SPE 115065

Scaling and Sensitivity Analysis of Gas-Oil Gravity Drainage EOR P.S. Jadhawar, SPE, and H.K. Sarma, SPE, Australian School of Petroleum, University of Adelaide

Copyright 2008, Society of Petroleum Engineers

This paper was prepared for presentation at the 2008 SPE Asia Pacific Oil & Gas Conference and Exhibition held in Perth, Australia, 2022 October 2008.

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 is one of the key enhanced oil recovery (EOR) methods. Significant volumes of the residual oil, remaining after earlier EOR methods, has been reported to be recovered through the gravity drainage mechanism, following the crestal gas injection in the horizontal, dipping or reef type oil reservoirs. The rate of oil recovery is controlled by the viscous/capillary/gravity forces, the rate of gas injection and oil production, the difference of oil and gas density, the oil relative permeability, the oil viscosity and number of other operational parameters. Risk analysis of these parameters helps to identify their relative dominance during gas-oil gravity drainage process. The interactions between various process controlling parameters is studied through development of scaling groups that govern the displacement process. Functional relationships between those scaling groups and their effect on the overall performance of immiscible gas-driven gravity drainage EOR are investigated in this study. This enables an estimation of fractional oil recovery for the combinations of scaling groups. The results of numerical sensitivity analysis through the reservoir simulations are presented to map the effective combinations of the dimensionless scaling groups for gas-oil gravity drainage EOR method. Introduction

Gas injection either in the immiscible or miscible mode (largely CO2) is the key process amongst the major contending methods of enhancing oil recovery. It can be carried out either in secondary or tertiary stage of the producing life of the reservoir in continuous mode, alternating cycles of water and gas or in gravity drainage mode. Continuous gas injection methods are largely impaired by the viscous instabilities, the severe gas-oil gravity segregation and the poor volumetric sweep efficiency. Moreover, the larger difference of the density between the injected gas and the in-situ reservoir fluid leads to severe gravity segregation effects. The cumulative effect is an uncontrolled gas flood front leading to the premature gas breakthrough in the producing wells and the unfavorable mobility ratio culminating into the severe viscous fingering. Further modifications in the injection modes could not completely eliminate these recovery impeding factors. Therefore, a method that uses the natural density based gravity segregation of the fluids to recover the bypassed oil in the unswept regions looks to be a more promising option.

Gravity forces are recognized to play an important role at nearly every stage of the producing life of the reservoir, whether it is primary depletion, secondary water or gas injection scheme or tertiary enhanced or improved oil recovery methods. They always compete with the viscous (flow rate per unit area) forces and the capillary (ratio of the fluid/fluid forces to the grain size) forces occurring in porous media in addition to the vertical barriers in the form of heterogeneity. In presence of these impeding factors less dense fluid gets trapped in the producing zone, further diminishing the oil recovery performance. Conversely, gravity forces can be taken into advantage through the gravity drainage mechanism to maximize oil recovery from the oil bearing zone under investigation. A number of investigations carried out in the laboratories and in the field (Bangla et al., 1991; Chatzis et al., 1988; Da Sle and Guo, 1990; Kulkarni and Rao, 2006) suggest the significance of the gas-oil gravity drainage process in view of the higher oil recoveries obtained in contrast to the conventional gas injection EOR methods. Gravity drainage by gas injection is commonly implemented in either dipping or pinnacle reef type reservoirs. Current study focuses on the application of the gas-assisted gravity-drainage mechanism to a horizontal type reservoir through the combination of the vertical injectors and horizontal production wells. Gas-oil gravity drainage EOR

Gravity drainage is a process in which gravity acts as a main driving force and where gas replaces voidage volume (Hagoort, 1980). Gas-oil gravity drainage is influenced by the difference of the density between the injected gas and the reservoir oil. Higher the density difference, more effective is the gravity segregation of the fluids and hence the downward

2 SPE 115065

gravity drainage of the oil. In a gas injection method based on the gravity drainage mechanism, gas is injected at the top of pay zone through the vertical or horizontal wells located at the top of the reservoir (Figure 1). The injected gas segregates to create a gas-oil interface which is then slowly displaced towards the simultaneously producing horizontal wells located at the bottom of the pay zone. During this process, the gas injection and oil production volumes are balanced precisely so that the reservoir system remains in the gravity dominated regime. This process is termed as gas assisted gravity drainage method of enhanced oil recovery (GAGD-EOR) (Jadhawar and Sarma, 2008; Rao et al., 2004).

Original GOC

WOC

Oil

Gas

Water

Controlled qo

Oil displaced down towards producer under gravity effect (density controlled flow)

CO2injectors (3)

Controlled ig

[V/ t]oil + water = [ V/ t]gas

H. Prod Wells (5) Horizontal Reservoir

BA new GOC

Figure 1: Conceptual GAGD-EOR method (Jadhawar and Sarma, 2008)

The controlled gas injection helps maintain the pressure on the advancing gas floodfront, so the oil column and the reservoir. This keeps the solution gas saturation sufficiently low thereby minimizing its liberation from the oil. The oil shrinkage is prevented and thus the oil viscosity remains at lower values. This further aids in the overall effectiveness of the gas-oil gravity drainage mechanism. Additionally, the gas injection and maintained reservoir pressure recompresses some of the dispersed gas in the oil zone. The oil gets dispersed and begins to fall under gravity the countercurrent to the gas flow when the gravity force dominates the viscous force (the velocity of the remaining dispersed gas). Oil is drained from the upstructure high pressure zone under the effect of the gravity downward towards the low pressure horizontal wells. The continued injected gas injection and simultaneous controlled oil production moves the GOC to lower position (shown by the line AB in Figure 1) indicating that the volumes of the reservoir oil produced has come from the gravity drainage mechanism. The injected gas replaces the voidage volume created by the simultaneous oil production.

