Pressure Measurements for Monitoring CO 2 Foam Pilots

: This study focuses on the use of pressure measurements to monitor the effectiveness of foam as a CO 2 mobility control agent in oil-producing reservoirs. When it is applied optimally, foam has excellent potential to improve reservoir sweep efﬁciency, as well as CO 2 utilization and storage, during CO 2 Enhanced Oil Recovery (EOR) processes. In this study, we present part of an integrated and novel workﬂow involving laboratory measurements, reservoir modeling and monitoring. Using the recorded bottom-hole pressure data from a CO 2 foam pilot study, we demonstrate how transient pressures could be used to monitor CO 2 foam development inside the reservoir. Results from a recent CO 2 foam pilot study in a heterogeneous carbonate ﬁeld in Permian Basin, USA, are presented. The injection pressure was used to evaluate the development of foam during various foam injection cycles. A high-resolution radial simulator was utilized to study the effect of foam on well injectivity, as well as on CO 2 mobility in the reservoir during the surfactant-alternating gas (SAG) process. Transient analysis indicated constant temperature behavior during all SAG cycles. On the other hand, differential pressures consistently increased during the surfactant injection and decreased during the subsequent CO 2 injection periods. Pressure buildup during the periods of surfactant injection indicated the development of a reduced mobility zone in the reservoir. The radial model proved to be useful to assess the reservoir foam strength during this pilot study. Transient analysis revealed that the differential pressures during the SAG cycles were higher than the pressures observed during the water-alternating gas (WAG) cycle which, in turn, showed foam generation and reduced CO 2 mobility in the reservoir. Although pressure data are a powerful indicator of foam strength, additional measurements may be required to describe the complex physics of in situ foam generation. In this pilot study, it appeared that the reservoir foam strength was weaker than that expected in the laboratory.


Introduction
CO 2 foam injection is an effective method for controlling CO 2 mobility during enhanced oil recovery (EOR) processes in petroleum reservoirs [1]. When it is performed optimally, CO 2 foam has excellent potential to improve sweep efficiency [2][3][4][5][6][7][8] and CO 2 storage potential. Foam is a mixture consisting of a continuous liquid phase (surfactant solution) and a gas phase (CO 2 ). This mixture becomes discontinuous due to the generation of thin liquid films called lamellae [9]. The mobility of foam depends on its texture: the finer the foam's texture, the lower the CO 2 mobility. It has been shown that foam density is a direct function of the density of the lamellae [10]. Laboratory studies clearly show that foam strength is very important in achieving the desired reservoir displacement efficiency. Additionally, the solubility of the surfactant in CO 2 and water phases, as well as the adsorption of CO 2 on rocks, play a crucial role during foam displacement [11].
Surfactants are commonly used to generate and stabilize foams in porous media. They are screened to ensure the success of a CO 2 foam. Recent research has suggested various surfactants (cationic, nonionic, and zwitterionic) as the main candidates for CO 2 foams in EOR [12]. Several studies have been conducted to examine the texture and stability of CO 2 foams as a function of the surfactant structure and formulation. These variables include the water/CO 2 ratio, surfactant concentration, water salinity, etc. Previous research shows that surfactant characteristics, along with foam strength, can be adjusted to ensure optimum foam displacement during CO 2 EOR processes. However, surfactant-based foams break down in the formation due to the presence of oil and the adsorption of the surfactant to rock, and at high temperatures and salinities. Therefore, it is also important to maintain foam strength (or stability) during the entire injection period in field applications. Recent work suggests that the addition of silica nanoparticles to surfactant-stabilized CO 2 foams may increase the strength and stability of foam systems [13].
There are several strategies to generate foam in porous media. These include the co-injection of gas (CO 2 )/surfactant or surfactant-alternating gas (CO 2 ) injection (the SAG method). In the co-injection process, the gas (CO 2 ) and the surfactant solution are simultaneously injected, and foam is formed in situ. In the SAG method, the surfactant and CO 2 are injected in alternating slugs. In low-permeability reservoirs, SAG injection may be preferred due to increased gas injectivity. Additionally, with the use of the SAG method, the contact between CO 2 and water is minimized, which may reduce corrosion in surface facilities and piping [14].
Laboratory studies using reservoir cores are used to define the optimum recipe at a given reservoir pressure, temperature, and water salinity. For the application of foam in reservoirs where heterogeneity is involved, reservoir monitoring is carried out to assess foam development under reservoir conditions. While seismic, resistivity, electromagnetic and pressure measurements have been suggested in the oil industry, foam monitoring is typically carried out through flow and bottom hole pressure measurements, injection logging and the use of fluid tracers. These measurements are, in turn, used to assess the effectiveness of foam as a mobility control method and, hence, provide a way in which to remedy any underperforming CO 2 floods. In this way, the design of the foam can be adjusted to improve oil recovery, CO 2 utilization and storage.
In this study, we present the pressure monitoring part of an integrated and novel workflow involving laboratory measurements, reservoir modeling and monitoring. The laboratory studies were conducted on reservoir core samples to determine the optimal foam formulation. Reservoir modeling was carried out to decide on optimum injection strategy, and extensive reservoir monitoring was conducted to assess the effectiveness of the designed foam under reservoir conditions. The results of this integrated research work provide important knowledge for future CO 2 EOR field applications.

