, in effect, increase Q in Eqs. 1 and 2 because of high mobility near the well and yet retain the smaller value of λrt

m that applies further from the well in those equations. Several injection strategies have been proposed to accomplish this (Shan and Rossen, 2004; Rossen et al, 2006; Jamshidnezhad et al., 2009; Kloet et al., 2009).

WAG itself is a means of increasing injectivity over simultaneous injection of gas and water. In other words, Stone (1982) and Jenkins' (1984) model, as extended by Rossen et al. (2009), may be pessimistic for vertical sweep efficiency when injection pressure is limited, because it does not account for the advantage WAG offers over co-injection in near-well mobility and injectivity. This paper examines this advantage. First we consider the expected increase in injectivity in WAG in one-dimensional radial flow, as a function of slug sizes of gas and water, starting with slugs small enough to satisfy Stone's asssumption that they mix near the well. Then we quantify the advantages of WAG over co-injection in vertical sweep efficiency in 2D cylindrical flow where injection pressure is limited. Like Stone and Jenkins we focus on the swept zone after the period of mobilization of oil, as an indicator of sweep efficiency expected during the period of oil recovery. Also like Stone and Jenkins, we consider homogeneous reservoirs as a simple basis for analysis.

SPE 124197 Injectivity and Gravity Segregation in WAG and SWAG Enhanced Oil Recovery 3

Stone more recently proposed an injection scheme of simultaneous injection of water and gas, where water is injected higher in the formation than gas (Stone, 2004(a,b); Jamshidnezhad et al., 2008; Rossen et al., 2009). Injection could be from two intervals in a single vertical well, or from two parallel, horizontal wells. Here for illustration we consider injection from two intervals of a single vertical well into a horizontal, cylindrical, homogeneous reservoir. Stone (2004(a)) and Rossen et al. (2009) showed that this process gives better sweep efficiency than simultaneous co-injection from the same location when the comparison is made at fixed injection rate. Rossen et al. further showed that, if injection pressure is fixed, the advantage of water-above-gas injection can be greatly increased by the increase in injectivity over co-injection. Water-above-gas injection gives greater injectivity because gas and water are injected from separate locations, into regions at high saturation and large relative permeability of the injected phase. The previous study of Rossen et al. (2009) showed only one example, with foam, and suffered from poor grid resolution near the injection well. Here we investigate the advantages of this process in increased injectivity with simulations with greater refinement near the injection well.

In the literature, "SWAG" can mean either simultaneous injection of gas and water from the same interval in a single well, or the recent proposal of Stone, i.e. simultaneous injection of water from a location higher in the formation than gas. Here, to distinguish these two processes, we refer to the first as "co-injection," and to the second as "water above gas."

Fluid and Reservoir Model In all cases we use the STARS simulator (Computer Modeling Group, Calgary, Alberta, Canada). This section describes the models used in the study of WAG; the model used for the study of injection of water above gas is described at the start of the section presenting that study.

We use three sets of contrasting relative-permeability functions for examination. In all cases immobile oil is present at its residual saturation. We present these cases to illustrate the range of behavior possible, not as predictive for a particular formation. First, we choose two cases for WAG: oil-wet relative-permeability curves taken from the Miocene Kareem Formation, United Arab Emirates (Fig. 4), with a residual oil saturation of 0.29 (Core Laboratories, 1982), and water-wet relative-permeability curves taken from the I-Sand Formation, Argentina (Fig. 5), with a residual oil saturation of 0.225 (Core Laboratories, 1982; see also Treiber et al., 1972). For a third case we apply relative-permeability curves describing strong foam in a strongly water-wet formation (Figs. 6 and 7) based on those of Renkema and Rossen (2007), with a residual oil saturation of 0.15. We assume that the mobility functions shown already account for the weakening effect of residual oil on foam strength. WAG injection with foam (alternating slugs of surfactant solution and gas) is called SAG. For simplicity below we refer to these three cases as the oil-wet, water-wet, and foam cases, respectively. In all cases there is no mutual solubility between oil, water or gas.

Fig. 8 shows total relative mobility as a function of water fractional flow for the three cases. In WAG or SAG injection the near-well region comes relatively rapidly to unit fractional flow of the given phase. WAG injection in the oil-wet and water-wet cases without foam gives only a modest advantage in injectivity because total relative mobility decreases monotonically as water fractional flow increases. Still, mobility increases more with gas injection than it decreases with water injection, so some benefit is expected. With foam, the lowest relative mobility occurs with intermediate fractional flow, i.e. with foam injection rather than SAG. Both gas and water injectivity are greater than that of foam. In fact, our foam model understates the increasing in injectivity with gas injection in SAG, because in the model foam does not collapse completely even at residual water saturation (cf. Kloet et al., 2009).

In all cases we assume cylindrical geometry. In order to better resolve the near-wellbore region crucial to injectivity we employ smaller grid blocks near the injection well. For the oil-wet case we use 20 grid blocks of radial increment 0.5 m near the injection well, followed by 340 grid blocks each 1 m wide. Thus the outer radius is 350 m. For the water-wet case we use twenty 0.5-m grid blocks near the injection well followed by 290 1-m grid blocks; outer radius is 300 m. For the foam case we use 250 1-m grid blocks. In all cases we simulate a 15° sector of the full cylinder, and a reservoir height of 20 m. For 1D radial simulations there is only one grid block in the z direction, of height 20 m. For the 2D simulations, there are 20 grid blocks in the z direction, each of height 1 m. The differences in outer radius reflect our desire to resolve segregation in each case with the same injection pressure.

