field scale simulation of cyclic solvent injection (csi)1

SPE 157804

Field Scale Simulation of Cyclic Solvent Injection (CSI) Jeannine Chang, Devon Canada John Ivory, Alberta Innovates - Technology Futures

Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Heavy Oil Conference Canada held in Calgary, Alberta, Canada, 1214 June 2012. 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

Only 5 - 10% of the oil in Lloydminster heavy oil reservoirs is recovered during cold production with sand (CHOPS). Cyclic

solvent injection (CSI) is the most promising post-CHOPS follow-up process. In CSI, a solvent mixture (e.g. methane-

propane) is injected and allowed to soak into the reservoir before production begins (Figure 1). CSI has been focused on

heavy oil recovery from post-CHOPS reservoirs that are too thin for an economic steam-based process. It has been piloted

by NEXEN and by Husky and was a fundamental part of the $40 million Joint Implementation of Vapour Extraction (JIVE)

solvent pilot program that ran from 20062010.

This paper describes field scale simulations of CSI performed with a comprehensive numerical model that uses mass transfer rate equations to represent non-equilibrium solvent solubility behaviour i.e. there is a delay before the solvent reaches its equilibrium solubility in oil. The model contains mechanisms to consider foaming or to ignore it depending on

the field behaviour. It has been used to match laboratory experiments, design CSI operating strategies, and to interpret CSI

field pilot results.

The paper summarizes the impact on simulation predictions of post-CHOPS reservoir characterizations where the wormhole

region was represented by one of the following five configurations: (1) an effective high permeability zone, (2) a dual

permeability zone, (3) a dilated zone around the well, (4) wormholes (20 cm diameter spokes) extending from the well

without branching, (5) wormholes extending from the well with branching from the main wormholes,. The different post-

CHOPS configurations lead to dramatically different reservoir access for solvent and to different predictions of CSI

performance.

The impacts of grid size, upscaling, well inflow parameter, solvent dissolution and exsolution rate constants, and injection

strategy were examined. The assumption of instant equilibrium solubility resulted in a 23% reduction in oil production

compared to when a delay in solvent dissolution and exsolution was allowed for. Increasing the grid block size by a factor of

9 reduced the predicted oil production five-fold. Assuming isothermal behaviour in the simulations decreased predicted oil

production by 17%.

Introduction

Primary cold production of heavy oil with sand (CHOPS) is commonly used in Lloydminster and Cold Lake to produce heavy oil

reservoirs (Sawatzky et al., 2002). As a result of reservoir pressure depletion and/or excessive water production, CHOPS becomes

uneconomic after about 5 - 15% of the initial oil has been recovered. Detailed studies of the cold production process have previously been

presented (Bratli et al., 1981, 1998, Chang 2000, Dusseault et al., 1989, 1998, and 1999, Geilikman and Dusseault 1997 and 1999, Risnes

et al., 1982, Sawatzky et al., 1996, 2002, and Tremblay et al., 1998, 1999, 2003, and 2009).

CSI has shown potential as a follow-up oil recovery process to CHOPS and has undergone pilot testing. Wormholes, created during

CHOPS, extend outward from production wells and provide access for solvent injection during CSI and larger contact area for solvent

dissolution in oil. Laboratory scale numerical simulation of CSI has been investigated at Alberta Innovates Technology Futures (AITF) for a number of years (Ivory et al., 2010) and a focus is now to use the previous learnings to improve field scale simulation of CSI as well

2 SPE 157804

as other solvent processes such as VAPEX and solvent drive thereby facilitating the development of improved injection and production

strategies. Improved representations of complex mechanisms such as non-equilibrium dissolution and exsolution of solvent, foamy oil

behaviour, and relative permeability hysteresis are being developed. In particular, the physical delay in both gas dissolution and gas

exsolution is represented by non-equilibrium behavior during both injection and production periods. In developing the CSI numerical

simulation models, the non-equilibrium representation of solvent (e.g. methane and propane) solubility, solvent/oil mixture

(methane/propane/oil mixture) viscosities, and the mixing parameters (diffusion, dispersion) of the process were incorporated into the

reservoir fluid model. Previous work at AITF for a laboratory scale experiment showed the difference between the predicted propane mole

fraction in oil and its equilibrium value during six CSI cycles (Figure 2). Predicted values for the CO2 - propane injection experiment were

dramatically different when non-equilibrium solubility effects were considered relative to when they were ignored (Table 1). Allowance

for non-equilibrium behaviour also affects the bottomhole pressure (BHP) during injection periods in field scale simulations (Figure 3).

For confidentiality reasons, the actual values are not shown in Figure 3. In general, the quicker the solvent dissolution the slower is the rise

in BHP during injection periods.

Table 1: Comparison of non-equilibrium and instant equilibrium simulation predictions

In predicting the effectiveness of CSI and in developing operating strategies, the assumed post-CHOPS reservoir situation resulting

from sand production is of key importance. AITF has developed its sand production model, which is supported in CMG STARS, and is an

Effective Permeability model in that the regions with a wormhole network are approximated with a high permeability determined by the sand production model. For due diligence, other post-CHOPS representations can be considered. In this paper, the effectiveness of CSI

was investigated for the following post-CHOPS representations (Figure 4): (1) an effective high permeability zone, (2) a dual permeability

zone (3) a dilated zone around the well, (4) wormholes (20 cm diameter spokes) extending from the well without branching, (5) wormholes

extending from the well with branching from the main wormholes.

Simulations were performed to examine the impact of:

o Using non-equilibrium dissolution and exsolution reaction kinetics to represent delays in solvent dissolution and exsolution o Non-equilibrium solubility rate parameters o Instant equilibrium versus non-equilibrium dissolution and exsolution o Grid block size

Development of CSI Models at AITF

Over the years, CSI models have been developed at AITF (formerly Alberta Research Council) based on non-equilibrium gas dissolution and exsolution behavior in solvent injection processes. In these models, the delay in a gaseous component dissolving or exsolving from the oil depends on the difference between its current concentration in the oil phase (xi) and its equilibrium concentration in the oil phase (xieqm). The latter is determined from its mole fraction in the gas phase, the temperature, and the pressure.