Pressure Testing for Foam Monitoring
In the petroleum industry, transient pressure testing is typically used to investigate reservoir characteristics such as permeability, reservoir boundaries, etc., as well as the well performance such as productivity or injectivity, skin effects, etc. Fall-off testing is an effective method for monitoring water or foam injection. Typically, fall-off tests are conducted by ceasing the injection and analyzing the transient pressure to assess any mobility changes near the injector [15]. In such tests, bottom-hole pressures are recorded at the injection well, and the data are used to examine the reservoir mobility changes caused by the injection. Foam injection affects the mobility distribution in the reservoir; therefore, the location of the foam front can be monitored, in principle, by fall-off tests. These tests rely on single-point pressure measurements and may lack the resolution required in layered formations.
Based on previous comparable studies with CO 2 injections [16], it has been suggested that crosswell pressure testing, in addition to seismic and electromagnetic data, could be deployed for CO 2 foam monitoring. In crosswell pressure testing, a series of pressure pulses is induced by shutting down the injector, and the pressure measurements are taken at the observation well. These measurements could be used to examine the inter-well Energies 2022, 15, 3035 3 of 16 reservoir connectivity. The main advantage of these tests is the larger investigation volume away from the injector.

Field Pilot Description
A surfactant-stabilized foam was chosen to reduce the CO 2 mobility in this field. The surfactant system was selected based on laboratory measurements of surfactant adsorption. The foam stability was also verified during these laboratory studies. A surfactantalternating gas (SAG) injection strategy was adapted, with 10 days of surfactant solution injection followed by 20 days of CO 2 injection. The pilot injection began in May 2019. Monitoring surveys during this pilot study included CO 2 injection profiles, CO 2 tracer tests, the collection of bottom-hole injection pressure/temperature and three-phase flow rates.
The pilot study was performed in the East Seminole Field, Permian Basin, West Texas, and the study area was an inverted 40 acre 5-spot pattern which included a central injection well and four surrounding producers ( Figure 1). The oil was produced from the San Andres formation, which is classified as a heterogeneous cyclical carbonate. The reservoir interval had an average permeability of 13 mD, pay thickness of 110 ft, and consisted of six flow zones separated by impermeable flow barriers. The pilot area was selected based on rapid CO 2 breakthrough, high GORs in the producers as well as relatively short well distances [17,18]. Two production wells, P1 and P4, were the focus of the baseline data collection and pilot monitoring because they exhibited the most rapid CO 2 breakthrough time from tertiary CO 2 injection. Composite logs from the pilot injection well indicated a 10 ft thick high permeability streak of 200 mD. Historical injection profiles showed that this zone has been taking most of the injected CO 2 . Therefore, this high permeability zone was targeted because foam can form in high permeability streaks and diverting flow to unswept regions of the reservoir with lower permeabilities. The reservoir and fluid properties are shown in Table 1. pulses is induced by shutting down the injector, and the pressure measurements are taken at the observation well. These measurements could be used to examine the inter-well reservoir connectivity. The main advantage of these tests is the larger investigation volume away from the injector.

Field Pilot Description
A surfactant-stabilized foam was chosen to reduce the CO2 mobility in this field. The surfactant system was selected based on laboratory measurements of surfactant adsorption. The foam stability was also verified during these laboratory studies. A surfactantalternating gas (SAG) injection strategy was adapted, with 10 days of surfactant solution injection followed by 20 days of CO2 injection. The pilot injection began in May 2019. Monitoring surveys during this pilot study included CO2 injection profiles, CO2 tracer tests, the collection of bottom-hole injection pressure/temperature and three-phase flow rates.
The pilot study was performed in the East Seminole Field, Permian Basin, West Texas, and the study area was an inverted 40 acre 5-spot pattern which included a central injection well and four surrounding producers ( Figure 1). The oil was produced from the San Andres formation, which is classified as a heterogeneous cyclical carbonate. The reservoir interval had an average permeability of 13 mD, pay thickness of 110 ft, and consisted of six flow zones separated by impermeable flow barriers. The pilot area was selected based on rapid CO2 breakthrough, high GORs in the producers as well as relatively short well distances [17,18]. Two production wells, P1 and P4, were the focus of the baseline data collection and pilot monitoring because they exhibited the most rapid CO2 breakthrough time from tertiary CO2 injection. Composite logs from the pilot injection well indicated a 10 ft thick high permeability streak of 200 mD. Historical injection profiles showed that this zone has been taking most of the injected CO2. Therefore, this high permeability zone was targeted because foam can form in high permeability streaks and diverting flow to unswept regions of the reservoir with lower permeabilities. The reservoir and fluid properties are shown in Table 1.