The first grid block, of radius 5 cm, represents the injection well itself. Within this grid block the injection well, as defined by the simulator, has radius 4 cm. The grid block has extremely large horizontal permeability (10,000 D) and zero vertical permeability, so effectively the entire grid block is the injection well. Since injection pressure varies as logarithm of wellbore radius, our 10-cm-diameter well in a 300 m cylindrical reservoir plays the same role as a 20-cm-diameter well in a 600-m cylindrical reservoir. Preventing segregation out to double the distance would require four times the injection rate, however (Eq. 2) and four times the pressure rise at the well (Eq. 3). In order to minimize the effects of pressure rise and compressibility, we work with the smaller wellbore and shorter radial distances. The production well, of radius 4 cm, is located in the outermost column of grid blocks. There was virtually no difference in pressure between that in the outermost grid blocks and that in the production well.

The reservoir has porosity 20%. The vertical and horizontal permeabilities are 100 and 1000 md, respectively. The initial reservoir pressure is 165 bar (16.5 MPa), which is also the pressure maintained at the production well. Injection pressure is set at 175 bar (17.5 MPa). The pressure difference between injection and production-well pressures is small enough that fluids are approximately incompressible.


The fluid properties (except for the effect of foam) are the same for all cases. Water viscosity is 1 cP (1 mPa s) and gas (supercritical CO2) viscosity (set by STARS) is about 0.0155 cP at reservoir conditions. Water density is 1000 kg/m3 and gas density is approximately 660 kg/m3 in the range of pressures present in our reservoirs. Liquid compressibility is set to zero while gas density, viscosity, and compressibility are determined by simulator. In cases of foam injection we allow sufficient injection for surfactant to propagate to the outer boundaries of the reservoir; thus surfactant adsorption is not an issue in these simulations.

Reservoir and fluid properties are summarized in Table 1. In this study we use fixed injection pressure for both co-injection and WAG. A valid comparison requires similar water-gas

ratio (WGR) in both cases: in our study, we sought WGR ~ 1:2. For injection rates set at standard conditions, this corresponds to a gas fraction of 0.99848, which was set for all co-injection cases. For a WAG process with fixed injection pressure, trial-and-error adjustment of injection periods is required to set water-gas ratio as desired. So, for example, in the 1D water-wet case, with cycle size 0.008 PV, gas is injected for 3 days and water is injected for 10 days, both at the same fixed injection pressure. The WGR for these slug sizes is 1:1.8. As slug size varies among our cases, the value of WGR varies in a narrow interval around the desired value of 1:2. Table 2 shows the variation of WGR in 1D simulations of WAG injection at different slug size for all relative-permeability curves. Variations were similar in the 2D simulations. We allowed variations in slug ratios from 1:1.8 to 1:2.2.

Determining Rg

In numerical simulation of co-injection processes, the position of complete segregation of gas and water, Rg, is obscured by numerical dispersion (cf. Fig. 43 below): the sharp boundary between the mixed and underride zone is smeared into a gradual transition over many grid blocks (Rossen et al., 2009; Stolwijk and Rossen, 2009). In particular, the value of Rg is overestimated if one takes the furthest advance of mobile gas (Sg ≥ Sgr) as the boundary of the mixed zone. Stolwijk and Rossen (2009) recommended using a gas saturation corresponding to a gas fractional flow fg a bit larger than zero as the criterion of the mixed zone, and noted that this still gives an overestimate of the value of Rg. We examined three criteria in our simulations: fg equal to 90% of the injected value, fg half of the injected value, and fg equal to 10% of the injected value. We found using a cutoff of fg equal to 50% of the injected value gives the closest match to the analytical result for co-injection (Eq. 2) for all cases examined. For example, in the oil-wet case with co-injection, using a cutoff of fg = 90%, 50% and 10% of the injected value gives Rg = 135, 123, and 111 m, respectively, while the analytical result (Eq. 2) is 120 m. In the water-wet case the three cutoffs give, respectively, 140, 125 and 113 m, compared to the analytical result of 121 m. For foam injection the three cutoffs give 134, 131 and 129 m, compared to the analytical result of 132 m. In Figs. 22 ff., the cutoff in water saturation is set to correspond to this cutoff in fg.

In some simulations of co-injection, the mixed zone shrinks to two grid blocks at the top of the formation for some distance before finally shrinking again to one grid block (Fig. 23 below is an example). In these cases, we extrapolate the trend of the boundary of the mixed zone through the second row of grid blocks. Thus, for example, in Fig. 23 we estimate Rg = 136 m rather than 144 m.

In WAG processes, the mixed zone advances and recedes with the cyclic injection of gas and water. We therefore report the furthest and shortest advance of gas after extrapolation using the same cutoffs as for co-injection for the same cases. As a second measure of gas sweep, we report the maximum and minimum volumes of gas in the reservoir during the cyclic injection of gas and water (cf. Kloet et al., 2009; Stolwijk and Rossen, 2009).

WAG Injectivity in 1D Stone (1982) contended that his model for co-injection applies to WAG processes as long as slugs mix in the near-well region (Fig. 2). Our goals for 1D simulations are (1) to determine how large slugs can be and still mix within the "mixed zone:" specifically, to give nearly steady water fractional flow and total mobility at the outer boundary of the mixed zone; (2) to determine the increase in injectivity with WAG over co-injection. Both criteria depend on slug size as a fraction of the volume contained within 0 < r ≤ Rg.

In each case we start with a reservoir filled with water and residual oil. It takes some time for injected gas to reach the outer boundary of the reservoir and for the reservoir to attain a repeating cyclic pattern. Fig. 9 illustrates behavior for the oil-wet case (Fig. 4). In this case after 81 days (0.108 PV) injection the reservoir reverts to repeated cyclic behavior. We considered cyclic behavior long after this repeating cycle was formed. In this and following figures properties are plotted for simplicity versus grid-block number rather than radial position. As a result, the near-well region is expanded in these plots.

