(PDF) Development a Mechanistic Numerical Simulator for Microgel Applications in Non-Cross Flow Heterogeneous Reservoirs

SPE-175058-MS Development of a Mechanistic Numerical Simulator for Preformed Particle Gel Applications in Non-Crossflow Heterogeneous Reservoirs Abdulmohsin Imqam, Missouri University of Science and Technology; Ali Goudarzi, The University of Texas at Austin; Mojdeh Delshad, The University of Texas at Austin; Baojun Bai, Missouri University of Science and Technology Copyright 2015, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Houston, Texas, USA, 28 –30 September 2015. 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 Water channeling is caused by reservoir heterogeneities that lead to the development of high-permeability streaks. A recent interest in microgel treatment using preformed particle gels (PPGs) has drawn more attention to reducing excess water production, improving sweep efficiency, and enhancing macroscopic oil recovery. The objective of this paper is to gain an inclusive understanding of PPG transport mechanisms through heterogeneous reservoirs. A numerical simulator was developed to characterize the propagation of PPGs through given reservoir. The simulator was used to optimize the gel treatment design to enhance oil recovery from un-swept, low-permeability, and oil-rich zones. A novel core flooding experiment was conducted to validate the developed mechanistic models. The experimental results using heterogeneous permeability model without cross flow showed large incremental oil recovery from the low permeability sand pack after treatment with PPGs. The developed models were implemented into the gel transport reservoir simulator to aid in the design and to optimize the water control processes using PPGs. The results obtained from the simulator indicated a good match with core flooding experiment results. The sensitivity analysis showed incremental oil recovery was strongly dependent on the permeability contrast, PPG concentration, and PPG treatment size. Introduction In the water flooding process, water preferentially flows through the high permeability, fractures, and large channels; causing a large amount of recycled water with little benefit to oil production. Excess unwanted water production will lead to many problems such as additional water treatment, environmental issues, increased disposal costs, corrosion, and scaling. Poor sweep efficiency has been identified as one of the most important reasons for lower oil recovery during the water flooding mechanism. Reservoirs generally comprise many layers of varying permeabil- ity. Reservoir heterogeneity is the primary reservoir conformance problem that leads to poor sweep efficiency. If a non-cross-flow heterogeneity exists between the low and high permeability layers during a water flood process, the high permeability layers are often occupied by a large fraction of the displacing water injection. Consequently, the layers with low permeability would be less touched by displacing water 2 SPE-175058-MS causing a large portion of unswept oil to be left in the low permeability layers. Due to such a limitation from conventional water flooding, many techniques were proposed to overcome poor sweep efficiency and to increase the oil recovery. Gel treatment is one of those techniques that was invented exclusively to economically remedy the inefficiency in sweeping reservoirs, which is accomplished by plugging high permeability layers and diverting the displacing fluid into low permeability layers. As a result, using gel treatment with water flooding would increase the macroscopic sweep efficiency and enhance oil recovery from both high and low permeability layers. Gel treatments are designed by adding a small concentration of crosslinker to the polymer solution to link the polymer molecules. Traditionally, in-situ gels have been widely used to control reservoir conformance. The mixture of polymers and crosslinkers, called gallants, are injected into the target formation and form a gel to fully or partially seal the formation at reservoir conditions (Sydansk and Moore, 1992). This technology, however, has several disadvantages: a lack of gelation time control, gelling uncertainty due to shear degradation, chromatographic separation between the polymer and crosslinker, and dilution by formation water and minerals; these factors restrict the application of in-situ gels for conventional reservoirs (Chauveteau et al., 1999, 2001, 2003; Coste et al., 2000; Bai et al., 2007a, 2007b). In recent years, newer preformed gel systems have been developed to overcome these disadvan- tages. These preformed gels have a better performance because they are created at surface facilities and are then injected into the target zones with no need for gelation to occur under reservoir conditions. Currently available commercial preformed gels include preformed particle gel (PPG), microgel, and submicron gel. They differ mainly in particle size, swelling ratio, and