Foam Formulation Design
The laboratory program aimed to determine the optimal foam formulation for the field test. This included surfactant-screening studies, evaluations of the optimal foam quality (gas fraction) and surfactant concentration and quantification of CO 2 EOR and CO 2 storage potential. Individual components of the laboratory program have been detailed elsewhere [12,13,17,18] and are briefly reviewed here.
Surfactant screening studies identified the nonionic water-soluble Huntsman L24-22, a linear ethoxylated alcohol (C12-14 EO22), for the field pilot study based upon minimal loss to the formation due to adsorption, adequate foam strength, and chemical stability [12]. Once the reservoir-specific surfactant was selected, the foam formulation was evaluated by determining the impact of surfactant concentration, gas fraction (foam quality) and flow velocity on foam strength at reservoir conditions [18]. The foam strength was quantitatively evaluated by the apparent foam viscosity, which was calculated from the steady-state pressure gradient at each gas fraction during foam quality scans and at each injection rate during foam rate scans [19]. As described in Section 6, foam model parameters for numeral modeling were derived from the foam quality and foam rate scans by curve-fitting regression [20][21][22].

Radial Model Set-Up and Initialization
In this pilot study, injection well pressures and temperatures were recorded using a down-hole memory pressure gauge during various surfactant, CO 2 and water injection periods. The transient analysis was conducted by examining the differential pressure (dP) and differential temperature (dT) over time for nine SAG cycles and one WAG cycle. A highresolution two-dimensional radial foam simulator was used to history-match the measured transient pressure data. The simulation model included the porosity and permeability distribution from a validated sector-scale model of the pilot pattern and surrounding producers [21]. The simulation foam model was used to examine the impact of foam and/or relative permeability on injectivity and mobility reduction when switching between surfactant solution and CO 2 in an SAG process.
The objectives of this study were as follows: • Evaluate whether foam has been generated based upon comparisons with measured BHP and injection rates; • Tune foam model to observed pressures during pilot if foam has formed; • Determine the foam propagation distance/rate if foam has formed.
The radial model used in this study was based upon a validated sector-level model of the pilot pattern and surrounding producers. The base sector model was calibrated to 40 years of waterflood and over 4 years of CO 2 injection data, before the pilot study. A workflow was developed to history-match the cumulative oil production and water-cut in the sector model [22].
The radial model included one injector (I1) which simulated the nine-cycle SAG pilot period. The grid contained 28 layers, which were refined from the validated sector model of the pilot pattern and surrounding wells. The radial grid extended to 700 ft from the injector and the grid sizes increased logarithmically from the injector. Layers and perforations were from the history-matched (HM) sector model (reference to Mohan's PhD/papers with HM models). The model included historical water and CO 2 injections before the pilot study. The simulations during the pilot study were controlled by the actual injection rates, and the simulated rates were compared with historical rates to ensure that the model could adhere to these controls. Figure 2 shows the permeability distribution in the radial model. Radial simulation model parameters are provided in Table 2.
Energies 2022, 15, x FOR PEER REVIEW 5 of 16 The radial model included one injector (I1) which simulated the nine-cycle SAG pilot period. The grid contained 28 layers, which were refined from the validated sector model of the pilot pattern and surrounding wells. The radial grid extended to 700 ft from the injector and the grid sizes increased logarithmically from the injector. Layers and perforations were from the history-matched (HM) sector model (reference to Mohan's PhD/papers with HM models). The model included historical water and CO2 injections before the pilot study. The simulations during the pilot study were controlled by the actual injection rates, and the simulated rates were compared with historical rates to ensure that the model could adhere to these controls. Figure 2 shows the permeability distribution in the radial model. Radial simulation model parameters are provided in Table 2.    Base values for foam model parameters were obtained by performing regression analysis on the quality scan data to fit the empirical foam model [21,23]. Figure 3 shows the foam characteristics obtained based on the regression analysis.
Base values for foam model parameters were obtained by performing regression analysis on the quality scan data to fit the empirical foam model [21,23]. Figure 3 shows the foam characteristics obtained based on the regression analysis. The simulation model was run using daily pilot study injection rates using the rate control option of the simulator.