At a given production rate, higher gas injection rates may result in gas coning and viscous fingering. At a given gas injection rate, higher oil production rates can also lead to the early gas breakthrough. This gas-driven EOR can be effectively changed into the gravity-dominated flow regime thereby controlling the rate at which the gas is injected and the oil is produced. The precise control of the gas injection rate and the oil production rate is essential for the success of the GAGD-EOR method. A gas velocity at which this countercurrent gas-oil flow occurs to segregate the oil and gas, and gravity drainage to begin, largely depends on the oil and gas density, and the rates of gas injection and oil production, the balance of the gravity-capillary-viscous forces, relative saturations of the oil, water and gas, vertical permeability, heterogeneities, amount of the dip (if exists) and number of other operational parameters.

GAGD-EOR method can be classified on the basis of the mode of gas injection (secondary or tertiary after waterflooding), type of the geological structures (pinnacle reef type, dipping and horizontal reservoirs) in which it is being implemented, the pressure of gas injection (below or above minimum miscibility pressure), the type of gas injected (CO2, air, nitrogen etc.) or based on the displacement mechanisms, as suggested by Schechter and Guo, 1996, that is the controlled gravity drainage, gravity-stable low-rate gas injection and the natural gravity drainage.

In practice, the gravity drainage mechanism for oil recovery enhancement can be worked out in one or more ways at any stage of the producing life of the reservoir (Lewis, 1944). The idealistic way is to produce the reservoir at the pressures above the bubble point pressure (undersaturated) by not allowing the gas to liberate in the oil zone. The reservoir pressure is maintained above the bubble point through the gas injection. Another approach is to restore the reservoir pressure partially by gas injection in the gas cap, and then controlling the rates of the gas injection and oil production. The operating pressures of

SPE 115065 3

the injection and production wells are also constrained during the whole process. Higher oil recoveries can be obtained in this way with the occurring phenomenon of gravity segregation and gravity drainage. Last method is the gravity drainage by blowdown. Second approach is adopted in the present study.

The results obtained in the laboratory based experimental investigations or the reservoir simulation work of the GAGD-EOR method can be applicable to the field reservoir through the scaling approach (Gharbi, 2002). The multiphase parameters responsible for the gravity-drainage oil recovery if analyzed by this approach, it is possible to predict the EOR performance at the field scale. Scaling through the dimensional analysis is investigated in this study with regards to its applicability to gas assisted gravity drainage method of enhanced oil recovery (GAGD-EOR). Operational parameters are varied systematically over the ranges of values. The data of multiphase operational parameters required for the scaling studies is generated through numerical simulation runs.

Scaling Gas-Oil Gravity Drainage EOR process

Coreflood experiments on the core sample of a particular reservoir are traditionally carried out to test the most suitable oil displacement method for that reservoir. The results so obtained may not be directly applicable and reliable on the field scale. However these results if presented in the form of scaling groups, it is possible to relate them to field scale for the direct implementation. Scaling is a procedure in which the results obtained at one scale size (small scale laboratory experiments) are applicable to another scale size (a large scale process). It leads to the definition of the dimensionless numbers known as dimensionless groups, forming a basis for comparison between various scales (Buckingham, 1914; Lozada and Farouq Ali, 1987; Shook et al., 1992; Gharbi, 2002). Any scaling law or model comprising dimensionless scaling groups can be derived through the dimensional analysis (Buckingham, 1914 ; Langhaar, 1951) and the inspectional analysis (Geertsma et al., 1956); (Greenkorn, 1964); (Ruark, 1935); (Shook et al., 1992). The scaled model so developed is a more realistic way of predicting the reservoir performance through the analysis of individual parameter influence on the ultimate oil recovery. The number of parameters involved in the problem statement thus gets reduced thereby eliminating the need of conversion between the units.

Dimensionless analysis is based on the knowledge of appropriate variables influencing oil displacement. Equations that describe the process are not needed in dimensionless analysis. It is an effective scaling tool simulating analogous field scale multiphase processes into laboratory, to represent an experiment or numerical model incorporating number of the operative spatial and/or physical mechanisms. Number of parameters affecting the performance of oil reservoirs (absolute and relative permeability, fluid viscosities, initial water and oil saturations, residual oil saturation, relative oil, gas and water permeability, rock porosity, gravity/ capillary/viscous forces, dip angle, reservoir heterogeneity, interfacial tension, wettability, spreading coefficient, physical and numerical dispersions, and the mass transfer) are so combined that their dimensions (composing the dimensionless groups) cancel each other out to form a final group with no dimensions. The effect on certain variables is then studied in terms of the group instead of individual variables in the group. In case of similar geometric scales, if the ratio of the dimensionless group on a larger geometric scale to a dimensionless group on a smaller geometric scale is kept equal to one, then mechanisms occurring on both the scales would be similar (Rappaport and Leas, 1953).

Application of scaling to multiphase flow in porous medium has been studied earlier for miscible and immiscible EOR processes. Immiscible water induced oil displacement was first studied by Leverett et al. (1942) through the dimensionless scaling groups. Later Croes and Scwarz (1955) presented the influence of the oil/water viscosity ratio on immiscible displacements through a diagram representing the cumulative oil recovery for the various water-oil viscosity ratios ranging from 1 to 500. They assumed linear displacement of the oil by water in homogeneous reservoir. Scaling relationship of immiscible displacement of oil by cold water derived through inspectional analysis was presented for the first time by Rapoport (1955). This was further extended by Geertsma et al. (1956) for hot water displacement and solvent displacement and by Carpenter et al. (1962) for the homogeneous media having different permeability in the communicating strata. Effects of gravity segregation in miscible and immiscible displacements in five spot models were presented by Craig et al. (1957) through two correlations. First one accounted the ratio of vertical to horizontal pressure gradient and the oil recovery at breakthrough for various mobility ratios. Second correlation represented the relation between the experimental oil recovery and a dimensionless gravity number.