swelling time (Imqam et al., 2014). PPGs are particles superabsorbent crosslinking polymer that can swell up to 200 times their original size in brine. A PPG is a particle between a micron and a millimeter in size that is formed at the surface. It is then dried and crushed into small particles for injection into a reservoir (Coste et al., 2000; Bai et al., 2007a, 2007b). Several experimental studies have been conducted to investigate the mechanism and performance of PPG injection to reduce unwanted water production and increase oil recovery. Bai et al. (2007b) investigated PPG transport mechanisms through porous media; they used etched glass micromodels and sand pack macromodels. They found that PPG propagation through porous media exhibited different patterns of behavior. They also reported that the PPG propagation pattern of behavior was dependent on the gel strength, threshold pressure, and pore throat structure. Zhang and Bai (2011) constructed transparent fracture models to visually track PPG transport through open fractures and to monitor water flow through the PPG that was placed in the fractures. They observed that the PPG propagated like a piston when the PPG size was larger than or close to the fracture width. In addition, they found that water injection through the PPG created several channels, allowing water to be produced from the outlet. Imqam et al. (2014a) investigated PPG injection and placement mechanisms through conduits or large channels, under conditions where the channel opening size was larger than, equal to, or smaller than the swollen PPG size. Their results indicated that PPG strength affected injectivity more significantly than did the particle opening ratio. Additionally, the size of the PPGs decreased during their transport though the channels due to both dehydration and breakdown. Subsequent work conducted by Imqam and Bai (2015a) to further understand the resistance of PPGs to water flow. They designed a large transparent channel to investigate factors such as PPG strength, PPG size, and load pressure on the PPG placement behavior. They reported that the PPG did not fully block the channel but rather formed gel pack permeability along the channel model. When Gel pack permeability decreased means PPG blocking efficiency to water flow increased. Results showed that the gel pack permeability decreased when the gel strength, particle size, and load pressure increased. Further work was also conducted by Imqam and Bai (2015b) to evaluate the PPG injection and resistance to water flow through super-K permeability formations. They used a sand pack model to evaluate the effects of the PPG strength, size, concentration, and sand permeability on PPG injection process and it’s resistance to water flow. They found that fully swollen gel particles have a better SPE-175058-MS 3 injectivity than partially swollen particles with a larger diameter. The blocking efficiency of PPGs to water flow increased as the strength, size, and concentration of the PPGs increased. All the previous work was focused on PPG propagation and placement through fractures, conduits, channels, and high permeability features. Imqam et al. (2014b) conducted a study on the effect of PPG placement on low permeability formations. They investigated the effect of gel strength and rock permeability on the PPG placement behavior. They observed that the PPG formed a permeable gel filter cake on the surface of low permeability rocks. The strength of the cake was dependent on gel strength, rock permeability, and injection pressure. The effect of water and oil flow on PPG behavior was studied by Imqam et al. (2014c). They used a closed fracture to study PPG placement behavior through fractures when there was both oil and water flow. During the water and oil cycle process, they noticed that the PPG always reduced the fracture permeability to water much more than to oil permeability. Imqam et al. (2014c) observed that a higher oil viscosity had better disproportionate permeability reduction than when the oil viscosity was low. Even after all of these laboratory experiments effort to evaluate the PPG, there is still a need to develop a reservoir simulator to upscale the lab results for field conditions and to optimize the PPG design. Goudariz et al. (2013, 2015) used an UTGEL simulator to simulate and match the lab data obtained from the fracture and sand pack homogenous rocks. They reported that the PPG transport models such as PPG rheology, adsorption, swelling ratio, and permeability reduction, were successfully developed and imple- mented in the reservoir simulator. Goudariz et al. (2014) extended the simulation work o study nano-PPG transport through core sandstone. They showed that the UTGEL simulator was capable of simulating and matching the lab results. However, the previous two simulations studies were only focused on evaluating the PPG in a single fracture with homogenous sand pack core permeability. They did not consider the heterogeneity