Foam Modeling
There are two approaches to modeling foam transport in porous media: an explicit texture population balance model [10,24].and an implicit texture local equilibrium model [25,26]. Population balance models explicitly represent the dynamics of lamella creation and destruction along with the effect of the resulting foam on gas mobility. Gas mobility is reduced according to bubble size (determined by the rates of creation and destruction of lamellae). Local equilibrium models implicitly represent the effect of bubble size by introducing factors for reducing gas mobility by foam as a function of water saturation, oil saturation, surfactant concentration, and shear thinning due to the flow rate. Local equilibrium models assume that foam is present anywhere gas and water are present, along with an adequate surfactant concentration. The effect of foam was modeled in this study using the local equilibrium approach.
The decrease in gas mobility during foam floods is accounted for in local equilibrium models by scaling the gas relative permeability for no foam floods (krg nf ) by a mobility reduction factor (FM), whereas the water relative permeabilities remain unchanged. (1) The effect of water saturation, shear rate, surfactant concentration and oil saturation [26] on the mobility reduction factor was studied, given by the expression: refers to the maximum gas mobility reduction that can be achieved. , , and capture the water saturation, shear rate, oil saturation and surfactant concentration dependence, respectively, all lying in the range of 0 to 1 (Equations (3) through (6)). The capillary number, , represents the relative effect of viscous and capillary forces. The simulation model was run using daily pilot study injection rates using the rate control option of the simulator.

Foam Modeling
There are two approaches to modeling foam transport in porous media: an explicit texture population balance model [10,24].and an implicit texture local equilibrium model [25,26]. Population balance models explicitly represent the dynamics of lamella creation and destruction along with the effect of the resulting foam on gas mobility. Gas mobility is reduced according to bubble size (determined by the rates of creation and destruction of lamellae). Local equilibrium models implicitly represent the effect of bubble size by introducing factors for reducing gas mobility by foam as a function of water saturation, oil saturation, surfactant concentration, and shear thinning due to the flow rate. Local equilibrium models assume that foam is present anywhere gas and water are present, along with an adequate surfactant concentration. The effect of foam was modeled in this study using the local equilibrium approach.
The decrease in gas mobility during foam floods is accounted for in local equilibrium models by scaling the gas relative permeability for no foam floods (k rg nf ) by a mobility reduction factor (FM), whereas the water relative permeabilities remain unchanged.
The effect of water saturation, shear rate, surfactant concentration and oil saturation [26] on the mobility reduction factor was studied, given by the expression: f mmmob refers to the maximum gas mobility reduction that can be achieved. F water , F shear , F oil and F sur f capture the water saturation, shear rate, oil saturation and surfactant concentration dependence, respectively, all lying in the range of 0 to 1 (Equations (3) through (6)). The capillary number, N ca , represents the relative effect of viscous and capillary forces.
Two water components were used to model foam behavior: one for surfactant solution and one for water. The base case foam parameters were derived from laboratory foam quality and rate scans and fitted to the empirical local equilibrium foam model by curvefitting regression [19][20][21][25][26][27].
The surfactant selected for the pilot was found to have very low adsorption reservoir rock in the laboratory; thus, adsorption was excluded from the simulation study. Figure 3 shows the foam quality and rate scan used to derive the model parameters, and Table 3 shows the base case foam model parameters.

Measured Injection Rates and Pressures
The reservoir response to foam was evaluated by analyzing the bottom-hole pressure (BHP) response during surfactant and CO 2 injection. Figure 4 shows the injection rates of the CO 2 (red curve) and surfactant solution (green curve) and the measured BHP (black curve) at the injector well for nine complete pilot SAG cycles. The injection rates during the pilot study were 520 and 470 rb/day for the surfactant solution and CO 2 , respectively. The volumetric ratio of injected CO 2 relative to the total volume of CO 2 and surfactant injected was used to evaluate injected foam quality per cycle. The aim was to inject foam at 70% quality (0.70 gas fraction) per cycle, as determined in the laboratory studies. The foam qualities ranged from 61% to 71%, which was within the designed target.
Two water components were used to model foam behavior: one for surfactant solution and one for water. The base case foam parameters were derived from laboratory foam quality and rate scans and fitted to the empirical local equilibrium foam model by curvefitting regression [19][20][21][25][26][27] The surfactant selected for the pilot was found to have very low adsorption reservoir rock in the laboratory; thus, adsorption was excluded from the simulation study. Figure 3 shows the foam quality and rate scan used to derive the model parameters, and Table 3 shows the base case foam model parameters.