Scaling criteria presented by Perkins and Collins (1960) accounted the relative permeability and capillary pressure curves through the representation of the reservoir heterogeneity. Geostatistical and generic characterization generated heterogeneity scaling groups were derived through image representation technique by Li and Lake (1995) to scale the immiscible oil displacement by waterflooding in heterogeneous reservoirs. Gharbi et al. (1995) used an artificial neural network technique to scale the immiscible displacements in homogeneous reservoir by using vertical wells through fine mesh simulation data.

The combined effects of the gravity, viscous and capillary forces were accommodated into a new dimensionless group by Grattoni et al. (2001). They developed a linear relationship between this new group and the total recovery based on the experimental investigations to include the pore scale effects. Flow through the heterogeneous 2D anisotropic reservoir was scaled by Gharbi (2002) through the inspectional analysis to match thirteen dimensionless scaling groups for the miscible solvent flooding.

Shook et al. (2002) presented dimensionless scaling groups for the waterflood applicable to represent the two phase flow through homogeneous 2-dimensional Cartesian dipping reservoir. Kulkarni and Rao (2006) presented the effect of dimensionless groups on the final recovery based on various immiscible and nearly miscible gas assisted gravity drainage field data and laboratory experimental data. The continuous CO2 flooding in a dipping waterflooded reservoir was scaled by

4 SPE 115065

Wood et al. (2006, 2008) through ten dimensionless groups to develop a screening model based on Box-Behnken experiments. The results obtained from CMGs GEM simulator are then used to predict the oil recovery and CO2 storage potential. Trivedi and Babadagli (2008) proposed new group incorporating the matrix-fracture diffusion transfer to scale the miscible displacement in fractured porous media based on the laboratory experiments.

In this paper, the GAGD-EOR method is scaled for the first time through the dimensionless scaling groups especially using gas injection and production pressures at the respective wells and gravity number dependent on the difference of the pressure between the injection well and producing well. Identification of the important parameters that dominate during GAGD-EOR method is carried out through the risk analysis using PALISADEs @RISK software. Due to lack of experimental data, CMGs IMEX simulator is used to generate the parametric data. The dimensionless groups are then used to study the sensitivity individual parameters by varying their values. The values of the parameters are then varied so that the final dimensionless group values remain constant to validate their application to the GAGD-EOR method. Dimensionless Scaling Groups: GAGD-EOR

In this study, an immiscible gas injection is carried in the non-dipping horizontal type reservoir for enhancing the oil recovery by gravity drainage mechanism. The knowledge of parameters that may influence the overall gravity drainage oil recovery is essential while selecting the scaling groups for the sensitivity analysis. Since the GAGD-EOR method is a top-down process, higher vertical permeability is favoured for the selected reservoir candidates. As the recovery method is driven by the gravity force, it is imperative that the dimensionless groups that have the critical parameters contributing to gravity (density) should be included in the scaling. Additionally the rate of gas injection is maintained constant for a recovery operation, which contributes to the relative fluid velocities within the reservoir. Moreover the pressures of the injection wells and the producing wells have been kept constant during the entire GAGD-EOR gas injection operations. Other important parameters include the relative mobilities and viscosities of the all operational phases (oil, water and gas) and residual oil saturations of water and gas. Keeping in mind these considerations with regards to GAGD-EOR method, the scaling groups are obtained through the dimensionless analysis.

Rigorous inspectional analysis procedures carried out in the previous studies for dipping reservoirs (Gharbi et al., 1998; Shook et al., 1992) to produced dimensionless scaling groups that can be modified to implement sensitivity analysis for the horizontal type reservoir under investigation in this study. Secondary waterflooding based gravity number (ratio of the gravity to the viscous forces) from Shook et al. (2002) is dependent on the rate of the water injection. To consider the GAGD-EOR process dependent constant pressures condition of the injection wells and the production wells, and the highly compressible nature of the injectant (CO2), the gravity number is modified to make it applicable to the horizontal type reservoir. Saturation groups are included in the scaling group to study the better understanding for the quantification of the oil recovered. The following 10 dimensionless groups are used to scale the GAGD-EOR process.

h

vL k

kHLR = Effective aspect ratio ..... (1)

tanHLN = Dip angle ... (2)

oro

wrwwo k

kM

//= Mobility ratio (Water-oil) . (3)

oro

grggo k

kM

//= Mobility ratio (CO2-oil) . (4)

T

rovgI u

gkLHN = Gravity number (based on the gas injection rate) .. (5)

PgHN gP

= Gravity Number (based on the gas injection and oil production pressures) ... (6)

MM

injinjD P

PP = Injection pressure group . (7)

MM

prodprodD P

PP = Producing pressure group . (8)

SPE 115065 5

orwS Residual oil saturation to water (water-oil system) .. (9)

orgS Residual oil saturation to gas (gas-oil system) (10) GAGD-EOR performance is analyzed using the fractional oil recovery in the form of dimensionless oil recovery (RD)

curves over the dimensionless time (tD). Dimensionless recovery is the amount of the oil recovered that was available just before the start of gas injection in the GAGD-EOR stage. Values of the involved parameters are varied so that the final groups values remain unchanged. Then the sensitivity of these groups towards the changes in the operational parameters is studied using numerical simulation results from the CMGIMEX software. If the ultimate dimensionless recovery performance over the dimensionless time, represented in the form of ratio of the cumulative gas volumes injected to the pore volume, matches for the cases under consideration then the dimensionless scaling group can sufficiently scale the GAGD-EOR process.