Equilibrium PVT behaviour is represented by the use of K values for each component i as follows:

i

ii x

yK (1)

Where:

xi = equilibrium mole fraction of i in oil phase and yi = equilibrium mole fraction of i in gas phase.

In the CMG STARS simulator, the equilibrium K value of a specific gas is calculated using a modified version of the Antoine

Equation,

))(

exp()(5

432

1

kvT

kvkvPkv

P

kvK

(2)

Where:

P = pressure (kPa)

T = temperature (K)

kv1, kv2, kv3, kv4, kv5 = coefficients for specific gases

The CH4 and C3H8 kv values that were used in the simulations are provided in Table 2.

Cumulative

Oil (cm

3)

C3H8 Recovery

(%)

CO2 Recovery

(%)

Nett Solvent-Oil Ratio

(liq cm3/cm

3)

Non-Equilibrium 1,698 72.8 64.1 0.60

Instant Equilibrium 809 92.3 97.4 0.34

SPE 157804 3

Table 2: Methane and propane kv values used in the simulations

Gas Dissolution

The non-equilibrium behaviour of gas dissolution in oil is represented by:

CH4G + CH4L 2 CH4L (3) C3H8G + C3H8L 2 C3H8L (4)

Where:

CH4L is dissolved methane in the oil phase

CH4G is methane in the gaseous phase

C3H8L is dissolved propane in the oil phase

C3H8G is propane in the gaseous phase

The dissolution rate for propane is:

2831

8383*83 ***83 n

GHCg

n

LHCGeqmHCoHC yNxxNkt

NLHC

Where:

k = rate constant for propane dissolution m3/moles/d if n1 = n2 = 1 Ng = Moles of gas phase/m

3 of grid block NC3H8L = Moles of propane in the oil phase/m

3 of grid block No = Moles of oil phase/m

3 of grid block = Porosity *oil saturation * oil molar density n1 = exponent for xC3H8eqm - xC3H8 n2 = exponent for yC3H8

The rate equation constants kC3H8, n1, and n2, can be determined from experimental results e.g. by history matching laboratory

experiments or field tests. Similar equations are used for methane dissolution.

The rate constants are dependent on temperature but because of the small temperature changes and because of the lack of experimental data available to determine this dependency, they were assumed to be independent of temperature in the simulations discussed in this report. Allowance for the temperature dependency of the rate constants is available in STARS. Gas Exsolution

Non-equilibrium gas exsolution with foam formation is represented as follows for CH4 and C3H8 by: CH4L SBubCH4 CH4G (5) C3H8L SBubC3H8 C3H8G (6) Where: SBubCH4 is a small CH4 bubble in the oil phase SBubC3H8 is a small C3H8 bubble in the oil phase Unless specified otherwise, a non-equilibrium treatment was used in this project for both gas dissolution and exsolution. As a result of

non-equilibrium behaviour, solvent components can still be dissolving at the beginning of a production period and come out of solution (exsolve) during the initial part of an injection period. Thus, although the simulations are slower, it is more representative of CSI to include all of the exsolution and reactions during both injection and production periods.

Methane Propane

kv1 (kPa) 476,664 726,374

kv2 (kPa-1

) 0 0

kv3 0 0

kv4 (C) -879.84 -1,872.46

kv5 (C) -265.99 -247.99

4 SPE 157804

Solvent/Oil Mixture Viscosity

The STARS default logarithmic mixing rule was used to determine the oil phase viscosity. iioillive X lnln (7) Where:

i = the pseudo-viscosity of component i. The dead oil viscosity and the dissolved methane and propane pseudo-viscosities at 23.4 C are provided in Figure 5. The dead oil

viscosity at this temperature was 18,775 mPa.s. A rock compressibility of 2.9 x 10-6 kPa-1 was used. Small gas bubbles were assigned a molar density of 41 gmol/STD m3 as obtained from the Ideal Gas Law.

Solvent/Oil Mixing Process

Solvent and oil are mixed in a reservoir as a result of the combined effect of convection, diffusion, dispersion, and dissolution. In diffusion, the flow of a component towards regions of lower concentration in a fluid phase is represented by Fick's First Law:

kCDSJ ijmijjijk /)( (8) Where:

ijkJ = Flux of component i in phase j in k direction (gmoles/m2/d)

= Porosity Sj= Saturation of phase j

Dmij = Molecular diffusion coefficient of component i in phase j (m2/d)

Cij/k = Concentration gradient of component i in phase j in k direction (gmoles/m3/m)

In a porous media, allowance is made for the increased flow length caused by tortuous flow paths through the pore spaces. As a

result, the apparent diffusion coefficient (D) used for porous media is lower than the molecular diffusion coefficient and:

mDD (9) Where:

= tortuosity.

Individual streamlines flow in a tortuous route through porous media. A "fluid particle" can transfer (disperse) from one streamline to another by diffusion or through turbulent eddies that disrupt the streamlines. Mechanical dispersion in porous media arises from complex flow paths, which create mechanical mixing that is independent of molecular diffusion. It is caused by velocity gradients, heterogeneous flow paths, and mechanical mixing.

Both longitudinal (in direction of flow) and lateral (orthogonal to flow) mixing are controlled by diffusion at low velocities and by convection at high velocities. Velocity variations parallel to the mean flow direction are greater than those that are perpendicular to the main flow. Thus, longitudinal dispersion is greater than transverse dispersion. At high velocities, Blackwell (1962) observed that longitudinal dispersion was about 24 times that of lateral dispersion.

Neuman (1990) examined over 130 longitudinal dispersivity values obtained from world-wide lab and field tracer studies in porous and fractured media. The dispersivity values ranged from less than 1 mm to greater than 1 km for studies ranging from less than 10 cm to greater than 100 km.

For laminar flow conditions in typical unconsolidated, random packs, dispersion correlations can be represented as follows (Perkins and Johnston, 1963):

Longitudinal dispersion correlation:

10.5 where 50

p pL

m m m

ud udK

D F D D

(10)

Transverse dispersion correlation:

41 0.0157 where 10p pT

m m m

ud udK

D F D D

(11)

Where: Dm = Molecular diffusion coefficient

dp = Particle diameter

SPE 157804 5

u = Local fluid velocity

= Inhomogeneity factor

F = Formation factor = 1/() also used for quantifying electrical conductivity through porous media In the simulations discussed in this report, a gas phase diffusion coefficient of 0.0144 m2/d and an oil phase diffusion coefficient of 0.0000432 m2/d were used. A mechanical dispersion coefficient of 0.005 m was used for both the gas and oil phases. The diffusion and dispersion coefficients were assumed to be independent of direction. No allowance was made for the fact that the apparent diffusion and dispersion coefficients are different for regions with wormholes due to their impact on tortuosity and flow patterns and velocities.