Fig. 9 suggests that saturations and mobilities are relatively constant except for a region near the well. Fig. 10 repeats the plot of Fig. 9 at large times with an expanded time scale, to emphasize the cyclic changes in gas saturation. Fig. 11 shows total relative mobility λrt (in (Pa s)-1) during the same cycles. The color scale in Fig. 11 masks slight cyclic variation in λrt even at the outer radius. Fig. 12 shows the magnitude of cyclic variations in λrt in WAG, divided by the value for co-injection, as a function of cycle size relative to the volume of the cylindrical region. There is some scatter in the trend in this figure, as with similar figures to follow, because of the small variations of WGR between individual simulations (Table 2). Fig. 12 shows that Stone's assumption (uniform and unchanging mobility in the mixed zone) is not satisfied exactly for any WAG process with any finite cycle size. But any acceptable level of variation corresponds to a given dimensionless cycle size (volume of fluids


injected/cycle relative to pore volume of region of interest). Cycles of 5% of a pore volume, for instance, correspond to about a 10% variation in total mobility at the outer limit of the region.

Fig. 13 illustrates the variation of injectivity during WAG injection with a cycle size of 0.059 PV. Also shown for comparison is average injectivity for WAG and for co-injection. Injectivity is much greater during gas injection than in co-injection, and the average value for WAG is about 24% greater than for co-injection, though this case violates the assumption of Stone in that mobility varies by 25% at the outer radius during the WAG cycles (Fig. 12). Fig. 14 compares average injectivity for WAG to that for co-injection as a function of cycle size. The benefits of increased injectivity increase with increasing cycle size, though the violation of Stone's assumption of uniform and unchanging mobilities (Fig. 12) also increases. About a 12% increase in injectivity is possible with small cycles that substantially satisfy Stone's assumption.

Figs. 15 and 16 correspond to Figs. 12 and 14, but for the water-wet relative-permeability curves (Fig. 5). As with the oil-wet relative-permeability curves, about a 13% increase in injectivity is possible with small slugs that satisfy the condition of uniform mobility far from the well, increasing to about a 30% increase with larger slugs sizes.

Figs. 17 and 18 show the corresponding results for SAG (foam) injection. The range of slugs sizes is smaller than in the previous two cases, but there appears relatively little benefit to injectivity from increasing slug size further (Fig. 18), while the variation of mobility far form the well increases (Fig. 17). About a 150% increase in injectivity is possible in a SAG process over steady foam injection, even for small slug sizes that satisfy Stone's assumption of uniform and unchanging mobility far from the injection well. Fig. 19 compares the variation of injectivity with time for SAG injection with the average injectivity for SAG and steady foam injection. In this case injectivity of the water slug in SAG is greater than for co-injection, because of the severe reduction in mobility at intermediate water fractions with foam (Fig. 8). There is a brief period of low injectivity at the start of injection of gas or water, as that phase displaces the other phase from the near-wellbore region.

Summary of Cases in 1D

In the two cases without foam modest increases in injectivity are possible, from about 12% with slugs small enough to satisfy Stone's criterion to about 30% with slugs large enough to cause significant variations of mobility at the outer edge of the region of interest. For the foam case the benefit of SAG injection over steady foam injection is greater, about 50% for small slugs and almost 150% for larger slugs. One expects (Eq. 2) that the increase in average injectivity would help in fighting gravity segregation. We test this supposition with 2D simulations as described in the next section.

WAG Injectivity and Gravity Segregation in 2D With fixed injection pressure WAG injection differs from co-injection of gas and water in three ways:

1. Injected water fraction varies with time 2. Injection rate varies with time (cf. Figs. 13 and 19) 3. Average injection rate is larger (Figs. 14, 16, and 18).

Eq. 2 predicts a benefit from larger average injection rate. Varying water fractional flow near the well not only gives a larger average injection rate, but, at times, larger pressure gradients further from the well, where most gravity segregation occurs (Fig. 3; see also Shan and Rossen (2004)). Fig. 20 shows pressure distribution at the end of water injection in the water-wet formation for a cycle size of 0.106 PV. Injection pressure is largely dissipated near the wellbore. Fig. 21 shows pressure distribution at the end of gas injection in the same WAG process. With small slugs, saturations and mobility are nearly uniform and constant far from the well, but that region does experience a variation of horizontal pressure gradient brought on by the variation of injection rate (Figs. 13 and 19).

Rg is not constant in a WAG or SAG process. Here we report the values of Rg at the end of injection of gas and liquid slugs in the WAG. We find that this corresponds roughly to the minimum and maximum values of Rg, respectively. For relatively small cycle sizes the two values are similar. For large slugs the maximum value may be ambiguous because there is no longer a recognizable mixed zone. We show examples below. As a second measure, we report maximum and minimum volumes of gas in the reservoir. Cycle size, in fraction of PV, is based on the pore volume of the cylindrical reservoir in each case. Since this varies from case to case, cycle size should be considered only for comparison within individual cases.

Fig. 22 shows the mixed zone for co-injection in the water-wet reservoir: Rg = 125 m. In this and following figures we use a cutoff of the water saturation corresponding to 50% of the injected gas fractional flow, to highlight the boundary of the mixed zone. With small slug size, 0.001 PV/cycle, the maximum and minimum values of Rg (Figs. 23 and 24) are 138 and 136 m, respectively. The difference between maximum and minimum values of Rg in WAG is small (only two grid blocks), but the difference with co-injection is significant, representing about a 20% increase in volume swept.