Risk Analysis of the operational parameters

The identification of the relative dominance of the parameters operational in the gas-oil gravity drainage EOR process is carried out using PALISADEs @RISK software. Correlation based approach is adopted for this purpose. Three dimensionless groups were selected because of the availability of variable parameters within the correlation. They are gravity number (Ng), water-oil mobility ratio (Mwo) and gas-oil mobility ratio (Mgo). Monte Carlo simulations are carried over the ranges of parameters given in Table 1 through 5000 iterations. Deterministic parameters (e.g.: length, depth etc.) do not change for the process under consideration for a given reservoir settings. Probabilistic parameters are defined in two types of probability distribution function (PDF), i.e. normal and triangular. Total fluid velocity, uT (ft/d) and mobility ratio are assumed as normal PDFs represented by its mean and standard deviation. Other parameters are defined as triangular PDFs with its minimum, most likely, and maximum value (Table 1). Values of the parameters (except gravity number and mobility ratio) are based on the gas injection gravity drainage field case studies.

Table 1: Ranges of the parameters (GAGD-EOR process) values used in the risk analysis

Parameter Deterministic Probabilistic

Mean Std Dev Minimum Most Likely Maximum

H (ft) 1500 L (ft) 30000

kz (mD) 1200 100 1200 3400 ro 0.28226 0.08318

(lb/ft3) 52.8872 10 52.8872 120 g (ft/s2) 32.174 uT (ft/D) 0.00647 0.00179

krw 0.18 0.3 0.48 kro 0.35 0.7 0.85 krg 0.1 0.3 0.4

o (cP) 0.19 0.5 3.7 w (cP) 0.25 0.3647 0.58

CO2 (cP) 0.0182 0.056 0.11

The Monte Carlo simulations using the @RISK software are first carried out separately on each of the group and then

cumulatively on all the groups. The risk analysis results are presented in Figure 2 [(a), (b)] and Figure 3 [(a), (b)] in the forms of Tornado diagrams. As seen in Figure 2 (a) for gravity number, the vertical permeability is shown to have the largest impact on the gravity number followed by the density difference between the injected CO2 and oil. It is so in GAGD-EOR process because the reservoir oil is displaced downward towards the horizontal producers placed at the bottom of the pay-zone. Good vertical communication between the layers is one of the necessary conditions. Also larger the density differences between the injected fluid and the reservoir oil, the higher are the gravity segregation effects and the gravity-drainage oil displacement. Total superficial velocity (uT) of the fluids and the end point oil mobility (ro) follow kv and . Total superficial velocity contributes the viscous forces which in turn competes with the gravity forces. This is also one of the important parameters while assessing the overall gravity drainage recovery performance.

6 SPE 115065

Correlations for Ng / det/B13

Correlation Coefficients

?ro / @RISK/H8 .056

uT (ft/s) / @RISK/H11-.414

?? (lb/ft3) / @RISK/H9 .534

kv (mD) / @RISK/H7 .703

@RISK Student VersionFor Academic Use Only

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

ro

Correlations for Mwo / det/B14

Correlation Coefficients

w (cP) / @RISK/H12-.225

kro / @RISK/H9-.24

krw / @RISK/H8 .282

o (cP) / @RISK/H11 .888

@RISK Student VersionFor Academic Use Only

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

(a) (b)

Figure 2: Tornado diagram: Relative dominance of multiphase parameters in GAGD-EOR process Gravity number (Ng) (b) Mobility ratio: water-oil (Mwo)

For GAGD-EOR application to a non-dipping horizontal reservoir in this study, the vertical permeability is kept constant. Also the difference in the density between the reservoir oil and the injected fluid (CO2) changes marginally during the process due to the immiscible gas injection. Therefore, these parameters are selected as the deterministic (constant) parameters. The next critical parameters - total superficial velocity of the fluids and the end point mobility of the oil - are considered as variable parameters in the sensitivity studies.

Correlations for Mgo / det/B15

Correlation Coefficients

kro / @RISK/H9-.231

krg / @RISK/H10 .309

CO2 (cP) / @RISK/H13-.414

o (cP) / @RISK/H11 .801

@RISK Student VersionFor Academic Use Only

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

(a) (b) Correlations for Ng / det/B13

Correlation Coefficients

o (cP) / @RISK/H11 .007

krw / @RISK/H8-.007

CO2 (cP) / @RISK/H13-.008

kro / @RISK/H9-.009

w (cP) / @RISK/H12 .01

krg / @RISK/H10 .017

o (cP) / @RISK/H11-.018

kro / @RISK/H9-.018

?ro / @RISK/H8 .038

uT (ft/s) / @RISK/H11-.386

?? (lb/ft3) / @RISK/H9 .561

kz (mD) / @RISK/H7 .694

@RISK Student VersionFor Academic Use Only

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

ro

Figure 3: Tornado diagram: Relative dominance of multiphase parameters in GAGD-EOR process (a) Mobility ratio (Mgo) (b) All the operational parameters

With regard to mobility ratios (Mwo and Mgo), the oil viscosity is shown to be the most critical parameter. Mobility ratio is directly proportional to the changes in the oil viscosity (Figure 3 (a) and (b)). Therefore, its reduction is one of the important objectives for enhanced oil recovery method especially through gas (CO2) injection. Relative permeability to water and oil, followed by the water viscosity, were shown to be next critical parameters for the Mwo. For gas-oil mobility ratio, gas viscosity is shown to be the next critical parameter followed by the relative permeability of gas and oil.