The oil-water and oil-gas relative permeability values were based on Stone's Method 2 with gas phase relative permeabilities

being lower during production periods because of the impact of trapped gas bubbles. The irreducible water saturation was 0.37, the critical

gas saturation was 0.05, the water-oil residual oil saturation was 0.29 and the gas-oil residual oil saturation was 0.15.

The complex interaction between solvent exsolution and exsolution and fluid flow in a reservoir model is represented in Figure 6.

CSI Simulations for Post-CHOPS Reservoir Characterization based on AITF CHOPS Model

For the Effective Permeability model, 2-D radial primary production simulations were first performed for an actual Lloydminster

well using AITF's sand transport and foamy oil models and the post-CHOPS reservoir results were then converted to a Cartesian grid for the CSI simulations. Initial Pre-CHOPS Reservoir Conditions

Some initial reservoir conditions were:

Pressure = 3,300 kPaa Temperature = 23.4 C Dead oil viscosity = 18,775 mPa.s GOR = 7 std m3/m3

Other pre-CHOPS reservoir conditions are provided in Table 3.

A good match of oil and water production during CHOPS was obtained (Figures 7a and 7b). The post-CHOPS permeability,

porosity, saturations, and oil phase mole fractions obtained from the history match were used as the initial conditions for simulating the solvent cycles. As it was the only layer with relatively high porosity and permeability, Layer 4 (K = 4) was the layer where the CHOPS simulations predicted that wormhole formation would occur. The increased permeability occurring from the creation of wormholes was represented by high effective permeability values in the Layer 4 grid blocks (Figure 8). Injection-Production Strategy

In this study, CSI generally consisted of three injection-production cycles in which the production period was 180 days in each cycle and the injection period was 30 days in Cycle 1, 40 days in Cycle 2, and 50 days in Cycle 3. The composition of the injected gas was 60% methane and 40% propane and the specified gas injection rate was 20,000 STD m3/d in each cycle until the injection pressure constraint of 3.5 MPaa was reached and the injection rate declined. Standard (surface) conditions were 15 C and 101.3 kPaa.

During production, the minimum bottom-hole pressure (BHP) was specified as either 150 or 200 kPaa, the maximum gas production rate as 20,000 STD m3/d and the maximum liquid rate at downhole conditions as 50 m3/d.

6 SPE 157804

Table 3: Pre-CHOPS reservoir properties

Results for Effective Permeability Simulations Effect of Increasing Reaction Rate Constants

Increasing the dissolution and exsolution reaction rate constants (frequency factors) by a factor of 100 enhanced solvent injectivity and decreased the BHP during an injection period. Oil production was marginally decreased by 2% from 3,524 to 3,453 m3 in the first cycle but the nett propane to oil ratio was dramatically increased from 0.04 to 0.15 liquid m3/m3. Effect of Grid Block Size - Upscaling

One-quarter symmetry was used in all of the CSI simulations and they covered one-quarter of the 400 m x 400 m area in which the vertical CSI well was in the centre. A 36 x 36 x 7 Cartesian grid was used for most of the simulations.

Table 4: Effect of frequency factors and dispersion coefficients

Run Grid FF Dissolution

(m3/gmole/day)

FF

Exsolution

(day-1

)

Dispersion

Coefficient

(m)

CSI Cumulative Oil at End

of Cycle - Full well basis

(m3)

Nett propane/Oil

(liquid m3/m

3)

Cycle 1 Cycle 2 Cycle 3 Cycle

1

Cycle

2

Cycle

3

Baseline Fine 0.0005 0.0005 0.005 4,139 9,041 13,769 0.15 0.03 0.03

Upscale

1 Coarse 0.0005 0.0005 0.005 322 1,343 2,788 2.08 0.68 0.36

Upscale

2 Coarse 0.00005 0.00005 0.005 3,003 4,792 - 0.16 0.30 -

Upscale

3 Coarse 0.05 0.05 0.005 4,206 7,584 10,968 0.04 0.03 0.05

Upscale

4 Coarse 0.5 0.5 0.005 4,871 7,245 9,199 0.00 0.00 0.00

Upscale

5 Coarse 0.05 0.0005 0.005 4,059 7,982 11,651 0.05 0.04 0.04

Upscale

6 Coarse 0.0005 0.05 0.005 4,382 8,688 12,285 0.11 0.08 0.07

Upscale

7 Coarse 0.0005 0.0005 0 4,198 8,830 11,763 0.13 0.03 0.00

Upscale

8 Coarse 0.0005 0.0005 0.1 4,339 8,872 13,510 0.12 0.11 0.09

Some simulations were performed using a 16 x 16 x 7 grid with larger grid blocks (Figure 9) in order to increase simulation speed. When all other parameters remained the same, the use of the coarse grid resulted in a much quicker reduction in BHP during production (Figure 10a) and much lower oil rates (Figure 10b). Adjustments of dissolution and exsolution rate parameters and of

Layer Thickness

(m) So Sw

Perm.