within the reservoir. The ultimate objective of this work was to develop a mechanistic simulator that can be adapted to model PPG use for improved oil recovery in heterogeneous reservoirs. It is aimed to investigate the factors that affect PPG efficiency to improve macroscopic efficiency in un-swept/oil rich low permeability layers. This work was designed to optimize PPG design by investigating the effects of the permeability contrast ratio, PPG slug volume, PPG concentration, and anisotropy on increasing oil recovery from non-crossflow heterogeneous reservoirs. The lab results were used as a base case to validate the results obtained from the developed mechanistic simulator. UTGEL Reservoir Simulator Development Description The UTGEL is a finite difference three-dimensional multiphase multi-component chemical composition reservoir simulator that can be used for modeling chemical enhanced oil recovery (EOR) processes. Its main applications are water flooding, controlling excess water production using different types of gels, and polymer flooding. The UTGEL can be used to model both laboratory and field scales. A compre- hensive module is available for polymer and gel rheological and transport properties, such as shear thinning viscosity, adsorption, resistance factor, and inaccessible pore volume. Mass Balance Equation The gel particle is treated as a solute in the aqueous phase. The mass balance equations are solved for water, oil, total anions, total divalent cations, and PPG species. The aqueous phase pressure is obtained by computing the overall mass balance of water and oil. The assumptions for developing the flow equations are as follow: ● The rock and fluids are slightly compressible. ● Darcy’s law applies. ● Mixing is ideal. ● Fickian dispersion with the full tensor dispersion coefficient is used. 4 SPE-175058-MS ● The boundary conditions of no flow and no dispersive flux across the impermeable boundaries are used for the flow equations. The mass conservation equation for each component in terms of the overall volume per unit of pore volume is defined as (1) where is the overall volumetric concentration of the component k. ␳K is the density of pure component k. C␬ᐉ is the concentration of the component k in phase ᐉ, is the volumetric flux of phase ᐉ, is the dispersive flux of the component k in phase ᐉ, and Q␬ is the injection or production rate for the component k per the bulk volume k. The overall volume of the component k per unit of pore volume is computed as follows: (2) where is the overall volumetric concentration of the component K, nc is the number of components, is the adsorbed concentration of species k, and Sᐉ is the saturation of phase ᐉ. PPG Transport Model There are many conditions that affect how particles flow and transport through porous media. The viscosity, resistance factor, and residual resistance factor are most important properties for modeling PPG flow in porous media. The resistance factor and residual resistance factor are functions of the salinity and flow rate based on the laboratory results. To model the flow of PPG particles through pore throats, the swelling ratio and subsequent size of the swelled particles need to be calculated. The average pore throat radius was calculated using porosity and permeability: (3) where the average permeability, , was approximated using the following: (4) where Kx, Ky, and Kz are directional permeabilities, uxᐉ, uyᐉ, uzᐉ are components of fluxes in each direction for the aqueous phase and uᐉ is the aqueous phase flux. In each grid cell, the pore throat size was calculated based on Equation 3, and then permeability and porosity were assigned to that grid cell. The PPG will move out of a grid block depending on the size of the particles in comparison to the pore throat diameter assigned to the grid block. If the PPG cannot pass through the grid block, the resistance factor is calculated and the aqueous viscosity is increased accordingly (Goudarzi et al., 2013, 2014). The conditions for passing PPG particle through the pore throat for weak and strong PPG particles (Bai et al., 2004) are as follows: ● For weak PPG particles: if the PPG particle diameter is less than 5.7 ⫻ dp. ● For strong PPG particles: if the PPG particle diameter is less than 1.3 ⫻ dp. where dp is the average pore throat diameter. Using the above criteria for weak and strong gels, the PPG particles would pass through the pore throat. If the above conditions for a specific gridlock hold and the PPG can pass through the pore throat, then the gel particles will enter that specific grid block and the SPE-175058-MS 5 PPG will cause resistance to the water flow. The PPG will increase the viscosity of the aqueous phase and a new effective viscosity for water will be calculated as defined below: (5) (6) The resistance factor (RF) is used during PPG injection. The residual resistance factor (RRF) is calculated for post water injection. This increase in water viscosity leads to reduction of water