Figs. 25 and 26 show the results with a cycle size of 0.034 PV: Rg = 200 and 225 m after gas injection and water injection, respectively. The larger value is perhaps a little misleading, because it represents gas about to enter the override zone rather than a large mixed zone. Nonetheless, it does represent additional formation swept by gas. Fig. 27 shows the maximum and minimum values of Rg as a function of WAG cycle size for the water-wet case. Rg increases by 12% to 14% for the smallest cycle shown (0.001 PV) and by a factor of over 2.4 for the largest cycle (0.106 PV). No maximum value is shown for the largest cycle injected because segregation occurs beyond the production well at 300 m. Fig. 28 shows the minimum and maximum amount of gas present in the reservoir, as a function of cycle size. The maximum gas volume in place increases greatly as cycle size increases, while the minimum also increase modestly. The smallest WAG cycle size tested gives an


increase in gas in place of 19% to 22%, and the largest cycle size an increase by a factor of 1.88 to 4.31 over co-injection, in agreement with the trend in Rg.

Fig. 29 shows the variation of injection rate for each phase as cycle size increases for WAG injection. Figs. 30, 31, and 32 corresponding to Figs. 27, 28, and 29, respectively for the oil-wet relative case. The smallest cycle size

shown in Fig. 30 (0.002 PV) gives an increase of 8% to 10% in Rg, and the largest cycle size (0.196 PV) gives an increase by a factor of 2.67 to 2.75. In terms of volume of gas in the reservoir, the smallest cycle size gives an increase 44% to 48% and the largest cycle an increase by a factor of 2.2 to 6.1.

It remains to distinguish the relative roles of the three differences between co-injection and WAG listed at the start of this section - increasing average injection rate, varying injection rate, and varying injected water fraction - in the increased sweep efficiency in WAG. We take as a base case WAG injection with cycle size of 0.008 PV in the water-wet reservoir, for which the maximum and minimum values of Rg 143 and 140 m; for co-injection in the water-wet reservoir at fixed injection pressure, Rg = 121 m. Fig. 33 shows sweep with co-injection at fixed WGR but the larger average injection rate that is possible with WAG. Rg is 140 m, greater than the value for co-injection at fixed pressure but less than the maximum value for WAG at fixed pressure. This larger injection rate would be impossible at fixed WGR and fixed injection pressure of 17.5 MPa; the case merely illustrates the advantage of WAG in making a greater average injection rate possible at fixed injection pressure.

To isolate the effect of varying injection rate, we inject at fixed WGR using the injection-rate history of the WAG: that is, injection rates that vary by about a factor of three, as they do in WAG at fixed injection pressure, but with fixed WGR throughout. Figs. 34 and 35 show the maximum and minimum values of Rg, 148 m and 141 m. Injection pressure during injection at the higher rate (18.8 MPa) substantially exceeds 17.5 MPa; this case illustrates the benefit of WAG in allowing periods of high injection rate at fixed injection pressure. This result outperforms all the other cases. This suggests that the benefits of WAG in overcoming gravity segregation arise from raising average injection rate (difference 3 listed above) and allowing periods of even higher injection rate (difference 2); varying injected water fraction (difference 1) makes this possible at fixed injection pressure, but by itself variable injected water fraction is harmful to sweep efficiency. The best case, hypothetically, would involve the benefits of increased injectivity but maintain constant WGR.

Fig. 36 shows the mixed zone during steady foam injection; Rg = 132 m. Fig. 37 shows water saturation with SAG with 0.002 PV/cycle, at the end of gas injection; the profile is very similar at the end of water injection. Rg is 178 m, an increase of 38% in Rg, implying a 90% increase in volume swept. Rg is larger with larger cycle size. Fig. 38 and 39 show results for 0.034 PV/cycle, with Rg = 233 m. Fig. 40 shows Rg as a function of cycle size for SAG. The smallest SAG slug size shown gives an Rg 38% larger than co-injection, and the biggest slug size gives Rg 81% larger than steady foam injection. Fig. 41 shows the maximum and minimum volumes of gas in the reservoir as a function of cycle size. For the smallest cycle size shown (0.002 PV) the volume of gas in the reservoir is 88% larger than for steady foam injection; for the largest cycle shown (0.034 PV) gas in place increases by a factor of 3.19 to 3.34. Fig. 42 shows how injection rates vary with cycle size in the SAG process.

Eq. 3 purports to relate segregation distance to injection pressure for co-injection processes regardless of the mobility of injected fluids (Rossen et al., 2009). In our cases, Rg for co-injection is about 125 m and 123m for the water wet and oil wet cases without foam (Figs. 27 and 29) and 132 m for foam (Figs. 36 and 40). This is remarkably good agreement with theory, given that foam mobility about two orders of magnitude lower in the mixed zone in SAG than mobility in the WAG processes (Fig. 8).

Injection of Water Above Gas Reservoir and Fluids Models

Again we used the STARS simulator. The reservoir grid in this case is cylindrical (360°), with 50 grid blocks in the horizontal direction and 100 in the vertical direction. In the horizontal direction the increment in radial distance per grid block is either 0.2 m or 4 m, giving reservoirs 10 m or 200 m in diameter. In all cases grid blocks are 0.2 m tall, giving a reservoir 20 m thick. Porosity is 0.25 and horizontal and vertical permeabilities are 100 and 50 md, respectively. The injection well is in the center of the first grid block, with radius 10 cm. The outer grid block, with the production well, has very large horizontal permeability but virtually zero vertical permeability, giving in effect an open outer boundary at the outer edge of the 49th grid block (at 9.8 and 196 m, respectively).

Reservoir temperature is assumed uniform at 40°C, and pressure at the open outer boundary constant at 13.8 MPa. As above, water density is 1000 kg/m3, and water viscosity 1 cP. "Gas" (supercritical CO2) density and viscosity are calculated by the simulator, but are around 680 kg/m3 and 0.0151 cP at 13.8 MPa. As with the study of WAG, we focus on steady state, after mobile oil is produced. There is a 0.29 saturation of immobile oil throughout the reservoir. We use the oil-wet relative permeabilities illustrated in Fig. 4.