(md)

7 (top) 0.15 0.0 1.0 0.05 0.02

6 0.23 0.37 0.63 0.20 40.8

5 0.53 0.70 0.30 0.26 277.1

4 0.99 0.79 0.21 0.31 1,563

3 1.14 0.66 0.34 0.25 290.7

2 0.38 0.55 0.45 0.14 11.1

1 0.15 0.15 0.85 0.06 0.0

SPE 157804 7

dispersion coefficients can be made to compensate for changes in predicted oil and gas production caused by increasing the size of grid blocks. Simulation run Upscale 1 in Table 4 had the same kinetic parameters and dispersion coefficients as the baseline fine grid run and the predicted oil production was an order of magnitude less than for the fine grid. Changing the frequency factor rate parameters significantly impacted predictions (Upscale 2 to Upscale 6) as did changing the dispersion coefficients (Upscale 7 and Upscale 8). For example, Upscale 6 had the rate constant for the exsolution reactions increased from 0.0005 to 0.05 day-1 and resulted in a reasonable approximation to the fine grid case in terms of gas injection, oil production and nett solvent to oil ratio (Table 4 and Figure 11). Alternatively, increasing the dispersion coefficients from 0.005 to 0.1 m (Upscale 8) also resulted in similar results to the fine grid case. Decreasing the dispersion coefficients to 0 m (Upscale 7) resulted in satisfactory oil production but the nett solvent to oil ratio was much lower than for the fine grid case. Fine tuning of the dispersion coefficients and/or non-equilibrium parameters can result in a close match for oil, water, and gas production between coarse and fine grid predictions. Isothermal versus Non-Isothermal Simulations

Performing non-isothermal simulations resulted in increased oil production in Cycle 1 by 17% (from 3,524 to 4,139 m3, Table 5) but the nett propane/oil ratio ratio (propane left in reservoir/oil produced) was unchanged at 0.15 at liquid m3/m3. Due to the heat of solution, the temperature rises during solvent dissolution in the oil and falls during solvent exsolution. During solvent dissolution, the rising temperature affects predictions as it causes a decrease in both the viscosity of the live oil components (dead oil, dissolved methane, and dissolved propane) and the solubility of methane and propane. Allowing for non-isothermal behaviour typically slows down simulations so this must be considered when deciding whether to use it. Many of the simulations discussed in this paper were based on non-isothermal conditions.

Table 5: Isothermal versus non-isothermal predictions

Oil Production

(m3)

Nett Propane/Oil

(liquid m3/m

3)

Isothermal 3,524 0.15

Non-

isothermal 4,139 0.15

Equilibrium versus Non-Equilibrium Solubility

Ignoring non-equilibrium behaviour dramatically impacts predictions and is difficult to justify. The use of instant equilibrium results in more rapid gas exsolution when the pressure is decreased during production and low oil production due to the severe reduction in the reservoir pressure and the elimination of bubble creation and foamy oil drive. In addition, the initial high gas flow rate negatively impacts oil production. Assuming that equilibrium solvent solubility is immediately obtained during both dissolution and exsolution resulted in lower injection pressures, greater gas injection and production, and lower oil production over 3 cycles (Figures 12 and 13). Oil production was marginally greater in Cycle 1 for the instant equilibrium situation but was much lower in Cycles 2 and 3.

As propane dissolved much more rapidly in oil for the instant equilibrium solubility simulations, these simulations predicted much lower reservoir pressures during an injection period than did non-equilibrium solubility simulations (Figure 14). This also results in reduced injection pressure as shown in Figure 3. The 2-D IJ profiles are shown for Layer 4 in this figure as this was the layer with a high effective permeability. I refers to the grid block number in the X direction and J to the grid block number in the Y direction. During a production period, the pressure decreased more slowly in the instant equilibrium simulations as propane came rapidly out of solution and helped maintain the reservoir pressure. In contrast, much of the propane was produced in the oil phase in the non-equilibrium simulations. Effect of Extra Exsolution Reaction

Foamy oil behaviour during exsolution is represented in AITF CSI models by assuming that each dissolved component first forms small pure bubbles dispersed in the oil phase prior to entering the free gas. A refined parallel model allows for cases where rapid gas exsolution occurs. The parallel bubble destruction reaction can also remove small bubbles created during CHOPS prior to solvent injection.

Use of the reaction bypassing bubble formation resulted in greater gas production in Cycle 1 as gas could exsolve more quickly

from solution (Figure 15a). In addition, oil production over 2 cycles was increased by 9% from 9,041 to 9,871 m3 (Figure 15b) by incorporating the extra gas exsolution reaction. Although the new reaction competed with the bubble forming reaction, it actually increased the amount of free bubbles produced at the well as a result of its effect in increasing the pressure drawdown rate during production due to increased gas production (Figures 16a, 16b, and 16c).

8 SPE 157804

Simulation Speed

Due to the complexity of the simulations, simulation speed was an issue. Parallel processing was routinely used with little difficulty although run speed was still slow. Dynamic refined gridding was tried but due to the cyclic nature of the process (resulting in constantly changing conditions) and numerical difficulties in simulating CSI, dynamic gridding had limited success and even impacted the results. The use of DynaGrid (based on oil phase mole fraction differences) reduced the predicted oil production by 28% and increased the predicted gas production by 22%. Thus, the selection of DynaGrid parameters needs to be improved for CSI simulations so as to increase simulation speed and minimize changes in results resulting from block amalgamations. Other DynaGrid simulations were made using different constraints (difference in pressure, gas phase mole fractions, and/or global mole fractions between grid blocks) and they too were unsuccessful.

Alternative Post-CHOPS Characterizations Reservoir Models Considered

In addition, to the AITF Effective Permeability model, CSI performance was predicted using a number of other models (Figure 4) after first performing primary production simulations. For the Dual Permeability, Dilated Zone, Spokes, and Spokes & Branches models, the simulations started at the initial pre-CHOPS pressure, temperature, and saturations with the pressure being drawn down prior to the initiation of CSI. Non-equilibrium solubility conditions were used for most of the Effective Permeability model simulations and for the Spokes and Spokes & Branches simulations. Dual Permeability Model

A Dual Permeability model (Figure 4b) was set up with fractures in Layer 4. The matrix represents the intact reservoir and the fractures represent the wormhole network. The fluid flow between the matrix and fracture represents the fluid flow between the intact reservoir and the wormhole network. The fracture porosity (= fracture volume/block volume) selected was 0.0067 and the fracture permeability was 10,000 Darcy. The horizontal fractures were spaced 10 cm apart. The initial properties (pressure, temperature, permeability, porosity, saturations) in the reservoir matrix were the same as those pre-CHOPS values that were used to obtain the initial (post-CHOPS) reservoir for the Effective Permeability model. Primary production was modelled without sand production and instant equilibrium solubility behavior was assumed because simulation of non-equilibrium behavior was slow and unstable. Dilated Zone Model