phase mobility, improvement in the mobility ratio, and subsequently delayed water production. Swelling Ratio Model The swelling ratio can be defined as the ratio of the PPG particle volume before and after swelling. Bai et al. (2010) and Imqam et al. (2014b) reported a relationship for the swelling ratio as a function of the salinity based on laboratory measurements. Both studies showed that PPG can swell very quickly within 60 minutes and that final swelling ratio depends on the salt concentration. The higher the salt concen- tration the lower the swelling ratio. This result is presumably due to the static electric repulsive force and charge balance. At low salt concentrations, the electric repulsive force will separate the gel molecules and create more space for water to enter (Bai et al., 2004; Imqam et al., 2014b). The following empirical correlation was developed to compare the swelling ratio vs. the effective salinity to fit the laboratory data: (7) where ap and np are model parameters, SF is the swelling ratio, and CSEP is the effective salinity (CSEP⫽ C5 ⫹ ␤P C6) in meq/ml, which takes into account the combined effect of anions (C5) and divalent cations (C6) on the swelling ratio. ␤P is the input parameter in the model and is obtained based on lab data. The effect of pH is not considered in this model. PPG Viscosity Model The UTGEL models the viscosity of an aqueous solution containing gel as a function of the gel concentration and the water viscosity as shown below (Thurston et al. 1987): (8) where Cppg, 1 is the PPG concentration in the aqueous phase, ␮w is the water viscosity, and Appg, 1 and Appg, 2 are model parameters. PPG Resistance Factor Model with Salinity Effect Gel can reduce the water effective permeability, where the degree of permeability reduction depends on the gel type, salinity, hardness, shear effects, and rock properties. The resistance factor (RF) is determined by the ratio of the differential pressure for the PPG injection to that of the initial water injection, which can be expressed as (9) where Kw and KPPG are effective permeabilities during water flood and PPG injection, ␮w and ␮PPG are water and PPG viscosities, and ⌬pwater, ⌬pPPG are the pressure drop during water flood and PPG injection. It is clear that the resistance factor decreases as the flow rate increases indicating the shear thinning behavior of PPGs (Zhang et al., 2010; Imqam et al, 2014a). The viscoelastic behavior of the PPG relates to the coil structure of the polyacrylamide molecules which produce a flexible nature (Green and Willhite 6 SPE-175058-MS 1998). The resistance factor is sensitive to the water hardness (i.e., calcium and magnesium concentra- tions). The following correlation was proposed but additional laboratory data is required to validate it (Goudarzi et al. 2015): (10) The resistance factor is expressed as (11) (12) where a11, a12 and b1 are model parameters, CSEP is the effective salinity (CSEP⫽ C5⫹␤P C6) in meq/ml, which takes into account the combined effect of anions (C5) and divalent cations (C6) on the resistance factor; is the equivalent shear rate; is the gel solution viscosity at that low shear rate; and Pa are model parameters; is the shear rate correction; |uᐉ| is the magnitude of the flux; and Krᐉ is the relative permeability of the phase ᐉ. The proposed model considers the effect of the flow rate and the salinity on the resistance factor. Residual Resistance Factor with Salinity Effect Model The residual resistance factor, RRF, is defined as the ratio of the pressure drop during post-water injection to the pressure drop during the initial water flood as follows: (13) where ⌬pBase Water, ⌬p Post Water are the pressure drop during the initial water and post-water injections. Similar to the resistance factor, the residual resistance factor decreases as the flow rate increases (Zhang et al., 2010; Imqam et al., 2014a). The residual resistance factor was sensitive to the brine hardness (i.e., calcium and magnesium concentrations). The following correlation was used but needs additional laboratory data for validation: (14) Accordingly, the final developed model for the residual resistance factor is expressed as follows: (15) where a21, a22, and b2 are model parameters and is the equivalent shear rate. The new proposed model considers the combined effects of the shear rate and the salinity on the residual resistance factor. PPG Retention Model A new model was developed and implemented into the simulator to consider the PPG retention. The UTGEL uses the Langmuir isotherm for PPG retention (adsorption) and includes the PPG concentration and salinity as shown below: (16) (17) where CPPG,1 is the PPG concentration in aqueous phase 1 and the parameters a14,1, a14,2, and b14 are the input parameters. SPE-175058-MS 7 Experimental Description to Validate the Simulator The following are descriptions of the materials and equipments used to conduct the heterogeneity experiment. Preformed Particle Gel (PPG). A