Endpoint Relative Permeability Research Articles

Assisted Upscaling of Miscible CO2-Enhanced Oil Recovery Floods Using an Artificial Neural Network-Based Optimisation Algorithm

Due to the high computing cost of the fine-scale compositional simulations needed to effectively model miscible CO2 flooding, upscaling techniques are needed to approximate the behaviour of these fine-scale grids on more realistic coarse-scale models. The use of transport coefficients to better represent small-scale interactions, such as the time-dependent flux of the components within the hydrocarbon phases (molecular diffusion), and the pseudoisation of relative permeabilities to ensure the matching of large-scale effects, such as the volumetric fluxes of the phases, are two of these procedures. Most times, a mismatch between the phase fluxes of the integrated fine-scale and that of the coarse-scale is observed. By adjusting or calibrating some of the generated coarse-scale pseudo functions, such as the transport coefficients, absolute permeability, or relative permeability endpoints, the accuracy of the upscaling results can be improved. This procedure can be treated a reservoir history matching problem which is typically computationally expensive. In this study, we provide a framework for representing the dynamics of small-scale molecular diffusion and macro-scale heterogeneity-induced channelling related to miscible CO2 displacements on upscaled coarser grid reservoir models. The method used was based on the pseudoisation of relative permeability and transport coefficients and was applied to two benchmark reservoir models from the Society of Petroleum Engineers (SPE). Our results demonstrated that using effectively calibrated transport coefficients improved the upscaling results, so that the calculated pseudo-relative permeability functions can be ignored. We proposed a unique approach to upscaling miscible floods that utilised a genetic algorithm and a neural-network-based proxy model to minimise the associated computing cost. The data-driven approximation model considerably decreased the computing cost associated with the assisted tuning technique, and the optimisation algorithm was used to reduce the error between the predictions of the upscaled models. In conclusion, the methodology described in this study effectively captured the small- and large-scale behaviour related to the miscible displacements on upscaled coarse-scale reservoir models while reduced associated computational costs.

Comparative analysis of hydrogen, methane and nitrogen relative permeability: Implications for Underground Hydrogen Storage

Underground Hydrogen Storage (UHS) is an emerging technology which aims to store terawatt-scale energy in the subsurface to alleviate daily and seasonal fluctuations in the ever-increasing renewable energy market. Depleted gas reservoirs and aquifers will be the main targets of storage which requires an understanding of the interaction between formation or cushion gas with native brine. A comprehensive comparison of the petrophysical and two-phase flow properties of the hydrogen-water, methane-water and nitrogen-water systems at in-situ conditions is the focus of our work. We conduct steady-state relative permeability experiments at 2.13 MPa and 298 K using identical capillary numbers of Nc=2.92×10−7 for all three systems. The saturation and in-situ contact angles are determined with segmentation of 3D micro-CT images. The contact angle of each system is almost identical at the irreducible water saturation, Swi, 44°, 46°, 45°, respectively, as is the interfacial tension of 72.0, 71.5 and 71mN/m, respectively. The capillary pressure-saturation relationships for each system have a maximum difference of 3.8 % which leads to approximately equivalent relative permeability in the Bentheimer sandstone core. The end-point relative permeabilities are krg0=0.049, krg0=0.045 and krg0=0.062 at irreducible water saturations of Swi=0.24, Swi=0.25 and Swi=0.23, respectively. All three gases demonstrate equivalent flow properties which indicates that both nitrogen and methane are suitable analogue gases for laboratory multiphase flow experiments and cushion gas to improve safety and the economics of commercial UHS projects. The results enable history matched depleted gas reservoir performance to be used as a guide for UHS.

Wettability modification effects on relative permeability end-points: Comparative analysis of surfactant agents for enhanced oil recovery

This research examines the impact of wettability alteration on the end points of relative permeability, a crucial property of fluids and porous media that influences the displacement processes of immiscible fluids through such media. The estimation of the mobility ratio for oil recovery relies on these end points, which are influenced by connate water saturation and residual oil saturation. To investigate this relationship, carbonate rock is generally subjected to wettability alteration using surfactant agents, and core flooding is employed to determine the relative permeability before and after the alteration. The wettability of the rock is commonly assessed through contact angle measurements. Two surfactants, TritonX-100 (Tx-100) and Cedar, were tested in reducing the wettability of the porous media for oil. The contact angle measurements revealed that Tx-100 was more effective for this purpose than Cedar. Furthermore, the relative permeability tests indicated that both surfactants decreased residual oil saturation, but Tx-100 also improved system pressure. In contrast, Cedar reduced residual oil saturation but increased system pressure, possibly because of its high viscosity. The results also demonstrate that injecting Tx-100 leads to a 14% increase in ultimate oil recovery compared with water injection, while Cedar injection increased the recovery factor by 5%. This difference may be attributed to the incomplete coverage of the pore wall by Cedar or its weaker chemical structure than Tx-100. Notably, in carbonate cores, neither non-ionic surfactant enhanced oil recovery.