In the Dilated Zone model (Figure 4c), it was assumed that there was dilation in a region (153.28 m x 153.28 m = 23,525 m2 on a full well basis) around the well causing a high permeability (1,000 Darcy) there and that there was no wormhole formation. As a result of slow run times, an instant equilibrium model was used to represent CSI. The high permeability region was in place at the beginning of primary production. Spokes Model

In the spokes model, it was assumed that wormholes emanated from the well (Figure 4d). The spokes were only in Layer 4 as it was assumed that this was the only layer with high enough porosity and permeability for wormholes to develop during CHOPS. The spokes were represented by 20 cm diameter source-sink horizontal wells whose length increased with time during primary production as shown in Table 6. The spokes were assigned a maximum BHP during injection of 3,500 kPaa and a minimum BHP during production of 200 kPaa. It was assumed that if large diameter wormholes did exist then the pressure drop in them would be low and they could be represented by source-sink horizontal wells. Representation of the spokes as shut-in horizontal wells where backflow is permitted rather than as producers with a specified minimum BHP (e.g. 150 kPaa) or as injectors with a maximum BHP (e.g. 3,500 kPaa) is an alternative approach that will be evaluated in the future.

Bubble destruction

Bubble formation

Dissolved Gas

Small Bubbles

Free Gas

SPE 157804 9

Spokes & Branches Model

The Spokes and Branches model included 20 cm diameter spokes extending in Layer 4 from the CSI well with offshoot 20 cm diameter branches emanating from the spokes (Table 6 and Figure 4e). The branches were orthogonal to the spokes from which they emanated.

Table 6: Length of spokes and branches versus time

Time

(days)

Spoke 1

Length

(days)

Spoke 2

Length

(days)

Spoke 3

Length

(days)

Branch 1

Length

(days)

Branch 2

Length

(days)

0 0.2 0.2 3.2 0 0

12 8.4 8.4 11.9 8.4 8.4

26 21.4 21.4 30.2 21.4 21.4

40 34.4 34.4 48.6 34.4 34.4

54 47.3 47.3 66.9 34.4 34.4

68 60.3 60.3 85.3 34.4 34.4

83 73.3 73.3 103.7 34.4 34.4

98 86.3 86.3 122.0 34.4 34.4

114 99.3 99.3 140.4 34.4 34.4

122 105.7 105.7 149.5 34.4 34.4

3657 105.7 105.7 149.5 34.4 34.4

Results for Different Models Primary Production

Gas injection and oil, water, and gas production during primary production and CSI are summarized in Table 7 for the different models. As outlined above, the Effective Permeability Instant Equilibrium and Non-Equilibrium CSI models started with the post-CHOPS reservoir characterization determined using AITFs CHOPS model.

Table 7: Primary production (full well basis) for different models

Model

Eqm

or

NE

Oil

(m3)

Water

(m3)

Gas

(STD m3)

AITF CHOPS model NE 15,677 3,593 568,901

Dual Permeability Eqm 14,606 228 929,036

Dilated Zone Eqm 5,460 33 35,708

Spokes NE 10,518 2,946 99,874

Spokes & Branches NE 6,005 1,512 79,580

Eqm = instant equilibrium solubility NE = Non-equilibrium solubility

Dual Permeability Model

For the Dual Permeability model, the oil rate was specified to be the actual field value for the first part of the primary production simulations. The oil rate was averaged during the latter half of the Dual Permeability primary production simulations in order that a constant rate would speed up the simulations. A match of the specified production was achieved.

The greater contact area due to wormhole formation resulted in high gas injectivity particularly for the Effective Permeability model (Figure 17). As compared to the Effective Permeability model, the Dual Permeability model resulted in the same gas injection in Cycle 1, more gas injection in Cycle 2, and less gas injection in Cycle 3. For the latter model, oil was produced at a similar rate during CSI

10 SPE 157804

as it had been during primary production (Figure 18). In contrast for the Effective Permeability model predictions, the oil rate was much higher during CSI than during primary production. Although the Dual Permeability and Effective Permeability models both matched specified primary oil production, there was substantially less oil production for three CSI cycles for the Dual Permeability model (1,968m3) as compared to 13,769 m3 (non-equilibrium) or 9,988 m3 (instant equilibrium) for the Effective Permeability system.

For the Effective Permeability non-equilibrium simulations, the solvent penetrated to near the edge of the reservoir although at low concentrations (Figure 19a). For the Effective Permeability and Dual Permeability instant equilibrium models, the propane did move upwards and downwards from Layer 4 but there was much less lateral penetration beyond the high permeability region (Figures 19b and 19c). This was probably because the instant equilibrium solubility conditions, which were assumed in these latter simulations, allowed rapid dissolution of injected propane and so it remained closer to the well.

The high oil saturation (Figure 20a) in the fracture network reduced gas injectivity in Cycle 3 of the Dual Permeability simulation (Figure 17). The oil saturation in the matrix adjoining the fractures was reduced to about 70% during primary production and to about 60% during CSI. Propane penetrated into the fractures and the adjoining matrix (Figure 20b). Although the oil saturations were significantly different in the matrix and fractures, their propane mole fractions in the oil phase were very similar. Dilated Zone Model

Apart from the exception discussed now, a well radial inflow parameter (permeability x completion length) of 1 x 105 md-m was specified in all of the simulations. With this parameter value, very low gas injection (Figure 17) and oil production (Figure 18) were predicted for the Dilated Zone configuration. Increasing the parameter by a factor of 100 resulted in a higher oil production for the Dilation Zone model but the primary gas production rate was increased by two orders of magnitude and was unacceptable. Spokes and Spokes & Branches Models

For both the Spokes and Spokes & Branches models the specified oil production during primary production could not be achieved during primary production (Table 7 and Figure 18) even though the oil rate was a well control parameter. Much lower rates were also obtained during CSI as compared to the Effective Permeability model. For the Spokes model, the oil rate was a little lower in the first CSI cycle than at the end of primary production but it was much higher in Cycle 2 (Figure 18).