Measured Injection Rates and Pressures
The reservoir response to foam was evaluated by analyzing the bottom-hole pressure (BHP) response during surfactant and CO2 injection. Figure 4 shows the injection rates of the CO2 (red curve) and surfactant solution (green curve) and the measured BHP (black curve) at the injector well for nine complete pilot SAG cycles. The injection rates during the pilot study were 520 and 470 rb/day for the surfactant solution and CO2, respectively. The volumetric ratio of injected CO2 relative to the total volume of CO2 and surfactant injected was used to evaluate injected foam quality per cycle. The aim was to inject foam at 70% quality (0.70 gas fraction) per cycle, as determined in the laboratory studies. The foam qualities ranged from 61% to 71%, which was within the designed target.

Base Case Simulations
The simulated BHP was compared with actual surveys to evaluate foam generation and CO 2 mobility reduction. Figure 5 shows the surfactant-alternating gas (SAG) simulation results, assuming the base case foam parameters (red curve). As can be seen in this plot, the simulated pressures were significantly higher than the measured BHP (black curve). In addition, the simulated pressures assuming a water-alternating gas (WAG) scenario are shown (blue curve), which were slightly lower but more consistent with the measured pressures, suggesting a weaker foam than that expected.

Base Case Simulations
The simulated BHP was compared with actual surveys to evaluate foam generation and CO2 mobility reduction. Figure 5 shows the surfactant-alternating gas (SAG) simulation results, assuming the base case foam parameters (red curve). As can be seen in this plot, the simulated pressures were significantly higher than the measured BHP (black curve). In addition, the simulated pressures assuming a water-alternating gas (WAG) scenario are shown (blue curve), which were slightly lower but more consistent with the measured pressures, suggesting a weaker foam than that expected. The radial simulation model assumed a constant effect of nearby wells, and this may only be true for limited times. To check this assumption, the injection and production rates within the pilot pattern were also plotted. Figure 6 shows the total injection rates for the pilot pattern. As can be seen from this plot, the total CO2 injection rate increased during Cycles 6 and 7 and decreased during Cycles 8 and 9. This is important since the radial well model only simulated the central injector and did not consider the effects of injection/production on the nearby wells. These non-steady conditions are addressed later in the transient analysis section.  The radial simulation model assumed a constant effect of nearby wells, and this may only be true for limited times. To check this assumption, the injection and production rates within the pilot pattern were also plotted. Figure 6 shows the total injection rates for the pilot pattern. As can be seen from this plot, the total CO 2 injection rate increased during Cycles 6 and 7 and decreased during Cycles 8 and 9. This is important since the radial well model only simulated the central injector and did not consider the effects of injection/production on the nearby wells. These non-steady conditions are addressed later in the transient analysis section.

Base Case Simulations
The simulated BHP was compared with actual surveys to evaluate foam generation and CO2 mobility reduction. Figure 5 shows the surfactant-alternating gas (SAG) simulation results, assuming the base case foam parameters (red curve). As can be seen in this plot, the simulated pressures were significantly higher than the measured BHP (black curve). In addition, the simulated pressures assuming a water-alternating gas (WAG) scenario are shown (blue curve), which were slightly lower but more consistent with the measured pressures, suggesting a weaker foam than that expected. The radial simulation model assumed a constant effect of nearby wells, and this may only be true for limited times. To check this assumption, the injection and production rates within the pilot pattern were also plotted. Figure 6 shows the total injection rates for the pilot pattern. As can be seen from this plot, the total CO2 injection rate increased during Cycles 6 and 7 and decreased during Cycles 8 and 9. This is important since the radial well model only simulated the central injector and did not consider the effects of injection/production on the nearby wells. These non-steady conditions are addressed later in the transient analysis section. Figure 6. Total injection and BHP measured for the pilot study. The black curve shows the measured bottom-hole pressure data. The green curve shows simulated results from the base case model. Figure 6. Total injection and BHP measured for the pilot study. The black curve shows the measured bottom-hole pressure data. The green curve shows simulated results from the base case model. Values for CO 2 and water injection rates (red and blue curves) are indicated on the secondary axis (rb/d).