Unlike the study of WAG, here we use fixed injection rates. In all cases, water is injected at a rate of 180 m3/d at 13.8 MPa. Gas is injected at 74,000 stnd m3/d, which represents 174 m3/d at 13.8 MPa. Thus the nominal injected WGR at reservoir conditions is about 1:1. We choose these injection rates in order to observe gravity segregation with co-injection roughly midway between the injection well and the outer reservoir radius when the outer radius is 200 m. For cases of injection of water above gas, water was injected from the top 95 grid blocks of the vertical well and gas from the bottom 5 grid blocks.

We use the simulations of the region within 10 m of the injection well to better resolve injectivity than possible in the case with 200-m outer radius. Therefore, in the smaller-scale study, the pressure of the production well, 10 m from the well, is set at the steady-state pressure in the third column of grid blocks from the well (specifically the grid block in the middle of this


column) in the case with 200-m radius, which corresponds a position to 10 m from the well. The injection pressure with the 10-m radius then effectively represents the injection pressure in the larger reservoir, with better resolution near the well.

Fig. 43 shows water saturation at steady state for co-injection in the 200-m reservoir. For comparison Fig. 43 also shows the same plot using the cutoff in water saturation used in the WAG study with the same relative-permeability curves. Using this cutoff, complete segregation occurs at about 92 m. The pressure at the injection well is 15.7 MPa in this simulation. The pressure in the third grid block (10 m) from the well does not vary much with vertical position, and is about 15.0 MPa. With the refined grid (0.2-m grid blocks out to a radius of 9.8 m), and the outer pressure set at 15.0 MPa, the injection-well pressure is 16.8 MPa. Compared to the large variation of pressure radially, there is little variation of pressure vertically in this case.

Fig. 44 shows water saturation at steady state for injection of water above gas in this 200-m reservoir. At the same fixed injection rate, the underride zone begins at a greater distance than with co-injection at the same injection rate, as predicted by theory (Rossen et al., 2009): at about 112 m. However, it is clear that gas here sweeps not an entire "mixed zone" but misses a region toward the top near the injection well. Theory (Rossen et al., 2009) predicts that at steady state there is a zone near the injection well toward the top which is not swept by gas, which is quite large in this case. The best injection strategy would then be to inject gas and water and smaller rates initially, to sweep the near-well region, and then at increasing rates to sweep the zone out to that shown in Fig. 44. The injection-well pressure in this case is 15.2 MPa, and the pressure in the third grid block, 10 m from the injection well, is 14.7 MPa. For simulation of the near-well region we therefore set pressure at the outer radius at 14.7 MPa. Fig. 45 shows pressure distribution in the near-well region. In spite of the much-longer injection interval for water, the water-well pressure is significantly greater than the gas-well pressure. If the water-injection interval were further lengthened, the water-well pressure would not be reduced much, though with a sufficiently small injection interval the gas-well pressure could be increased toward the same value as that of the water well. Therefore, the estimate of the injection pressure from this simulation, 16.4 MPa, is close to the optimal value that could be attained by adjusting water- and gas-injection intervals. The rise in injection pressure above reservoir pressure is about 15% lower with injection of water above gas than with co-injection.

The modest increase injectivity in this example is far less than that estimated before (about a factor of three: Rossen et al., 2009) with foam. Fig. 8 provides the explanation: the difference between mobility with co-injection and single-phase injection is much greater with foam than within normal water-gas flow. This study represents the first extension to water-gas injection without foam, and with better resolution near the injection well. It suggests that the benefits for injectivity with injection of water above gas are much less with normal gas-water flow than with foam. Conclusions 1. The model for gravity segregation in gas EOR proposed by Stone (1982) and Jenkins (1984) applies to processes with

fixed injection rate as long as slugs mix in the near-well region and mobility is uniform further from the well, where most gravity segregation occurs. As extended by Rossen and Shen (2007) to cases with fixed injection pressure, the model is pessimistic for WAG processes because it underestimates injectivity and therefore injection rate.

2. Studies of WAG and SAG foam processes in 1D radial flow show that it is possible to satisfy the criteria of nearly uniform and constant mobility far from the well with sufficiently small slug sizes. With slugs that satisfy this criterion, injectivity is 10 to 30% greater than co-injection for WAG and 50-150% greater for foam in the cases examined. The largest increases in injectivity are for slug sizes that violate the assumption of uniform and constant mobility far from the well. The increase in injectivity is a result of creating a region near the well of single-phase phase flow during WAG.

3. Studies in 2D radial flow confirm the benefits predicted from the 1D study. In the two WAG examples examined, increases in volume swept of 19 to 22% and 44 to 48% are possible with small slugs, and increases by a factor of 1.9 to 4.3 or 2.2 to 6.1 with larger slugs. For the foam case, even small slugs give an increase by a factor of about 3.3 in volume swept.

4. Injection of water and gas from separate intervals of a vertical well, with water injection above gas, gives a modest increase in injectivity over co-injection - about 15% in the case examined. This is far smaller than the advantage estimated for a foam case in a separate study. As in the WAG and SAG cases presented here, there is a greater benefit from separate injection of water and gas in foam EOR than without foam, because of the large reduction in mobility with foam when gas and water flow together.

Nomenclature fg = gas fractional flow g = gravitational acceleration H = height of reservoir kz, kh = vertical and horizontal absolute permeability, respectively L = length of rectangular reservoir Lg = distance to point of segregation in rectangular reservoir p(Rg) = pressure at radial position Rg p(Rw) = pressure at injection well Q = total volumetric injection rate of both phases r = radial position in cylindrical reservoir


Rw = radius of wellbore in cylindrical reservoir Rg = radial distance to point of complete segregation in cylindrical reservoir Sw = water saturation W = width of rectangular reservoir in direction perpendicular to flow WGR = water-gas ratio z = vertical position in reservoir Greek Symbols λrt

m = total relative mobility in mixed zone ρw, ρg = density of water and gas, respectively

Acknowledgements We thank the Computer Modeling Group for use of the simulator STARS, and in particular Adel Hammouda help with its implementation. We thanks Core Laboratories, Inc., for permission to use the oil-wet and water-wet relative permeability curves from their instructional materials.