Oil saturation changes were mainly limited to areas where the spokes were (Figure 21a). Oil flow occurred from the outer

regions of the reservoir to the spokes in the high permeability Layer 4. This flow occurred even during injection periods as a result of the high pressure at the outer regions of the reservoir. Although not shown here, oil flow from the outer regions towards a CSI well also occurred in Effective Permeability simulations during injection periods until the outer reservoir pressure had been somewhat depleted. There was limited gas phase flow from the outer regions towards the spokes (Figure 21b) as methane remained in solution there because the pressure was still high. There was low gas saturation at the end of primary production and very little gas formation during CSI for the Spokes model. Similar behaviour was observed for the Spokes & Branches model. Predicted oil production for two CSI cycles with the Spokes model was only 3,235 m3 as compared to 9,041 m3 for 2 cycles with the Effective Permeability model.

In Layer 4, most of the pressure changes during CSI injection and production periods occurred where the spokes were (Figure 22a) and the production period pressure profiles for the Spokes and Spokes & Branches models were very similar except for the region near the branches, which had lower pressure values even during the injection period. There was very little pressure build-up during the injection period of the Spokes & Branches model simulation. The low pressure values obtained during injection resulted in very little oil production during CSI. During CSI, the pressure from Layer 4 was transmitted above and below so that a pressure profile for any layer was similar to that for Layer 4 (Figure 22b).

For Cycle 1 with the Spokes & Branches Model, the desired gas injection rate of 20,000 STD m3/d (full well basis) was

maintained for the entire 30 day injection period. Despite this, predicted oil production for Cycle 1 was only 168 m3 as compared to 4,139 and 630 m3, respectively for the Effective Permeability and Spokes models. The nett propane to oil ratio was considerably higher for the Spokes and Spokes & Branches models as compared to the Effective Permeability predictions (Table 8). The branches were too close to the vertical well and as a result had a negative rather than a positive impact on oil production. For the Spokes model, propane dissolution in oil was also limited to the region near the spokes (Figures 23 and 24) and the extent of this region was actually increased during production periods. The branches in the Spokes & Branches model changed where the propane dissolved as compared to when the Spokes model was used. The propane did not penetrate as far along the middle spoke as it did when there were no branches (Spokes model). In the former case there was more propane dissolved nearer the vertical well. If branches were further from the vertical well and extended into oil sand that would not be contacted by the main spokes then increased oil production could be expected although interference between the spokes and branches could still occur.

SPE 157804 11

Table 8: Comparison of Effective Permeability, Spokes, and Spokes & Branches model predictions

Oil Production

(m3)

Nett Propane/Oil

(liquid m3/m

3)

Effective

Permeability 4,139 0.15

Spokes 630 1.14

Spokes &

Branches 168 4.91

Nett Propane/Oil Ratio = (Propane injected Propane produced)/Oil produced

Conclusions

o Oil recovery from CSI is mostly limited to high permeability regions created during CHOPS.

o As compared to fine grid blocks, the use of coarse grid blocks in Effective Permeability model simulations resulted in a much quicker reduction in BHP during production and much lower oil rates as a result of rapid reservoir depressurization. One needs to

adjust parameter(s) to compensate for this behaviour if using coarse grid blocks.

o Changing the frequency factors for gas exsolution and/or dissolution and/or changing the dispersion coefficient values is an effective upscaling strategy.

o Ignoring non-equilibrium behaviour dramatically impacts the results and is difficult to justify especially for large grid blocks. The use of instant equilibrium results in rapid gas exsolution during production and low oil production as a result of the severe reduction

of the reservoir pressure and the elimination of foamy oil behavior.

o Increasing the reaction rate constants (frequency factors) from 0.0005 to 0.05 increased propane injectivity and decreased the BHP during an injection period. The impact on oil production was small (decreased by only 2%).

o Gas exsolution rates were increased when an extra reaction was used to bypass gas bubble formation during gas exsolution. It resulted in a 9% increase in oil production. The new reaction increased the amount of free bubbles produced at the well because it

increased the pressure drawdown rate during production.

o Performing non-isothermal simulations decreased the injection BHP and the amount of gas injected and resulted in increased oil production by 11%. Allowing for non-isothermal behaviour typically slows down simulations so this must be considered when

deciding whether to use it.

o Although the Dual Permeability and Effective Permeability models both matched specified primary oil production, there was an order of magnitude less oil production during CSI for the Dual Permeability model using instant equilibrium solubility conditions as

compared to non-equilibrium or instant equilibrium Effective Permeability model predictions.

o For the Dilated Zone model, increasing the well radial inflow parameter by a factor of 100 doubled primary oil production but increased gas production by two orders of magnitude.

o For both the Spokes and Spokes & Branches models, the predicted primary oil production was much less than the actual field values even though the oil rate was used as a well control. Much lower oil rates were also obtained during CSI as compared to the

Effective Permeability model.

o Predicted oil production for two CSI cycles with the Spokes model was about one-third of that predicted by the Effective Permeability model.

o Predicted oil production for one CSI cycle with the Spokes & Branches model was about one-seventh of that predicted by the Effective Permeability model.

o A single cycle should not be used to estimate solvent recovery as it will be low due to an unrecoverable (by pressure reduction alone) solvent inventory being built up in the part of the reservoir to where solvent penetrates. In later cycles, a greater percentage

of the injected solvent is recovered as the total solvent retention at the end of each cycle only increases a relatively small amount.

o CSI simulations are complex and slow and do not generally respond well to a dynamic refined grid approach as they are not very stable and parameters are changing frequently due to the cyclic nature of the process. Parallel simulations somewhat improve the

simulation speed.

12 SPE 157804

References

Blackwell, R.J. 1962. Laboratory Studies of Macroscopic Dispersion Phenomena. SPE J. March, 18.

Bratli, R. K. and Risnes, R. 1981. Stability and Failure of Sand Arches. SPE J. April, 236248.

Bratli, R.K. Dusseault M.B. Tronvoll, J. and Santarelli, F. 1998. Sand Management Protocol Increases Production Rates, Reduces

Completion Costs. SPE International, Proc. Trinidad and Tobago Biennial SPE Conf. Port-of-Spain.

Chang, J. 2000. System Dynamics Approaches for Sand Production Simulation and Prediction (a Semi-Analytical Implementation). MSc

Thesis, Waterloo.