Sensitivity Studies
Due to uncertainty in foam model parameters derived from laboratory data, sensitivity runs were set up to first test key foam model parameters. The following foam model parameters were adjusted for the sensitivity study: • FMMOB: The reference mobility reduction factor; • FMDRY: The limiting water saturation below which the foam is no longer effective; • EPDRY: A weighting factor which controls the sharpness of the change in mobility; • FOAMSO: The maximum oil saturation above which foam is no longer effective. Table 4 shows the parameter ranges for the sensitivity study.  Figure 7 shows the sensitivity to foam strength parameters (FMMOB). As expected, the simulated pressures agreed better with the measured BHP, because the foam strength was controlled by the set FMMOB value. Sensitivity simulations for other foam parameters showed less of an impact; therefore, they are not shown here. These results clearly show that the foam was formed down-hole, and it was weaker than expected. Values for CO2 and water injection rates (red and blue curves) are indicated on the secondary axis (rb/d).

Sensitivity Studies
Due to uncertainty in foam model parameters derived from laboratory data, sensitivity runs were set up to first test key foam model parameters. The following foam model parameters were adjusted for the sensitivity study: • FMMOB: The reference mobility reduction factor; • FMDRY: The limiting water saturation below which the foam is no longer effective; • EPDRY: A weighting factor which controls the sharpness of the change in mobility; • FOAMSO: The maximum oil saturation above which foam is no longer effective. Table 4 shows the parameter ranges for the sensitivity study.  Figure 7 shows the sensitivity to foam strength parameters (FMMOB). As expected, the simulated pressures agreed better with the measured BHP, because the foam strength was controlled by the set FMMOB value. Sensitivity simulations for other foam parameters showed less of an impact; therefore, they are not shown here. These results clearly show that the foam was formed down-hole, and it was weaker than expected.

Transient Pressure Analysis
An alternative analysis was carried out using the pressure changes (instead of the absolute pressures) for each cycle. This analysis showed consistent results for both surfactant and CO2 injection periods. Transient analysis represented a useful tool to analyze

Transient Pressure Analysis
An alternative analysis was carried out using the pressure changes (instead of the absolute pressures) for each cycle. This analysis showed consistent results for both surfactant and CO 2 injection periods. Transient analysis represented a useful tool to analyze unsteady-state flow at the pilot injector. Figure 8 shows dP/dT over time for the first five SAG cycles. Delta pressure (dP) and delta temperature (dT) values were calculated by subtracting the absolute values from the last stabilized pressure and temperature before each injection cycle, a technique widely used in transient pressure analysis. Similarly, delta t (dt) refers to the differential time from the start of a particular injection cycle. Differential pressure (dP) increased for each surfactant cycle, which may be related to a foam bank developing further into the reservoir. The dP values were in the order Cycle 1 < Cycle 2 < Cycle 3 < Cycle 4 < Cycle 5.
unsteady-state flow at the pilot injector. Figure 8 shows dP/dT over time for the first five SAG cycles. Delta pressure (dP) and delta temperature (dT) values were calculated by subtracting the absolute values from the last stabilized pressure and temperature before each injection cycle, a technique widely used in transient pressure analysis. Similarly, delta t (dt) refers to the differential time from the start of a particular injection cycle. Differential pressure (dP) increased for each surfactant cycle, which may be related to a foam bank developing further into the reservoir. The dP values were in the order Cycle 1 < Cycle 2 < Cycle 3 < Cycle 4 < Cycle 5. The increased BHP during surfactant cycles could also be related to relative permeability and/or viscosity effects. A WAG was run at the end of the pilot to rule this out. As shown in Figure 9, the dP during the final SAG cycle (red curve) was higher than the dP observed during the final WAG (blue curve). The higher dP of the SAG cycles compared with the WAG indicated reduced the mobility during the SAG cycles and confirmed foam generation.  The increased BHP during surfactant cycles could also be related to relative permeability and/or viscosity effects. A WAG was run at the end of the pilot to rule this out. As shown in Figure 9, the dP during the final SAG cycle (red curve) was higher than the dP observed during the final WAG (blue curve). The higher dP of the SAG cycles compared with the WAG indicated reduced the mobility during the SAG cycles and confirmed foam generation.
Energies 2022, 15, x FOR PEER REVIEW 10 of 16 unsteady-state flow at the pilot injector. Figure 8 shows dP/dT over time for the first five SAG cycles. Delta pressure (dP) and delta temperature (dT) values were calculated by subtracting the absolute values from the last stabilized pressure and temperature before each injection cycle, a technique widely used in transient pressure analysis. Similarly, delta t (dt) refers to the differential time from the start of a particular injection cycle. Differential pressure (dP) increased for each surfactant cycle, which may be related to a foam bank developing further into the reservoir. The dP values were in the order Cycle 1 < Cycle 2 < Cycle 3 < Cycle 4 < Cycle 5. Figure 8. Transient pressures and temperatures for the first five SAG cycles. dP1 corresponds to slug 1, dP2 to slug 2, and so on.
The increased BHP during surfactant cycles could also be related to relative permeability and/or viscosity effects. A WAG was run at the end of the pilot to rule this out. As shown in Figure 9, the dP during the final SAG cycle (red curve) was higher than the dP observed during the final WAG (blue curve). The higher dP of the SAG cycles compared with the WAG indicated reduced the mobility during the SAG cycles and confirmed foam generation.  The transient analysis was also applied to CO 2 injection periods independently. These results, along with the extended fall-off period, are shown in Figure 10.
The transient analysis was also applied to CO2 injection periods independently. These results, along with the extended fall-off period, are shown in Figure 10.