SPE 115065 7

Sensitivity Analysis: GAGD-EOR In sensitivity studies, the value of each scaling group under consideration representing GAGD-EOR process is calculated.

Using data obtained in the reservoir simulations for each individually-changed parameter in each of the group, the fractional oil recovery in the form of dimensionless recovery (RD) over the dimensionless time (tD) for each of the case is obtained. The dimensionless recovery (RD) is the percentage of the available oil in place (for GAGD-EOR study) recovered after the CO2 injection whereas the dimensionless time (tD) is the ratio of the cumulative CO2 volume injected and pore volume. In all sensitivity studies, Case-II shown in Table 2 is taken as the basis for varying the parametric values in the scaling group under consideration thereby keeping the values of other scaling groups constant.

Reservoir Description

The reservoir model is a three-dimensional hypothetical system constructed using the CMGs commercial implicit explicit black oil simulator IMEX. A conventional Cartesian grid without corner point geometry or local grid refinement is used in this purpose - 50 blocks in the X-direction, 30 blocks in the Y-direction and the 10 layers in the Z-direction constitutes 15000 grid block model with dimensions 600ft, 400ft and 150ft in I, J and K-directions respectively. Cell (1,1,1) is at a depth of 8000 feet at the centre of the cell top.

The homogeneous anisotropic reservoir is based on parameters (cf. Table 1) adopted from the field data in the literature. The average reservoir porosity is 0.22% and I and J-direction permeabilities are 1200 mD with a ratio of vertical to horizontal permeabilities (Kv/Kh) of 1.0. The four-component (oil, gas, water and chase gas) pseudomiscible option with no chase gas was invoked to simulate three phase flow of fluids. The reservoir fluid used is the 35 oAPI gravity black oil with the solution gas gravity of 0.65. The PVT properties of the oil and gas were generated using correlations incorporated in the CMGs WINPROP module. The associated formation water properties namely the salinity, formation volume factor, compressibility, viscosity and the density are also simulated using WINPROP at the reference pressure of 4000 and the reference depth of 9250 psi. The solvent (CO2) properties including solution gas ratio, formation volume factor, the viscosity and the mixing parameter between the oil and solvent responsible for the miscibility were determined using the pseudomiscible option of WINPROP.

The reservoir is considered a water-wet reservoir. The respective values of the connate water saturation (0.15), the critical gas saturation (0.05) and end point saturations of oil, gas and water were assigned in the model to calculate the relative permeability values using the Stone-II model. All Corey exponents were set at 2.0. The relative permeability curves were constructed using these values. The initial reservoir temperature is 180 oF with an average reservoir pressure of 3837 psi. The saturation pressure of the reservoir oil is 3703.327 psi. The oil-water-contact (OWC) and the gas-oil-contact (GOC) are at the depths of 8450 ft and the 9150 respectively with the pay zone thickness of 700 ft. With these data the initialization of the model yields the relative in-place distribution of oil, water and gas of 6138 MMSTB, 1296 BCF and 6316 MMSTB, respectively. Total 21 wells were used in the reservoir development stage that included 10 production wells (perforated in the layers 5, 6 and 7) in primary production stage, three vertical water injection wells (layer 10) in the secondary production stage, three CO2 vertical injectors (layer 3) and five horizontal producers (layer 7) in GAGD-EOR stage.

Gravity number group

Depth, height and vertical permeability of the reservoir, relative permeability and viscosity of the oil, the difference of the density between the oil and injected gas, acceleration due to gravity and the total superficial velocity of the fluids constitutes the gravity number that is based on the constant gas injection rate constraint. Risk analysis of these parameters showed that the superficial velocity is the most critical parameter with the constant vertical permeability and the injected gas and oil density difference for a GAGD-EOR setting given in Table 2. Therefore the average total superficial velocity of the fluids is adapted from IMEX simulations while studying the sensitivity of gravity number. Its variation with the dimensionless recovery is as shown in figure 4a. uT increases with the higher injection rates. For a particular injection rate, it increases gradually yielding nearly stable gravity number (Figure 4b). With the further advancement of the gas floodfront towards the wellbore, uT increased at higher rate. Gravity number further decreased corresponding to the uT variation. It sharply rises after the gas breakthrough. With each successive higher gas injection rate combination, the lower gravity number responses were observed. These results suggest that the gravity number is sensitive to the superficial velocity (gas injection rates) changes, which is in agreement with the risk analysis on the gravity number. Respective gravity drainage oil recovery performance is analyzed by constructing dimensionless recovery (RD) vs. dimensionless time (tD) (Figure 5a). At low gravity numbers, higher dimensionless recoveries are obtained as seen in Case-I while for the higher gravity number Case-III, lower oil recoveries were obtained. This suggests that the dimensionless recoveries are inversely proportional to the gravity number. In all the cases gravity number variation is not very significant owing to the dominating gravity drainage oil recovery mechanism.