References Christensen, J.R., Stenby, E.H., Skauge, A.: "Review of WAG Field Experience," SPE 39883, proceedings from the SPE International

Petroleum Conference and Exhibition of Mexico held in Villahermose , Mexico , 3-5 March 1998. Core Laboratories Inc.: “A course in Special Core Analysis,” Dallas, Texas, 1982. Jamshidnezhad, M., et al.: "Well Stimulation and Gravity Segregation in Gas Improved Oil Recovery," SPE 112375, presented at the SPE

Formation Damage Symposium, Lafayette, LA, 13-15 Feb. 2008; SPE Journal, in press (2009). Jamshidnezhad, M., van der Bol, L., and Rossen W. R.: "Injection of Water above Gas for Improved Sweep in Gas IOR: Performance in

3D," paper IPTC 12556 presented at the International Petroleum Technology Conference, Kuala Lumpur, Malaysia, 3–5 December 2008.

Jenkins, M. K., 1984: "An Analytical Model for Water/Gas Miscible Displacements," SPE 12632, presented at the SPE/DOE Symposium on Enhanced Oil Recovery, Tulsa, OK, April 15-18, 1984.

Kloet, M. B., Renkema, W. J., and Rossen, W. R., "Optimal Design Criteria for SAG Foam Processes in Heterogeneous Reservoirs," SPE 121581 presented at the SPE EUROPEC/EAGE Annual Conference and Exhibition, Amsterdam, The Netherlands, 8–11 June 2009.

LaForce, T. L., and Orr, F. M.: " Four-Component Gas/Water/Oil Displacements in One Dimension: Part III, Development of Miscibility," Transport Porous Media, in press (2009).

Lake, L. W.: Enhanced Oil Recovery, Prentice Hall, Englewood Cliffs, NJ (1989). Renkema, W. J., and Rossen, W. R.: "Success of SAG Foam Processes in Heterogeneous Reservoirs," SPE 110408, presented at the SPE

Annual Technical Conference and Exhibition held in Anaheim, California, U.S.A., 11–14 November 2007. Rossen, W. R., van Duijn, C. J., Nguyen, Q. P., Shen, C., and Vikingstad, A. K., "Injection Strategies to Overcome Gravity Segregation in

Simultaneous Gas and Liquid Injection Into Homogeneous Reservoirs," SPE 99794 presented at the 2006 SPE/DOE Symposium on Improved Oil Recovery, Tulsa, OK, 22-26 April, 2006; SPE Journal, in press (2009).

Rossen, W. R., and Shen, C., "Gravity Segregation in Gas-Injection IOR," SPE 107262, presented at the SPE Europec/EAGE Annual Conference and Exhibition, London, 11–14 June 2007.

Rossen, W. R., and van Duijn, C. J., "Gravity Segregation in Steady-State Horizontal Flow in Homogeneous Reservoirs," J. Petr. Sci. Eng. 43, 99-111 (2004).

Sanchez, N. L.: “Management of Water Alternating Gas (WAG) Injection Projects,” SPE 53714 prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Caracas, Venezuela, 21–23 April 1999.

Shan, D. and Rossen, W.R., “Optimal Injection Strategies for Foam IOR,” SPE Journal 9 (June 2004), 132-150. Stolwijk, G. H., and Rossen, W. R.: "Gravity Segregation in Gas IOR in Heterogeneous Reservoirs," presented at the 15th European

Symposium on Improved Oil Recovery, Paris, France, 27 – 29 April 2009. Stone, H. L.: "Vertical Conformance in an Alternating Water-Miscible Gas Flood," SPE 11130, presented at the SPE Annual Tech. Conf.

and Exhibition, New Orleans, LA, 26-29 Sept. 26-29 1982. Stone, H. L.: "A Simultaneous Water and Gas Flood Design with Extraordinary Vertical Gas Sweep," SPE paper 91724, presented at the

2004(a) SPE International Petroleum Conference, Puebla, Mexico, 7-9 November, 2004(a). Stone, H. L.: USA Provisional Patent no. 60/469,700; International Patent Application no. PCT/US 2004/014519, 2004(b). Treiber, L. E., Archer, D. L., Owens, W. W.: "A Laboratory Evaluation of the Wettability of Fifty Oil-Producing Reservoirs," SPE Journal

(Dec. 1972), 531-540.


Table 1. Reservoir and fluid properties used in this study

Oil-Wet Case Reservoir properties Reservoir size (r, θ, z) 350 m, 15°, 20 m 1D Number of grid blocks 361 × 1 × 1 2D Number of grid blocks 361 × 1 × 20 Swi 0.71 Sgi 0 Soi 0.29 Water-Wet Case Reservoir properties Reservoir size (r, θ, z) 300 m, 15°, 20 m 1D Number of grid blocks 311 × 1 × 1 2D Number of grid blocks 311 × 1 × 20 Swi 0.775 Sgi 0 Soi 0.225 Foam-Case Reservoir properties Reservoir size (r, θ, z) 250 m, 15°, 20 m 1D Number of grid blocks 251 × 1 × 1 2D Number of grid blocks 251 × 1 × 20 Swi 0.85 Sgi 0 Soi 0.15 Horizontal permeability 1000 mD Vertical permeability 100 mD Porosity 20% Fluid properties Water viscosity 1 cP Gas viscosity 0.0155 cP Water density 1000 kg/m3 Gas density 660 kg/m3 Initial condition Reservoir pressure 165 bar (16.5 MPa) Reservoir temperature 50°C Injection pressure 175 bar (17.5 MPa) Wellbore radius 0.04 m