Direct measurement of hydrogen relative permeability hysteresis for underground hydrogen storage

Underground Hydrogen Storage (UHS) is a long-term storage solution which utilises hydrogen as an energy carrier to store large-scale excess renewable energy in the subsurface. Key petrophysical properties, such as wettability and interfacial tension of hydrogen and water have been discovered which provide a practical basis for simulation models. Our work directly measures relative permeability hysteresis during co-injection core floods of hydrogen and water with a capillary number of Nc=2.92×10−7. Segmented micro-CT images are used to determine saturation in the Bentheimer sandstone. Our results demonstrate that hydrogen relative permeability in sandstones is very low, with an end-point relative permeability of krg0=0.049 at Swi= 0.24. Capillary trapping results in residual gas saturation of Sgr= 0.4. Wettability analysis confirms the system is water-wet, with contact angles of 57° at Sgr and 44° at Swi. These results improve the reliability of numerical simulations and demonstrate the possible challenges involved with the commercial application of UHS.

Three-dimensional core reconstruction and performance evaluation of CO2 displacement in a tight oil reservoir

In this study, a three-dimensional tight sandstone core was reconstructed digitally using serials thin sections cut from a core sample used in laboratory carbon dioxide (CO2) flooding experiments. Based on the digital core, multiphase flow simulations were carried out to evaluate the performance of three prior laboratory-tested injection strategies: CO2 continuous injection, water alternative gas (WAG: CO2) injection, and cyclic CO2 injection. The chosen image-based reconstruction led to a close porosity and permeability match with the sampled core in an economical way. The numerical evaluation closely replicated the laboratory-tested procedures, thus providing realistic fluid distributions before CO2 injection. To determine saturation functions for CO2 injection after water flooding, sensitivities of endpoint relative permeability and capillary pressure to CO2 continuous injection were quantified. Water relative permeability was identified as a key factor. The saturation functions were used in a history match between simulations and laboratory data where close agreements were observed for all three CO2 injection strategies. Then critical enhanced oil recovery (EOR) operational parameters (soaking time, slug ratio, cycle size, and test duration) were optimized to maximize CO2 displacement performance, which led to the following observations: (1) While extended soaking after CO2 continuous injection increased incremental oil recovery, such increase was limited due to concurrent soaking during low-rate CO2 injection. (2) In WAG injection, CO2 and brine slug sizes and ratios were optimized: increasing the cycle size performed better than adjusting the slug ratio for favorable mobility control and efficient CO2 EOR. (3) For cyclic CO2 injection, the total CO2 injection volume was the most important factor, followed by the number of cycles, to allow CO2 diffusion into tight core to maximize the swept pore volumes. The history-matched simulations suggest that both WAG and cyclic CO2 injection can achieve high displacement effectiveness for the tight reservoir, compared with that achieved with slight soaking after CO2 continuous injection. The injected brine slugs in the WAG injection reduced the CO2 needed at the expense of reduced storage capacity. Compared to WAG, cyclic CO2 injection, though realizing the highest oil recovery and gas storage, requires more CO2.

Reservoir simulation of the CO[formula omitted] storage potential for the depositional environments of West Siberia

We evaluate the CO2 storage potential for the depositional environments of the West Siberian sedimentary basin. Particularly, we investigate the prospect of storing large volumes of CO2 in the alluvial fan, barrier island, deltaic, and fluvial environments. We employ several detailed 3-D models of petroleum reservoirs as proxies for the saline aquifers occurring in the basin under the listed environments. By simulating supercritical CO2 injection into several reservoir sectors, we compare the environments in terms of their prospects for the underground storage of CO2. We estimate the maximum capacity and storage potential for the entire sectors by considering them the resources licensed for an industrial-scale Carbon Capture and Storage (CCS) project. The scenarios with a single and multiple injection wells are assessed in the evaluation, which might be of interest for the elaboration of feasible regulations and policies in the area. We find out that the barrier island deposits are characterized by maximum potential, whereas the fluvial environments are the least suitable for deploying CCS. We demonstrate that for the barrier island environments, the storage potential is most sensitive to the relative permeability end-points. We also test several scaling concepts for extending our estimates for a single-well injection to a multi-well scenarios and generally from a site-specific to regional scale. We conclude that due to the interference between nearby wells, the storage potential for a single well scenario cannot reliably be scaled to the case of CO2 injection through a group of wells.