8 SPE 115065

Table 2: Multiphase operational parameters considered for the sensitivity analysis of GAGD-EOR process. Group value of one of the scaling group is varied while keeping other group values constant

Parameters Case-I Case-II Case-III Groups Case-I Case-II Case-III

L (ft) 30000 30000 30000 RL 20 20 20

w (ft) 12000 12000 12000 N 0 0 0

H (ft) 1500 1500 1500 Mw 0.21 0.21 0.21

P (psia) 3837 3837 3837 Mg 1.36 1.36 1.36

T (oF) 180 180 180 Soi 0.85 0.85 0.85

kV (md) 1200 1200 1200 Sorw 0.2 0.2 0.2

kH (md) 1200 1200 1200 Sorg 0.1 0.1 0.1

o (lb/ft3) 53.002 53.002 53.002 CO2 (lb/ft3) 0.1148 0.1148 0.1148

o (cP) 0.2026 0.2026 0.2026 w (cP) 0.3687 0.3687 0.3687

CO2 (cP) 0.056 0.056 0.056 krw 0.3 0.3 0.3 kro 0.8 0.8 0.8 krg 0.3 0.3 0.3

ICO2(SCFD) 5.10E+07 6.75E+07 9.00E+07

0.0E+00

2.0E-08

4.0E-08

6.0E-08

8.0E-08

1.0E-07

1.2E-07

1.4E-07

1.6E-07

0 5 10 15 20 25 30 35

Tota

l sup

erfic

ial v

eloc

ity o

f the

flui

ds, u

T (f

t/s)_

Dimensionless Recovery, RD (%)

Case-I

Case-II

case-III

0.0E+00

1.0E+12

2.0E+12

3.0E+12

4.0E+12

5.0E+12

6.0E+12

7.0E+12

8.0E+12

9.0E+12

1.0E+13

0 5 10 15 20 25 30

Gra

vity

Num

ber,

Ng

Dimensionless Recovery, RD (%)

Effectofgravityonrecovery Case-ICase-II

Case-III

(a) (b)

Figure 4 (a) Total superficial velocity (uT) and (b) Gravity Number (Ng) vs dimensionless recovery (RD)

GAGD oil recovery is based on the constant gas injection and oil producing pressure as well. Therefore the gravity number based on these parameters is obtained by converting the gas injection rate constraints to the pressure constraints. The term describing the potential difference across the reservoir due to viscous forces (uT.L/kv.) is replaced by the difference of the pressure between the gas injection well and the oil production well (Pinj-Pprod). Three sample reservoirs with the pressure based gravity numbers of 17000, 11600 and 8200 are created. For this purpose, the reservoir parameters of the Case-II given in Table 2 are used to vary pressure parameter while keeping other scaling group values constant. Figure 5b depicts the dimensionless recovery performance of these sample reservoirs. As seen in figure, the pressure dependent gravity number produced very similar dimensionless GAGD-EOR performance.

SPE 115065 9

0.0E+00

5.0E+00

1.0E+01

1.5E+01

2.0E+01

2.5E+01

3.0E+01

3.5E+01

0 5 10 15 20 25 30 35

Dim

ension

less

Recovery,

RD

(%)

Dimensionlesstime,tD

Case-I

case-II

Case-III

0

5

10

15

20

25

30

35

0 5 10 15 20 25

Dim

ensio

nles

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D) %

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Ng-P 1.7E+04Ng-P 1.16E+04

Ng-P 8.2E+03

(a) (b)

Figure 5: Dimensionless recovery (RD) vs. Dimensionless time (tD) of the GAGD-EOR process using scaling group (a) Gravity number (injection rate based) and (b) pressure based gravity number.

Pressure group

Three combinations of the injection well and producing well pressures are used while keeping other scaling group values constant (Case-II combination shown in Table-2). They are 2800 psia and 2650 psia, 2750 and 2550, and 2700 and 2450 with their respective dimensionless group values of injection and producing pressure groups as given in Figure 6. At higher values of the injection and producing pressure group, a lower recovery is obtained. At lower pressure combination, the oil recovery yield is higher with a delayed production of about 7 years compared to the highest pressure group combination. Flattened recovery curves are the oil recoveries obtained after gas breakthrough. Hence, the amount of oil displaced in the GAGD-EOR process is inversely related to the pressure at the gas injection and oil production well, so the injection pressure and production pressure group.

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PinjD 0.5253 PprodD 0.4767PinjD 0.5350 PprodD 0.4961 PinjD 0.5447 PprodD 0.5156

Figure 6: Dimensionless oil recovery performance of GAGD-EOR method for three sample pressure groups. Other scaling group values are kept constant.

Mobility ratio group Mobility ratio represents the relative mobility of the phases present in the reservoir. Movement of the oil, water and gas at

the reservoir conditions play an important role on the outcome of the recovery performance of the water and gas injection operations. An unfavorable mobilities of these phases results in oil bypassing, viscous fingering, channeling. Sensitivity of mobility ratios on the GAGD-EOR process is studied in three settings for water-oil and CO2-oil system.

For the sensitivity studies of the water-oil mobility ratio (Mwo), relative permeability of water is varied from 0.18, 0.3 and 0.48 while relative permeability to oil is kept constant at 0.8. Other dimensionless group values were maintained constant. Dimensionless recovery performance over the dimensionless time is as shown in Figure 7a. The results indicate that water-oil mobility ratio of three cases start to differ after few years of the production, which continue to rise in the later stage of the flooding operations. Higher oil recovery is obtained at lower Mwo suggesting that the dimensionless oil recovery is inversely

10 SPE 115065

proportional to the water-oil mobility ratio in GAGD-EOR method. For gas (CO2)-oil mobility sensitivity study, four sample reservoirs were created with the scaling group values of 0.45, 0.90, 1.36 and 1.81 by varying the relative gas permeability as 0.1, 0.2, 0.3 and 0.4. Dimensionless recoveries obtained over the dimensionless time are as depicted in Figure 7b. Dimensionless recovery performance curves start to differ from each other in the middle of flood. It becomes more pronounced in the last quarter of the gas flooding, which further increases after gas breakthrough (flattened portion of the curve). This is in contrast with the flood performance of the water-oil mobility ratio. Deviations between the individual recoveries were high in the middle of the flood which continues to rise. In case of the Mgo, the relative mobility of the CO2 to displace the oil in the reservoir downward towards the producing wells is critical for the success of the GAGD-EOR method.