Fall-Off Comparison
Due to operational reasons, the central injector was shut in for an extended period before Cycle 9. This created a fall-off test, which was also used to test different foam scenarios. Figure 11 shows the simulated results versus the measured dP/dT response during this fall-off period. As indicated, the simulated case with a lower FMMOB value (gray curve) followed the measured response more closely than the cases with higher mobility reduction (yellow and blue curves). In addition, the WAG case had a much lower pressure response, compared with the cases with foam and the observed data. This may indicate that a relatively weak foam was generated in the reservoir.

Fall-Off Comparison
Due to operational reasons, the central injector was shut in for an extended period before Cycle 9. This created a fall-off test, which was also used to test different foam scenarios. Figure 11 shows the simulated results versus the measured dP/dT response during this fall-off period. As indicated, the simulated case with a lower FMMOB value (gray curve) followed the measured response more closely than the cases with higher mobility reduction (yellow and blue curves). In addition, the WAG case had a much lower pressure response, compared with the cases with foam and the observed data. This may indicate that a relatively weak foam was generated in the reservoir. The transient analysis was also applied to CO2 injection periods independently. These results, along with the extended fall-off period, are shown in Figure 10.

Fall-Off Comparison
Due to operational reasons, the central injector was shut in for an extended period before Cycle 9. This created a fall-off test, which was also used to test different foam scenarios. Figure 11 shows the simulated results versus the measured dP/dT response during this fall-off period. As indicated, the simulated case with a lower FMMOB value (gray curve) followed the measured response more closely than the cases with higher mobility reduction (yellow and blue curves). In addition, the WAG case had a much lower pressure response, compared with the cases with foam and the observed data. This may indicate that a relatively weak foam was generated in the reservoir.

Transient Surfactant and CO 2 Injection Comparisons
Transient data were also used to compare the model pressure response with the measured pressures during surfactant and CO 2 injection periods. These are shown in Figures 12 and 13, respectively. These comparisons showed similar results to those observed during the fall-off period, suggesting weak foam strength.

Transient Surfactant and CO2 Injection Comparisons
Transient data were also used to compare the model pressure response with the measured pressures during surfactant and CO2 injection periods. These are shown in Figures 12 and 13, respectively. These comparisons showed similar results to those observed during the fall-off period, suggesting weak foam strength.

Foam Propagation
One of the important objectives of this study was to determine the foam propagation distance/rate if foam had formed. For this, a history-matched simulation model with tuned parameters was used. The simulator modeled foam as an effective concentration of surfactant transported in the gas (CO2) phase. Figure 14 shows the simulated foam propagation for the weak foam case (FMMOB = 1.9) at the end of each surfactant/CO2 cycle for

Transient Surfactant and CO2 Injection Comparisons
Transient data were also used to compare the model pressure response with the measured pressures during surfactant and CO2 injection periods. These are shown in Figures 12 and 13, respectively. These comparisons showed similar results to those observed during the fall-off period, suggesting weak foam strength.

Foam Propagation
One of the important objectives of this study was to determine the foam propagation distance/rate if foam had formed. For this, a history-matched simulation model with tuned parameters was used. The simulator modeled foam as an effective concentration of surfactant transported in the gas (CO2) phase. Figure 14 shows the simulated foam propagation for the weak foam case (FMMOB = 1.9) at the end of each surfactant/CO2 cycle for

Foam Propagation
One of the important objectives of this study was to determine the foam propagation distance/rate if foam had formed. For this, a history-matched simulation model with tuned parameters was used. The simulator modeled foam as an effective concentration of surfactant transported in the gas (CO 2 ) phase. Figure 14 shows the simulated foam propagation for the weak foam case (FMMOB = 1.9) at the end of each surfactant/CO 2 cycle for Cycles 1, 5 and 8. These plots clearly indicate that foam had advanced deep in high-permeability layers during the pilot study. Cycles 1, 5 and 8. These plots clearly indicate that foam had advanced deep in high-permeability layers during the pilot study.