superabsorbent polymer was used as a PPG to conduct the experiment. Dry particles with a mesh size of 170-200 (90-75 micron) were swollen in a 1% sodium chloride (NaCl) solution. A gel concentration of 2000 ppm was used. Brine Concentration and Oil Viscosity. A 1 wt% of NaCl was used for brine flooding and to prepare the swollen PPGs. Heavy oil with a viscosity of 195 cp at 70 °F was used to saturate the sand pack model. Magnetic Stirring Vessel. An accumulator with a 1200 ml capacity and a maximum adjusted impeller speed of 1800 r/min was used to inject the PPG into a high permeability sand pack model. The impeller was placed at the bottom of the accumulator to keep the PPG dispersed in the brine before it was injected into the model. Sand Packs. Two sizes of silica sand were used to obtain different permeability contrast between the models. Both 18-20 and 100-120 mesh sizes were used to obtain a high and low permeability sand pack, respectively. Silica sand was packed into two separate tubes having the same length and area. Experimental Setup The setup used in this experiment is shown in Figure 1. Two tubes of the same dimensions (20 cm in length and 2.7 cm in diameter) were used to contain the silica sand pack. Two horizontal (parallel in position) tubes were packed with different sizes of sand grains to model the permeability contrast present in reservoirs. A syringe pump was used to inject the suspended PPG, brine, and oil from accumulators into the sand pack models. Two pressure transducers were mounted in the front of each sand pack model to acquire the injection pressure change during the brine flooding and the gel treatment processes. The test tubes were kept at the outlets of each sand pack to collect the volume of the effluents. The collected volume was used to determine the gel penetration into each sand pack’s permeability layer. Figure 1—Schematic diagram of the apparatus used in the non-crossflow experiment. Experimental Procedures The experiment was designed to investigate the effect of heterogeneous sand formations on the injection pressure, oil recovery factors, and water cut measurements. The following are the procedures used to conduct the experiment. 8 SPE-175058-MS Preparing and saturating the sand pack models A vibrator machine was used to prepare the different sizes of silica sand so that the desired sand pack permeability could be obtained. The sand pack models were vacuumed for at least 6 hr. They were fully saturated with 1% NaCl to determine the pore volume, porosity, and permeability. Oil with a high viscosity was injected from the accumulator into each sand pack at a rate of 1 ml/min. The oil was injected until no water was produced and the injection pressure became stable. The brine volume produced was recorded to determine the original oil in place (OOIP) and the irreducible water saturation for each sand pack model. The permeability, pore volume, porosity, irreducible water saturation, and original oil in place obtained for the experiment are summarized in Table 1. Table 1—Sand Pack Permeability Properties for a Permeability Contrast Ratio of 44 Test # Permeability Contrast ratio Permeability (Darcy) Pore volume (gm) Porosity (%) Swi (%) OOIP (cc) 1 44 High 22.1 41.87 34.84 26 30.8 Low 0.5 24.9 20.72 12 21.8 The both sand packs (low and high permeability) were connected to each other (as illustrated in Figure 1) and the first water flooding process began. First water flooding A 1% NaCl solution was injected into both low and high permeability layers at a rate of 1 ml/min to simulate secondary oil recovery conditions. The oil and water production from each permeability level was recorded separately for every 3 ml. The brine was injected into the sand packs until no oil was produced and the brine injection pressure became stable. Both the oil recovery and the water cut were determined for the low and the high sand pack permeability during the first water flooding. PPG treatment The PPGs that had been swollen in the 1% NaCl solution with a concentration of 2000 ppm were injected into the sand packs at a rate of 1 ml/min after the first water flooding processes were complete. The volume of oil and water production at the outlet was monitored during the 0.5 PV of PPG injection treatment. Second water flooding A 1% NaCl solution was injected again at the same injection rate after the PPG treatment to determine if the PPG performance would improve oil recovery from the low permeability or un-swept zones. Brine was also injected until no oil was produced at the outlets and the injection pressure became stable. Results and Analysis This section discusses the results obtained from the experiment and simulation. The simulation results include the matching lab data and synthetic simulation results. Core Flooding Experimental Results The injection pressure, oil recovery, and water cut obtained from the heterogeneity experiment with a permeability contrast ratio of 44 are discussed as follow. Injection pressure