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(a) (b)

Figure 7: Curves depicting the dimensionless oil recovery vs. dimensionless time (tD) for the sensitivity analysis of (a) water-oil mobility ratio (Mwo) (b) gas-oil mobility ratio (Mgo)in GAGD-EOR method. Other Scaling group vlaues are kept constant.

Residual oil saturations

Residual oil saturation to water (Sorw) and gas (Sorg) is studied for its sensitivity in the GAGD-EOR process. Residual oil saturation to water is varied in three cases mainly, 0.2, 0.25 and 0.3 while residual oil saturation to gas is varied as 0.1, 0.2 and 0.3. Other dimensionless scaling group values are kept constant. Results of the sensitivity analysis are as shown in Figure 8a for the residual oil saturation to water and Figure 8b for the residual oil saturation to gas.

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Figure 8: Dimensionless recovery performance of GAGD-EOR process for the residual oil saturations to water (Sorw) and gas (Sorg). Values of other dimensionless scaling groups are kept constant while varying the values of the Sorw and Sorg

Results represented through the dimensionless oil recovery showed that the residual oil saturation to water and gas has considerable impact even with a minor variation in their values. In case of residual oil saturation of water, the dimensionless recovery is low for the higher Sorw values. It begins to deviate right from the start of the GAGD CO2 injection from other dimensionless recoveries of the lower residual oil saturations. For the residual oil saturation of gas, these deviations are higher. At the lower residual oil saturation to gas, very high dimensionless oil recovery is obtained compared to the residual oil saturation to water. Flattened shape of the curves represents the oil recoveries after CO2 breakthrough. Lower residual oil saturation to gas delays the gas breakthrough as seen for Sorg of 0.1 by the changed course of the dimensionless recover

SPE 115065 11

curve. On the other side the higher Sorg (0.3) yield early gas breakthrough. For the Sorw dimensionless recoveries, the gas breakthrough time was about similar. These results indicate that Sorw and Sorg should be included in the scaling GAGD-EPR process. Validation of the dimensionless scaling groups

The functional relationship between the dimensionless scaling groups and an immiscible GAGD-EOR performance in all of the sensitivity studies is mapped through numerical simulations over the CMGS IMEX simulator. Now the dimensionless recovery performance obtained through the dimensionless scaling groups should be matched for its validation. To achieve this, the parameters making up the dimensionless scaling groups are changed so that the final values of the all the scaling groups remain unchanged. Dimensionless recoveries of the sample reservoirs with equal dimensionless group values if closely agrees with each other all the times, then these scaling groups could be sufficient to scale the GAGD-EOR process at the field scale.

The individual values of the dimensional properties (of the operational multiphase parameters of the GAGD-EOR

process) and dimensionless scaling groups are as given in Table 3 and Table 4, respectively. Vertical and horizontal permeability, end point relative permeabilities of water, oil and gas, saturations of oil, gas and water are changed in three reservoir samples (I, II and III) so that the values of 10 dimensionless scaling groups remain constant. Vertical and horizontal permeability values are varied as 1200 mD, 1050 mD and 1400 mD. krw and krg values are varied as 0.3, 0.27 and 0.24 whereas kro values are changed as 0.8, 0.72 and 0.64. The pressures in the gas injection and oil production wells are used in obtaining the final injection pressure group, producing pressure group and the gravity number values. The calculated scaling group values are as given in Table 4.

The dimensionless recovery for three cases is plotted against the dimensionless time for three sample reservoirs as

depicted in Figure 7. CMGs IMEX simulator is used to obtain the data required for validation of the scaling groups. The results depicted in the figure showed that the dimensionless recoveries obtained for all the reservoirs under investigation are identical. Maps produced are in close agreement with each other by just 10-12% variation until CO2 breakthrough. This indicates that the results in the dimensionless quantities are reproducible. They are independent of scale. Therefore any reservoir with the equal values of these groups should have same dimensionless recovery. Therefore, the results obtained using the dimensionless groups in this study should be sufficient for scaling of GAGD-EOR process.

Table 3: Dimensional properties of three sample reservoirs, (based on the pressures of gas injection and oil production wells)

Table 4: Dimensionless group values of the threesample cases of reservoirs

Parameters Reservoir-I Reservoir-II Reservoir-III

L (ft) 30000 30000 30000

W (ft) 12000 12000 12000

H (ft) 1500 1500 1500

P (psia) 3837 3837 3837

T (oF) 180 180 180

kV (md) 1200 1050 1400kH (md) 1200 1050 1400o (lb/ft3) 53.002 53.002 53.002

CO2 (lb/ft3) 0.1148 0.1148 0.1148

o (cP) 0.2026 0.2026 0.2026

w (cP) 0.3687 0.3687 0.3687

CO2 (cP) 0.056 0.056 0.056

Pi (psia) 2800 2800 2800

PP (psia) 2650 2650 2650

PMM (psia) 5140 5140 5140

krw 0.3 0.27 0.24kro 0.8 0.72 0.64krg 0.3 0.27 0.24

Scaling groups Reservoir-I Reservoir-II Reservoir-III

RL 20 20 20

N 0 0 0

Mw 0.21 0.21 0.21

Mg 1.36 1.36 1.36

NgP 1.70E+04 1.70E+04 1.70E+04

PiD 0.54 0.54 0.54

PPD 0.52 0.52 0.52

Soi 0.85 0.85 0.85

Sorw 0.2 0.2 0.2

Sorg 0.1 0.1 0.1

12 SPE 115065

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Dimensionless Groups Validation