Results and Discussion
The simulation model assuming the base case foam parameters for the SAG scenario gave significantly higher pressures than the measured pressures. This clearly shows that the simulated foam (or resistance) was stronger than that which occurred in reservoir conditions. The simulated WAG scenario (or no foam case) provided a lower bound for these pressures; therefore, based on the history-matched results, it could be concluded that the generated foam was weaker than expected.
Transient analysis showed that the temperature response was quite similar during all SAG cycles. On the other hand, differential pressures consistently increased during periods of surfactant injection and decreased during the subsequent CO2 injection periods. The pressure increase (buildup) during surfactant injection clearly suggests the development of a mobility bank in the reservoir. Transient analysis also showed that the differential pressures during the SAG cycles were higher than the pressures observed during the WAG cycle. This revealed foam generation and reduced CO2 mobility during this pilot development.
History matching using different foam parameters showed that a large reduction in the foam mobility reduction factor (FMMOB) was needed to match the measured bottomhole pressure data. Other foam parameters were also selectively adjusted, and results showed they had less of an impact on the overall pressure match. However, considering the non-unique nature of parameter estimation [28], the effects of these foam parameters should be addressed by more direct indicators of foam saturation, such as resistivity measurements [16].

Results and Discussion
The simulation model assuming the base case foam parameters for the SAG scenario gave significantly higher pressures than the measured pressures. This clearly shows that the simulated foam (or resistance) was stronger than that which occurred in reservoir conditions. The simulated WAG scenario (or no foam case) provided a lower bound for these pressures; therefore, based on the history-matched results, it could be concluded that the generated foam was weaker than expected.
Transient analysis showed that the temperature response was quite similar during all SAG cycles. On the other hand, differential pressures consistently increased during periods of surfactant injection and decreased during the subsequent CO 2 injection periods. The pressure increase (buildup) during surfactant injection clearly suggests the development of a mobility bank in the reservoir. Transient analysis also showed that the differential pressures during the SAG cycles were higher than the pressures observed during the WAG cycle. This revealed foam generation and reduced CO 2 mobility during this pilot development.
History matching using different foam parameters showed that a large reduction in the foam mobility reduction factor (FMMOB) was needed to match the measured bottomhole pressure data. Other foam parameters were also selectively adjusted, and results showed they had less of an impact on the overall pressure match. However, considering the non-unique nature of parameter estimation [28], the effects of these foam parameters should be addressed by more direct indicators of foam saturation, such as resistivity measurements [16].
The effectiveness of the foam could also be independently determined by improvements in the overall oil recovery against the base water/gas injection within the pilot area. A production analysis conducted after the pilot indicated a significant increase in both cumulative oil and water production compared to the baseline period before the pilot.
However, a large increase in water production was also observed, which may be related to a fracturing campaign conducted on pilot wells at the onset of the pilot. Therefore, no definite conclusions were drawn from this pilot with regard to the effectiveness of the foam based on the oil production increase.

Conclusions
In this study, we presented a novel technique to study the development of foam in reservoir conditions. The method was used to assess the effectiveness of CO 2 foam in a pilot study conducted in the East Seminole Field, Permian Basin, West Texas. In the selected pilot area, foam was utilized to reduce CO 2 mobility to improve sweep efficiency, oil recovery, and CO 2 storage potential. Injection pressure and temperature data were used to evaluate the reservoir response during various surfactant, CO 2 and water injection periods. Transient analyses were conducted for all SAG cycles, as well as one WAG cycle. A highresolution two-dimensional radial flow model was used to history-match the measured differential pressures.
The radial model proved to be useful for assessing the reservoir foam strength during this pilot study. Although the pressure data alone may not be sufficient to describe the complex physics of in situ foam generation, this study shows that it is a strong indicator of foam strength. In this pilot, it appears that the reservoir foam strength was weaker than expected based on laboratory measurements.
The proposed method of transient analysis has been found to be quite useful in assessing the development and progression of foam in the reservoir. This analysis showed a consistent increase during all SAG cycles. In addition, differential pressures during the SAG periods were higher than those observed during a comparable WAG cycle. This revealed foam generation and reduced CO 2 mobility during the pilot. Based on the detailed comparisons and the transient analysis of measured bottom-hole pressure data, it could be concluded that foam was generated down-hole. However, the history-matched foam model was weaker than that expected based on laboratory studies.
Sensitivity studies show that the foam mobility reduction factor (FMMOB) is the most dominant parameter. Based on the history-matched model simulations, it could be concluded that the foam significantly advanced in high-permeability layers during this pilot study.