measurements The injection pressure measured during the first water flooding, the PPG injection, and the second water flooding is plotted in Figure 2. During the first water flooding, the injection pressure was slightly different at each low and high permeability layers. These differences were related to the differences in permeability SPE-175058-MS 9 between the layers. The pressure became stable at approximately 0.5 psi for both permeabilities when around 0.5 PV of brine was injected. Figure 2—Injection pressure measurement during water flooding and PPG treatments. During the PPG treatment, the injection pressure rose significantly more than the previous injection pressure during water flooding. It increased sharply in both the low and the high permeability layers. The PPG injection was less obvious in the low permeability than in those with high permeability. The PPG injection pressure rose to 7 psi (approximately 14 times more than the pressure recorded in the first water flooding). Water was injected again after the PPG treatment was complete. The injection pressure began to decline, becoming stable after around 2 PV of water injection. The post-water injection pressure, however, was still much larger than the water injection pressure before the PPG injection. The injection pressure after the PPG treatment increased approximately 10 times more than the injection pressure recorded before the PPG injection. Oil recovery The oil recovery determined for the low permeability layer, the high permeability layer, and the total permeability as a function of the production pore volume are plotted in Figures 3 and 4. 10 SPE-175058-MS Figure 3—Oil recovery for (a) a low permeability of 0.5 Darcy and (b) a high permeability of 22.1 Darcy. Figure 4 —Oil recovery obtained from low or high permeability and the total permeability. In the initial water flooding, a large volume of oil was recovered from the high permeability layer in contrast to a very small volume of oil being recovered from the low permeability layer (Figure 3). The production pore volume results indicated that a larger amount of water flowed through the high permeability layer than through the low permeability layer. Therefore, low oil recovery was obtained from the low permeability layer. Nearly all of the injected water during this stage was diverted into the high permeability layer. More than 2 PV of water was injected through the high permeability layer. In contrast, less than 0.1 PV of water was injected through the low permeability layer. During the PPG injection, the sweep efficiency of the heterogeneous improved and the amount of oil recovered from the low permeability layer began to rise. A significant amount of oil was recovered from the low permeability layer during the second water flooding. A large amount of PPG suspension remained in the high permeability layer, helping reduce the permeability contrast between the layers. This helped to improve the sweep efficiency of the heteroge- SPE-175058-MS 11 neous layers and increased oil recovery from the low permeability layer. The oil recovered from the low permeability layer rose substantially more than it did in the high permeability layer. The recovery factor obtained from the low permeability increased to 35%. This significant increase in oil recovery reveals the PPGs efficiency in blocking the high permeability layer and diverting most of the water flooding flow to the low permeability layer. Figure 4 illustrates the oil recovery from the high permeability (upper curve), total oil recovery (middle curve), and the oil recovery from the low permeability (lower curve) as a function of the total injection pore volume. The oil recovery of the high permeability layer during the initial water flooding was higher than that of the low permeability layer. The oil recovery reached approximately 50% in the high permeability layer; it reached approximately 1% in the low permeability layer. As a result, the high permeability contrast ratio created a large oil volume that remained in the low permeability layer. During the second water flooding, however, the amount of oil recovered from the low permeability layer increased. It approached the total oil recovery. At the end of the second water flooding process, the oil recovered from the low permeability layer reached 35 %, while the oil recovered from the high permeability layer reached 52%. Thus, PPGs can effectively increase the oil recovered from oil-rich, low permeability layer. Water cut The water cut measurements for the both high and low permeabilities (total permeability) as a function of the total injection pore volume is plotted in Figure 5. During the first water flooding, the water cut percentage increased substantially during the first 0.5 PV brine injection. The water cut began to stabilize when 1 PV of brine was injected. The water cut was higher than 90% at the end of the first water flooding. When the PPG was injected, the water cut began to fall slightly. When the second water flooding was resumed, the water cut significantly dropped to around 80%. The water cut fluctuated during the second water flooding between 80 and 90%. This decline in water cut indicates that the PPG was effectively blocking the water channels and diverting the water floods to displace more oil from the low permeability layer. Figure 5—The water cut for the total permeabilities. 