Table 2. The variation of WGR in WAG injection (1D Simulations)

Oil Wet Water Wet Foam

Slug size WGR Slug size WGR Slug size WGR 0.002 1 : 2 0.001 1 : 1.9 0.002 1 : 2.2 0.004 1 : 1.9 0.008 1 : 1.8 0.003 1 : 2 0.014 1 : 1.9 0.022 1 : 1.9 0.007 1 : 2 0.059 1 : 2.1 0.034 1 : 2 0.015 1 : 2.1 0.196 1 : 2.1 0.106 1 : 2.1 0.034 1 : 2.2


Fig. 1. Schematic of three uniform zones in model of Stone (1982) and Jenkins (1984).

gas

or w

ater

(alte

rnat

ing)

slugs mix; non-

uniform satura-tions

uniform saturations

gas

or w

ater

(alte

rnat

ing)

slugs mix; non-

uniform satura-tions

uniform saturations

Fig. 2. Schematic of assumption of Stone (1982) and Jenkins (1982) that mixing of slugs in a WAG process occurs in a region near the well that is small compared to the region in which gravity segregation occurs.

00.10.20.30.40.50.60.70.80.9

1

0.1 1 10 100 1000r

frac

tion

of p

ress

ure

diss

ipat

ed

or fr

actio

n of

gra

vity

seg

rega

tion

achi

eved

Fig. 3. Fraction of injection pressure dissipated and fraction of injected fluids lost from mixed zone as functions of distance from injection well, in a case where Rg = 500 m. The two curves for fraction of injection pressure dissipated reflect different assumptions about the shape of the mixed zone (Rossen and Shen, 2004; Jamshidnezhad et al., 2009). From Jamshidnezhad et al. (2009).

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Water saturation

Rel

ativ

e pe

rmea

bilit

y

krwkrow

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Liquid saturation

Rel

ativ

e pe

rmea

bilit

y

krgkrog

Fig. 4. Relative-permeability curves from the oil-wet Miocene Kareem Formation, UAE (Core Laboratories,1982).


0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Water saturation

Rel

ativ

e pe

rmea

bilit

y

krwkrow

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

Liquid saturation

Rel

ativ

e pe

rmea

bilit

y

krgkrog

Fig. 5. Relative-permeability curves from the water-wet I-Sand Formation, Argentina (Core Laboratories,1982).

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

Water saturation

Rel

ativ

e pe

rmea

bilit

y

krwkrg

Fig. 6. Relative-permeability curves used to describe foam flow, from Renkema and Rossen (2007). Effective gas relative permeability here accounts for all effects of foam on gas mobility. Foam greatly reduces gas mobility for water saturations above a threshold value, which here is 0.36. An immobile oil saturation of 0.15 is assumed in this plot.

0.00001

0.0001

0.001

0.01

0.1

1

0 0.2 0.4 0.6 0.8 1

Water saturation

Rel

ativ

e pe

rmea

bilit

y

krwkrg

Fig. 7. Gas-water relative-permeability functions used to describe foam flow, from Renkema and Rossen (2007). Note shift to log scale for relative permeabilities. An immobile oil saturation of 0.15 is assumed in this plot.


1

10

100

1,000

10,000

100,000

0 0.2 0.4 0.6 0.8 1

Water fractional flow

Tota

l rel

ativ

e m

obili

ty (1

/Pa

s)

Oil WetWater wetFoam

Fig. 8. Total relative mobility (1/Pa s) as a function of water fractional flow for each of the three sets of relative-permeability curves in Figs. 4 to 7. In both oil-wet and water-wet cases total relative mobility decreases monotonically with increasing water fraction. For foam, the lowest total relative mobility occurs at intermediate water fraction. The WAG simulations in this study correspond to average injected water fraction about 0.33; the study of injection of water above gas to a water fraction about 0.5.

Fig. 9. Gas saturation as a function of position (grid block number) and time for the case of oil-wet relative permeabilities. In this case a cycle of gas and water injection represents 0.004 PV.

Fig. 10. Gas saturation as a function of location and time for WAG injection, oil-wet case, after reaching steadily repeating behavior, for cycles of 0.004 PV. This figure represents Fig. 9 with an expanded time scale.


Fig. 11. Total relative mobility (1/Pa s) as a function of location and time for WAG injection, oil-wet case, with cycles of 0.004 PV, at long times; cf. Fig. 10.

0.001

0.01

0.1

1

10

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21

Cycle size PVinj

Fluc

tuat

ion

Fig. 12. Fluctuations in total relative mobility at the outer radius of the 1D reservoir, as a fraction of the value of total relative mobility for co-injection, as a function of cycle size for WAG processes in the oil-wet reservoir. Co-injection corresponds to zero fluctuation at vanishing slug size.

Fig. 13. Injectivity during cyclic WAG injection into the oil-wet reservoir, with 29 days water injection and 10 days gas injection (0.059 PV/cycle). The red line is average injectivity of the WAG process; the blue line, injectivity for co-injection. The WAG process shows an increase in average injectivity by a factor of 1.24 over co-injection.


0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21

Cycle size PVinj

Inje

ctiv

ity (m

3 /d/b

ar)

Fig. 14. Average injectivity in WAG injection as a function of cycle size in the oil-wet reservoir.

0.001

0.01

0.1

1

10

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Cycle size PVinj

Fluc

tuat

ion

Fig. 15. Fluctuations in total relative mobility at the outer radius of the 1D reservoir, as a fraction of the value of total relative mobility for co-injection, as a function of cycle size for WAG processes in the water-wet reservoir. Co-injection corresponds to zero fluctuation at vanishing slug size.

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

0.25

0.26

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Cycle size PVinj

Inje

ctiv

ity (m

3 /d/b

ar)

Fig. 16. Average injectivity in WAG injection as a function of cycle size in the water-wet reservoir.