reservoir-I

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Reservoir-III

Figure 9: Dimensionless recovery vs. Dimensionless time for the Sample reservoirs I, II and III. Operational parameters of the scaling groups are changed while holding the values of each of the dimensionless scaling groups constant. Very close agreement is reached between three sample reservoirs suggesting that the dimensionless scaling groups used in this study can appropriately scale the GAGD-EOR process. Conclusions In this study, GAGD-EOR process is scaled with a special emphasis on the pressure-based gravity number and the residual oil saturations of water and gas. Keeping in mind the various limitations and assumptions imposed in this study, the following conclusions can be drawn:

1. Small changes in the residual oil saturations of water and oil can highly impact the GAGD oil recovery performance. 2. Dimensionless oil recovery performance study through the dimensionless groups indicates that the pressure-based

gravity number is more appropriate to scale the GAGD-EOR method compared to the gas injection rate based gravity number.

3. The validation tests conducted on the scaling groups used in this study suggests that these groups could be adequate to scale GAGD-EOR process especially in horizontal type (non-dipping) reservoir.

Acknowledgements

The authors would like to thank Santos Limited for its support to research on the CO2 EOR process within the Centre for Improved Oil Recovery at the Australian School of Petroleum, University of Adelaide. The first author is a recipient of the Santos Post-Graduate scholarship. Nomenclature Bo = Formation Volume Factor of the oil, Res bbl/STB, [L3/L3]

Bg = Formation Volume Factor of the gas, SCF/STB, [L3/L3] Bsolvent = Formation Volume Factor of the solvent [L3/L3] g = acceleration due to gravity, ft/s2 [L/t2] H = thickness of the reservoir, ft [L] ig = rate of gas injection, SCFD kv = vertical permeability, mD, psia [L2] kh = horizontal permeability within the reservoir, mD, psia [L2] kro = permeability to oil of the porous medium, mD, psia [L2] krg = permeability to gas of the porous medium, mD, psia [L2] krw = permeability to water of the porous medium, mD, psia [L2] L = characteristic length of reservoir or Well spacing, ft [L] Mwo = water-oil mobility ratio, bbls [L3] Mgo = gas-oil mobility ratio, bbls [L3] Np = cumulative oil production, bbls [L3] NgI = Gravity number based on the gas injection rate, dimensionless NgP = Gravity number based on the pressure difference between the gas injection and oil production wells, dimensionless N = Dip angle group, dimensionless

SPE 115065 13

Pinj = gas injection pressure, psia [M/LT2] Pprod = Oil recovery (producing) pressure, psia [M/LT2] PMM = minimum miscibility pressure, psia [M/LT2] P = difference of pressure between the gas injection pressure and oil recovery pressure, psia [M/LT2] qo = rate of the oil production, bpd, [L3/T] RL = Effective Aspect ratio, dimensionless Rs = solution gas-oil ratio RD = Dimensionless recovery

orwS = residual oil saturation to water (water-oil system)

orgS = residual oil saturation to gas (gas-oil system) t = time [T] tD = Dimensionless time T = Temperature, oF [] uT = Average superficial velocity, ft/s, [L/T] W = width (diameter of core) of the reservoir, ft [L]

Greek Symbols

o = density of reservoir fluid (oil), lb/ ft3[M/L3] g = density of the gas, lb/ ft3[M/L3] = difference of the density between the reservoir fluid (oil) and the injected gas, lb/ ft3 [M/L3] ro = mobility of oil within the porous medium rg = mobility of gas within the porous medium rw = mobility of water within the porous medium = Porosity, fraction = angle of dip (tilt) of a particular reservoir section with respect to the horizontal o = viscosity of the oil, cP [M/LT] g = viscosity of the gas, cP [M/LT] solvent = viscosity of the solvent, cP [M/LT]

Subscripts

x = x-direction y = y-direction z = z-direction V = vertical H = horizontal s = solution g = gas o = oil s = solvent

SI Metric Conversion Factors 141.5 / (131.5+ oAPI) E + 00 = g/cm3 bbl 0.15899 E + 00 = m3 cp 1 E + 00 = mPa.s (oF 32) 0.55 E + 00 = oC ft 3.048 E + 00 = m md 9.869 E - 09 = m2 psi 6.895 E + 00 = KPa References Bangla, V.K., Yau, F. and Hendricks, G.R. 1991. Reservoir performance of a Gravity stable vertical CO2 miscible flood: Wolfcamp

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Society of Petroleum Engineers Journal, 2: 9-12. Chatzis, I., Kantzas, A. and Dullien, F.A.L. 1988. On the investigation of Gravity Assisted Inert Gas Injection Using Micromodels, Long

Berea Sandstone Cores, and Computer-Assisted Tomography. SPE paper presented at the 63rd SPE Annual Technical Conference and Exhibition Houston, TX, October 2-5.

14 SPE 115065

Craig, F.F., Sanderlin, J.L. and Moore, D.W. 1957. A Laboratory Study of Gravity Segregation in Frontal Drives. SPE 676-G, Petroleum Transactions, AIME, 210: 275282.

Croes, G.A. and Schwarz, N. 1995. Dimensionally scaled experiments and theories on the water-drive processes. Trans. AIME, 204: 35-42. Da Sle, W.J. and Guo, D.S. 1990. Assessment of a vertical hydrocarbon miscible flood in the Westpem Nisku D Reef. SPE Reservoir

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