12 SPE-175058-MS UTGEL Simulator Results Simulation of heterogeneous parallel sandpack A 2D Cartesian model (two layers) was used to simulate the water and PPG injection into the heterogeneous sandpack without crossflow to model the oil recovery and water cut measurements from the experiment (Figure 6). The upper layer had a high permeability of 22,100 md and the lower layer had a lower permeability zone of 500 md. Similar to the experiment, there was no crossflow between layers. Due to the high permeability contrast between the layers, different residual oil saturations, relative permeability endpoints, and relative permeability exponents were assigned to each layer. Figure 6 —Simulation model for the heterogeneous sand pack experiment (without crossflow). After saturating and preparing both sand packs, they were flooded with 1.74 PVs of brine at the flow rate of 1 ml/min and then flooded with 0.3 PVs of PPG at the rate of 1 ml/min. Finally, 1.74 PVs of post-water was injected again at the same rate of 1 ml/min. The oil recovery was nearly 46% OOIP. A summary of the rock and fluid properties used in the experimental design is shown in Table 2. Table 2—Fluid and Petrophysical properties used in the simulator. Resistance factor and residual resistance factor parameters are based on the measured data. To model a heterogeneous sandpack experiment, the following equations for the resistance factor and residual resistance factor were used in the simulator as a function of the salinity and flow rate in each grid block. SPE-175058-MS 13 (18) (19) Different values of the residual oil saturation and relative permeability parameters were assigned for the high and low permeability sandpacks without communication between the layers. A comparison of the measured and simulated oil recovery is shown in Figure 7. The water cut is compared in Figure 8. The favorable comparison of the simulated and the experimental results indicated that the gel transport models could accurately model gel injection behavior. Figure 7—Comparison of measured and simulated oil recovery. Figure 8 —Comparison of measured and simulated water cut. 14 SPE-175058-MS Simulation of synthetic cases Base case A Cartesian model was designed to simulate the PPG injection for conformance improve- ment. The injection was at a constant rate and the production was at a constant pressure. The base case had a high permeability layer of 1500 md located in the middle, while the upper and lower layers had a permeability of 50 md as shown in Figure 9. A constant PPG concentration of 1000 ppm was injected at the injection well and it was monitored to determine if and how it would improve the recovery by blocking the high permeability layer and diverting water into the low permeability upper and lower layers. Figure 9 —Simulation model and permeability representation. There was an interaction between layers, and the kv/kh ratio of 0.1 was used for the crossflow between layers. Table 3 gives the input data including model properties and the PPG injection design. The water flood was compared with the PPG injection and the results indicated considerable improvement in oil recovery (around 7% OOIP incremental) as shown in Figure 10. The simulation results illustrated that the layer with the higher permeability was more favorable to the injected PPG and that the injected water will divert into the upper and lower layers. Several simulations were performed to study the impact of the injection design and reservoir properties. SPE-175058-MS 15 Table 3—Base case data used for the PPG study and sensitivity simulations. Figure 10 —Comparison of oil recovery between the water flood and the PPG flood for the base case. PPG treatment size The typical treatment size was around 5% of the channel volume (CV). However, this can vary from 5% to 15% of the channel volume depending on the PPG dilution, vertical to horizontal permeability ratio, and dispersion among other factors. Figures 11 and 12 show the incremental oil recovery and water cut sensitivity to the gel treatment size, respectively. The results demonstrate that higher treatment size is favorable. However, it should be noted that increasing the PPG slug above 15% would not considerably improve the oil recovery, although it will increase the PPG treatment cost. 16 SPE-175058-MS Figure 11—Comparison of the oil recovery for different treatment sizes. Figure 12—Comparison of the water cut for different treatment sizes PPG concentration The PPG treatment concentration for the base case was chosen to be 1000 ppm. However, concentrations of 10000 and 15000 