0.00001

0.0001

0.001

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Cycle size PVinj

Fluc

tuat

ion

Fig. 17. Fluctuations in total relative mobility, at the outer radius of the 1D reservoir, as a fraction of the value of total relative mobility for co-injection, as a function of cycle size for SAG (foam) processes. Co-injection corresponds to zero fluctuation at vanishing slug size.

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Cycle size PVinj

Inje

ctiv

ity (m

3 /d/b

ar)

Fig. 18. Average injectivity in WAG injection as a function of SAG cycle size in the foam case.

Fig. 19. Injectivity during SAG injection (40 days water injection and 60 days gas injection; total cycle size 0.015 PV) after steady, repeating pattern is attained, and steady injection of foam in 1D reservoir. The SAG process shows an increase in average injectivity by a factor of 2.13 over steady injection of foam.


Fig. 20. Pressure distribution (kPa) at the end of water injection, cycle size 0.106 PV, water-wet reservoir. Pressure is largely dissipated near the wellbore.

Fig. 21. Pressure distribution (kPa) at the end of gas injection, cycle size 0.106 PV, water-wet reservoir. Injection pressure is dissipated over wider portion of the reservoir than in co-injection (Fig. 20).

Fig. 22. Water-saturation profile for co-injection in water-wet reservoir; Rg = 125 m.


Fig. 23. Water saturation at the end of gas injection in WAG in water-wet reservoir with cycle size of 0.001 PV; Rg = 136 m.

Fig. 24. Water saturation at the end of water injection in WAG in water-wet reservoir with cycle size of 0.001 PV; Rg = 138 m.




0

50

100

150

200

250

300

350

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Cycle size PVinj

Rg (m

)WAG max RgWAG min Rgco-injection Rg

Fig. 27. Maximum and minimum values of Rg as a function of WAG cycle size in water-wet reservoir. No maximum Rg is shown because segregation happens beyond the production well at 300 m.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Cycle size PVinj

Volu

me

swep

t (M

M m

3 )

WAG max volumeWAG min volumeco-injection volume

Fig. 28. Maximum and minimum volume of gas in reservoir as function of WAG cycle size in 2D water-wet case.

0

20

40

60

80

100

120

140

160

0.00 0.02 0.04 0.06 0.08 0.10 0.12

Cycle size PVinj

Rat

e (m

3 /d) co-injection water rate

co-injection gas rateco-injection total rateWAG water rateWAG gas rate

Fig. 29. Maximum and minimum injection rate as a function of WAG cycle size in 2D water-wet case.


0

50

100

150

200

250

300

350

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21

Cycle size PVinj

Rg (m

)

WAG max RgWAG min Rgco-injection Rg

Fig. 30. Maximum and minimum values of Rg as a function of WAG cycle size in oil-wet case.

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21

Cycle size PVinj

Volu

me

swep

t (M

M m

3 )

WAG max volumeWAG min volumeco-injection volume

Fig. 31. Maximum and minimum volume of gas in reservoir as function of WAG cycle size in 2D oil-wet case.

0

50

100

150

200

250

300

350

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21

Cycle size PVinj

Rat

e (m

3 /d) co-injection water rate

co-injection gas rateco-injection total rateWAG water rateWAG gas rate

Fig. 32. Maximum and minimum injection rate as a function of WAG cycle size in 2D oil-wet case.


Fig. 33. Water-saturation profile in co-injection process (fixed WGR) using constant injection rate set to the average injection rate of WAG with 0.008 PV cycle: Rg = 140 m.

Fig. 34. Water-saturation profile showing minimum Rg = 141 m in co-injection process using injection-rate history of WAG with 0.008 PV cycle and fixed water fractional flow.

Fig. 35. Water-saturation profile showing maximum Rg = 148 m in co-injection process using injection-rate history of WAG with 0.008 PV cycle and fixed water fractional flow.


Fig. 36. Water-saturation profile for co-injection of foam; Rg = 132 m.

Fig. 37. Water saturation at the end of gas injection in SAG with cycle size of 0.002 PV; Rg = 178 m. This radius of segregation is indistinguishable from that at the end of water injection.




0

50

100

150

200

250

300

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Cycle size PVinj

Rg (m

)SAG Rgsteady foam injection Rg

Fig. 40. Rg as a function of SAG cycle size in foam case. We find virtually no variation in Rg values with time for these cycle sizes.

0

0.5

1

1.5

2

2.5

3

3.5

4

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Cycle size PVinj

Volu

me

swep

t (M

M m

3 )

SAG max volumeSAG min volumesteady foam injection volume

Fig. 41. Maximum and minimum volume of gas in reservoir as function of WAG cycle size in 2D foam case.

0

1

2

3

4

5

6

7

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

Cycle size PVinj

Rat

e (m

3 /d)

steady foam injection water ratesteady foam injection gas ratesteady foam injection total rateSAG water rateSAG gas rate

Fig. 42. Maximum and minimum injection rate as a function of SAG cycle size in 2D foam case.


Fig. 43. Water-saturation distribution for co-injection for comparison with injection of water above gas. Right-hand plot uses same cutoff for water saturation as used in the WAG study with the same (oil-wet) relative-permeability curves. The mixed zone extends 92 m.

Fig. 44. Water-saturation distribution for injection of water above gas at same injection rates as in Fig. 43. Gas is injected from bottom 5 grid blocks (5% of formation interval) and water from top 95. Right-hand plot uses same cutoff for water saturation as used in the WAG study with the oil-wet relative-permeability curves. The underride zone begins at 116 m.

Fig. 45. Pressure distribution in injection of water above gas; same case as in Fig. 44, but simulation of flow within 10 m of well, with pressure at 10 m set at pressure in third column of grid blocks in Fig. 44. Note lower pressure in gas-injection interval at bottom of well.

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