Dusseault, M.B. Santarelli, F.J. 1989. A Conceptual Model for Massive Solid Production in Poorly-Consolidated Sandstones. Proc. ISRM

Int. Symp. on Rock at Great Depth, eds: Maury, V. and Fourmaintreaux. D., Balkema, Rotterdam, 2, 789-797.

Dusseault, M.B. El-Sayed, A. 1999. CHOP-Cold Heavy Oil Production. Proceedings 10th European Improved Oil Recovery Symposium,

EAGE, Brighton, August, Poster number 086.

Dusseault, M.B. Geilikman, M.B. and Spanos, T. 1998. Mechanisms of Massive Sand Production in Heavy Oils. Proceedings of the 7th

International Conference on Heavy Oils and Tar Sands, Beijing, PRC, 14p.

Geilikman, MB, Dusseault MB, 1997. Dynamics of Wormholes and Enhancement of Fluid Production. Paper presented at the 48th Annual

Technical Meeting of the Petroleum Society in Calgary, Alberta, Canada.

Geilikman, MB, Dusseault MB, 1999. Sand Production Caused by Foamy Oil Flow. Transport in Porous Media, 35 (2):25972.

Ivory, J. Chang, J. Coates R. and Forshner, K. 2010. Investigation of Cyclic Solvent Injection Process for Heavy Oil Recovery. J. Cdn. Pet.

Tech. 49 (8):2-13.

Kristoff, B.J. Knorr, K. D. Preston. C.K. Worth, K. and Sawatzky, R. 2008. Joint Implementation of Vapour ExtractionHeavy Oil Recovery Process. Paper 2008-468 presented at the World Heavy Oil Congress, Edmonton, Alberta, Canada, 1012 March.

Perkins TK, Johnston OC, 1963. A Review of Diffusion and Dispersion in Porous Media. SPE J. March, 7084.

Neuman SP, 1990. Universal Scaling of Hydraulic Conductivities and Dispersivities in Geologic Media. Water Resources Research, 26

(8):174958.

Risnes R, Bratli RK. And Horsrud, P. 1982. Sand Arching a Case Study. Proceedings of the European Petroleum Conference, EUR, 310:31318.

Sawatzky RP, Lillico DA, Vlcsak G, et al., 1996. Initiation of Sand Production in the Cold Production Process. Presented at the Petroleum

Society of CIM 47th Annual Technical Meeting, Calgary, Alberta, Canada, June.

Sawatzky RP, Lillico DA, Tremblay, et al., 2002. Tracking Cold Production Footprints. Paper 2002-086, presented at the Petroleum

Societys Canadian International Petroleum Conference, Calgary, Alberta, Canada, 1113 June.

Tremblay B. 2003. Modelling of Sand Transport through Wormholes. Paper 2003-101, presented at the Petroleum Societys Canadian International Petroleum Conference, Calgary, Alberta, Canada.

Tremblay, B. Sedgwick, G. Forshner, K. 1998. Modeling of Sand Production from Wells on Primary Recovery. J. Cdn. Pet. Tech. 37

(3):4150.

Tremblay, B. Sedgwick, G. and Vu, D. 1999. A Review of Cold Production in Heavy Oil Reservoirs. Tenth European Symposium on

Improved Oil Recovery, Brighton, UK.

Uddin, M. 2005. Numerical Studies of Gas Exsolution in a Live Heavy-Oil Reservoir. Paper SPE/PS-CIM/CHOA 97739, SPE International

Thermal Operations and Heavy Oil Symposium, Calgary, Alberta, Canada, 13 November.

SPE 157804 13

Oil

Solvent dissolved in oil

CSI well on production

Pressure Profile

Oil

Solvent dissolved in oil

CSI well on injection

Pressure Profile

Bubble

s

200 kPaa

3000 kPaa

Figure 4: Propane non-equilibrium solubility during an experiment

xC3H8Leqm

xC3H8L

xC3H8Leqm

xC3H8L

Cycle1 Cycle 2 Cycle 3 Cycle 4 Cycle 5 Cycle 6

Slow solvent dissolution

Instant solvent dissolution

Insoluble gas

FF=0.01

FF=0

Figure 2: Propane non-equilibrium solubility during

a CSI experiment Figure 3: Effect of dissolution rate on well BHP

during injection

Figure 4: 1/4 symmetry representation of different reservoir configurations being tested

Wormhole diameter = 20 cm Spoke 1

Spok

e 3

Spoke

2

Permeability = 1.56 darcy


Spok

e 3

Spoke

2


Spokes model

Spoke 1

Spok

e 3

Spoke

2

Branch 2

Bra

nch

1



Spok

e 3

Spoke

2

Branch 2

Bra

nch

1


Wormhole diameter = 20 cm

Spokes & Branches model

Porosity = 0.3


Porosity = 0.7

Permeability

= 1,000 darcy

Porosity = 0.3


Porosity = 0.7

Permeability

= 1,000 darcy

Dilated Zone model

200 m

Figure 1: Reservoir behaviour during CSI

e) d) c)

b) a) VW

High perm

region

VW

High perm

region

Effective Permeability model

Frac Perm = 10,000 darcy

Frac Trans = 1,000

In blocks with fractures,

Frac Vol/Block Vol = 0.067

Fractures


Frac Perm = 10,000 darcy

Frac Trans = 1,000

In blocks with fractures,

Frac Vol/Block Vol = 0.067

Fractures


Dual Permeability model

Dual permeability

Figure 1: Reservoir behaviour during CSI

14 SPE 157804

1

10

100

1000

10000

100000

0 0.2 0.4 0.6 0.8 1

Vis

co

sit

y (

mP

a.s

)

CH4 or C3H8 Mole Fraction in Oil

Oil-CH4

Oil-C3H8

240

2

Figure 7: CHOPS (a) oil production and (b) water production using AITF cold production model

Figure 5: Live oil viscosity

Figure 6: Solubilty and fluid transport mechanisms

Grid Block n Grid Block n + 1

SPE 157804 15

Figure 10: Impact of grid size on (a) BHP and (b) oil production (1/4 well basis)

Figure 8: Post-CHOPS porosity and effective permeability (AITF radial model)