ppm were used to investigate the PPG concentration effect on the oil recovery. Figure 13 shows the incremental oil recovery sensitivity to the PPG concentration. The results demonstrate that a higher PPG concentration is favorable. However, it should be noted that increasing the PPG concentration above 15000 ppm would not greatly improve the oil recovery. SPE-175058-MS 17 Figure 13—Comparison of oil recovery for different PPG concentrations Permeability contrast The permeability contrast is one of the key factors affecting the success of this conformance treatment. As shown in Figure 14, higher contrast is desirable for better efficiency because with high permeability contrast, the thief zone takes more of the injected PPG, and its performance will increase. Figure 14 —Impact of the permeability contrast (thief zone and the rest of the reservoir) on the incremental oil recovery. Crossflow The vertical to horizontal permeability ratio (Kv/kh) is another factor that can impact the performance of the PPG treatment. The lower the kv/kh ratio, the more the PPG will be placed into high permeability, with more effective permeability reduction. However, when there is a large kv/kh ratio, the PPG can divert into low permeability zones which is undesirable. Figure 15 shows the impact of the kv/kh ratio on the incremental oil recovery. 18 SPE-175058-MS Figure 15—Impact of the Kv / Kh ratio on the incremental oil recovery. Conclusion This paper presented the recent development in the UTGEL reservoir simulator for preformed particle gel treatment. Six models were successfully implemented in the simulator. Experimental core flooding results were used to validate simulation results. Sensitivity analyses were performed for better PPG treatment design in the heterogeneous reservoirs without cross flow. The following are the main conclusions drawn from this study: ● The experimental results indicated that oil recovery from the low permeability sandpacks was improved significantly after PPG injection. ● The water injection pressure after PPG treatment increased significantly more than the water injection pressure before PPG injection. ● A numerical model with flow and transport capability was successfully developed for preformed particle gel to aid in the design and optimization of the PPG water control processes. ● Water flooding cycles and PPG treatment results were modeled and were successful history matched. ● The simulation results indicated that high permeability contrast is desirable for PPG injection. PPG increases sweep efficiency as the contrast in the permeability increases. ● We developed models for gel rheology, retention, swelling ratio, resistance factor, and residual resistance factor based on the laboratory results and implemented them in the gel simulator. ● The simulator results illustrated that the PPG key design variables are treatment size, PPG concentration, permeability contrast, and the ratio of vertical to horizontal permeability. Acknowledgement The funding for this project is provided by RPSEA subcontract #11123-32 for water management in a small producer program. RPSEA ( www.rpsea.org) is a nonprofit corporation whose mission is to provide a stewardship role in ensuring the focused research, development and deployment of safe and environ- mentally responsible technology that can effectively deliver hydrocarbons from domestic resources to the citizens of the United States. SPE-175058-MS 19 Nomenclature Appg,1, Appg,2 Gel viscosity parameters in UTGEL a11, a12, b1 Resistance factor model parameters a21, a22, b2 Residual resistance factor model parameters a14,1, a14,2, b14 PPG retention model parameters ap, np Swelling ratio model parameters PPG concentration in aqueous phase, Adsorbed concentration of PPG , ppm , Overall volumetric concentration of component k, Adsorbed concentration of species ␬ C␬ᐉ Concentration of component k in phase ᐉ, volume fraction CSEP Effective salinity, meq/ml Dispersive flux of component k in phase ᐉ dp, rh Average pore throat diameter, Pore throat radius, ft k, Permeability, Average permeability, md kw, kPPG Effective permeability during water flood , Effective permeability during PPG injection kx, ky, kz Directional permeabilities, md krᐉ Relative permeability for phaseᐉ Q␬ Injection or production rate for component ␬ per bulk volume, ft3/Day ⌬PPPG PPG injection pressure drop, psi ⌬PBaseWater, PPostWater Initial water injection pressure drop, Post water injection pressure drop, psi RF, RRF Resistance factor, Residual Resistance factor SF Swelling ratio Sᐉ Saturation of phase u1 Aqueous phase flux ux1, uy1, uz1 Components of darcy flux for aqueous phase, ft/Day ␳␬ Density of pure component ␬, lb/ft3 ␮aqueous phase Water phase viscosity (cp) ␮1, ␮w, ␮PPG Aqueous solution containing gel viscosity, Water viscosity, PPG viscosity, cp Shear rate correction ␾ Porosity References Bai, B., Li, L., Liu, Y., Liu, H., Wang, Z., and You, C. 2007a. 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