Figure 9: Fine and coarse grids used in simulations

Porosity

Permeability

md

250 m

3.6

m

> 10,000 darcy

Porosity

Permeability

md

250 m

3.6

mPorosity

Permeability

mdPorosity

Permeability

md

250 m

3.6

m

> 10,000 darcy

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

Fine grid

Coarse grid

a) b)

36 x 36 x 7 16 x 16 x 7VW

6.49 x 6.49 m 1 x 1 m

High perm

region

Permeability:

5,000 to 100,000 darcy

1 x 1 m19.47 x 19.47 m

High perm

region

VWVW

36 x 36 x 7 16 x 16 x 7VW

6.49 x 6.49 m 1 x 1 m

High perm

region

Permeability:

5,000 to 100,000 darcy

1 x 1 m19.47 x 19.47 m

High perm

region

VWVWVW

1 m x 19.47 m 1 m x 6.49 m

36 x 36 x 7 16 x 16 x 7

16 SPE 157804

Figure 12: Impact of equilibrium versus non-equilibrium on (a) BHP and gas injection (1/4 well basis)

Figure 13: Impact of equilibrium versus non-equilibrium on (a) oil and (b) gas production (1/4 well basis)

Figure 11: Upscaling simulation results - cumulative oil production (1/4 well basis)

Fine grid = 10

Upscale 6, FFD = 0.0005, FFE = 0.05

Upscale 2, FF

D = FFE = 0.0

0005

Upscale 1, sam

e properties as

fine grid

= 0

Upscale 4, FFD = FFE = 0.5

Upscale

3, FFD

= 0.05,

FFE = 0

.05

Fine grid = 10

Upscale 6, FFD = 0.0005, FFE = 0.05

Upscale 2, FF

D = FFE = 0.0

0005

Upscale 1, sam

e properties as

fine grid

= 0

Upscale 4, FFD = FFE = 0.5

Upscale

3, FFD

= 0.05,

FFE = 0

.05

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

a) b)

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

Equilibrium

Equilibrium

Non-equilibrium

Non-equilibrium

a) b)

SPE 157804 17

Figure 14: 2-D (IJ) pressure profile in high permeability Layer 4 at end of first injection and production periods

Figure 15: Impact of extra exsolution (bypass of bubble formation) reaction on (a) gas and (b) oil production (1/4

well basis)

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

Equilibrium (30 days)

Non-equilibrium (30 days)



kPaa





kPaa

Figure 16: Impact of extra exsolution (bypass of bubble formation) reaction on propane production (a) C3H8G, (b)

C3H8L, and (c) SBubC3H8 (1/4 well basis)

Extra reaction

Extra reaction

No extra reaction

No extra

reaction

Extra reaction

Extra reaction

No extra reaction

No extra

reaction

Extra reaction

Extra reaction

No extra reaction

No extra

reaction

Extra reaction

Extra reaction

No extra reaction

No extra

reaction

a) b)

a) b)

c)

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

Extra reaction

Extra reaction

No extra

reaction

No extra

reaction

Extra reaction

No extra reaction

18 SPE 157804

Figure 18: Cumulative oil produced for different models

(1/4 well basis)

Dual permeability

Effective permeability

Spokes

Dilated zone (kh=1x105)


Spokes & Branches

Dual permeability

Effective permeability

Spokes



Spokes & Branches

Dual perm

eability

Effective p

ermeability

Spokes

Dilated zone (kh=1x

105)


Spokes & Branche

s

Dual perm

eability

Effective p

ermeability

Spokes

Dilated zone (kh=1x

105)


Spokes & Branche

s

Primary Production CSI

Figure 17: Cumulative gas injected for different

models (1/4 well basis)

Figure 20: Dual permeability model Layer 4 (a) Oil saturation and (b) propane mole fraction in oil phase in matrix and fractures

Figure 19: C3H8 mole fraction in oil phase for (a) Effective Permeability (non-equilibrium), (b) Effective Permeability

(non-equilibrium), and (c) Dual permeability models

FracturesMatrix

0 days

3,707 days, end of

Injection Period 3

3,227 days, end of

Primary Production

3,887 days, end of

Production Period 3

FracturesMatrix

0 days

3,707 days, end of

Injection Period 3

3,227 days, end of

Primary Production

3,887 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

Matrix Fracture

3,707 days, end of

Production Period 3

b)

a)

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3

Dual PermEffective Perm

< 1 x 10-5

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3


< 1 x 10-5

< 1 x 10-5

< 1 x 10-5

3,887 days, end of

Production Period 3

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3


< 1 x 10-5

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3


< 1 x 10-5

< 1 x 10-5

< 1 x 10-5

3,887 days, end of

Production Period 3

b) a)

End Inj. 3

End Prod. 3

< 0.00001

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3


< 1 x 10-5

3,707 days, end of

Injection Period 3

3,887 days, end of

Injection Period 3


< 1 x 10-5

< 1 x 10-5

< 1 x 10-5

3,887 days, end of

Production Period 3

c)

SPE 157804 19

Figure 22: (a) pressure in Layer 4 and (b) reservoir pressure for Spokes and Spokes & Branches models

Figure 21: Spokes model (a) oil saturation and oil velocity vectors and (b) gas saturation and gas velocity vectors in high permeability Layer 4

Spokes Spokes & Branches B) Spokes Spokes & Branches a)

3,227 days. End of Primary Production

3,437 days. End of

Production Period 1

3,257 days. End of Injection Period 1

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

b) Spokes & Branches

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaa3,227 days, end of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

0 days

3,227 days, end of

Primary Production0 days

3,227 days, end of

Primary Production

3,437 days, end of CSI

Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

a) Spokes

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa


3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

a) Spokes

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa


3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

a) Spokes

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa


3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2


Injection Period 2


Production 2


Injection Period 2


Production 1


Injection Period 1

a) Spokes

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

3,657 days, end

of CSI

Production

Period 2

3,477 days, end

of CSI Injection

Period 2

kPaakPaa


3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

3,227 days, end

of Primary

Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1


Production

0 days

3,437 days, end of

CSI Production

Period 2

3,257 days, end

of CSI Injection

Period 1

kPaakPaa

0 days

3,227 days, end of


3,227 days, end of

Primary Production


Production 1


Injection Period 1


Production 1


Injection Period 1


Production 2

3,47

field scale simulation of cyclic solvent injection (csi)1

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