Effect of Temperature on Two-Phase Gas/Oil Relative Permeability in Viscous Oil Reservoirs: A Combined Experimental and History-Matching-Based Analysis

Summary Thermal enhanced oil recovery (TEOR) is the most widely accepted method for exploiting the heavy oil reservoirs in North America. In addition to improving the mobility of oil due to its viscosity reduction, the high temperature down in the hole due to the injection of the vapor phase may significantly alter the fluid flow performance and behavior, as represented by the relative permeability to fluids in the formations. Therefore, in TEOR, the relative permeabilities can change with a change in temperature. Also, there is no model that accounts for the change in temperature on two-phase gas/oil relative permeability. Further, the gas/oil relative permeability and its dependence on temperature are required data for the numerical simulation of TEOR. Very few studies are available on this topic with no emerging consensus on a general behavior of such effects. The scarcity of such studies is mostly due to experimental problems to make reliable measurements. Therefore, the primary objective of this study was to overcome the experimental issues and investigate the effect of temperature on gas/oil relative permeability. Oil displacement tests were carried out in a 45-cm-long sandpack at temperatures ranging from 64°C to 210°C using a viscous mineral oil (PAO-100), deionized water, and nitrogen gas. It was found that the unsteady-state method was susceptible to several experimental artifacts in viscous oil systems due to a very adverse mobility ratio. However, despite such experimental artifacts, a careful analysis of the displacement data led to obtaining meaningful two-phase gas/oil relative permeability curves. These curves were used to interpret the relative permeability curves for gas/heavy oil systems using the experimentally obtained displacement results. We noted that at the end of gasflooding, the “final” residual oil saturation (Sor) still eluded us even after several pore volumes (PVs) of gas injection. This rendered the experimentally determined endpoint gas relative permeability (krge) and Sor unreliable. In contrast, the irreducible water saturation (Swir) and the endpoint oil relative permeability (kroe) were experimentally achievable. The complete two-phase gas/heavy oil relative permeability curves are inferred with a newly developed systematic history-matching algorithm in this study. This systematic history-matching technique helped us to determine the uncertain parameters of the oil/gas relative permeability curves, such as the two exponents of the Corey equation (No and Ng), Sor and krge. The history match showed that kroe and Swir were experimentally achievable and were reliably interpreted, except these four parameters (i.e., Corey exponents, true residual oil saturation, and gas endpoint relative permeability) were interpreted from simulations rather than from experiments. Based on our findings, a new correlation has been proposed to model the effect of temperature on two-phase gas/heavy oil relative permeability.

Evaluation of Relative Permeability Curves in Sandstone Core Flooding Using Computational Fluid Dynamics

Geological carbon sequestration is a proven method of safely storing carbon dioxide in formations, thereby reducing atmospheric carbon imprint and mitigating global warming. The relative permeability to carbon dioxide versus brine/water in geological formations determines flow characteristics of one fluid in the presence of another. The objective of this research is to evaluate the relative permeability to carbon dioxide in both the gas phase and the supercritical state in the presence of water in a Vedder sandstone core sample. The sandstone sample used is medium- to fine-grain arkosic artenite containing primarily quartz, potassium feldspar, plagioclase, and biotite. The effect of the viscosity ratio between the non-wetting phase and the wetting phase, on the relative permeability to the non-wetting phase, is studied. Computational fluid dynamics (CFD) is used for this study. Results show that with the same amount of irreducible water fraction, the endpoint relative permeability to the non-wetting phase is approximately one order of magnitude lower for supercritical carbon dioxide than for gaseous carbon dioxide. The endpoint relative permeability does not change significantly with the change in inlet pressure for gaseous carbon dioxide. Additionally, the endpoint relative permeability to the non-wetting phase increases with an increase in the viscosity ratio. Results suggest that CFD can be effectively used to study relative permeability, precluding expensive experiments.

Wettability Alteration to Reduce Water Blockage in Low-Permeability Sandstone Reservoirs

This study is a continuation of our previous work, which focused on a near-wellbore water blockage alleviation by applying a thermally cured silane-functionalized benzoxazine to modify rock wettability. In this new analysis, we have demonstrated that the resin can be applied in low-permeability sandstones (approximately 15 mD as opposed to 100 to 200 mD in the previous study) to change the rock surface wettability from water-wet to intermediate gas-wet. We have also demonstrated that curing temperatures as low as 125 °C (as opposed to 180 °C in our previous study) can significantly change wettability, indicating surface functionalization through the silane moiety and ring-opening polymerization of the benzoxazine moiety. In drainage core flooding experiments at 2.5 wt.% resin loading, compared to untreated samples, brine recovery increments of 6.3 to 6.9% were obtained for curing temperatures of 125 to 180 °C, respectively. A maximum 20% increment in the end-point relative gas permeability was achieved at a curing temperature of 180 °C. A coupled experimental and numerical study, conducted at core and wellbore scales, demonstrates the potential effectiveness of our chemical treatment in improving gas productivity at the field scale. Reservoir simulations indicate a 2.9 to 10.6% improvement in gas deliverability for a treatment radius of 4 to 16 m, respectively.

Pore-scale Analysis of CO2-brine Displacement in Berea Sandstone and Its Implications to CO2 Injectivity

For storage in deep saline formations, where CO2 is injected into the pore spaces of rocks previously occupied by saline groundwater (brine), relative permeability is a key input parameter for predictive models. CO2 injectivity is considered to reach the maximum value at the CO2 endpoint relative permeability when brine saturation becomes irreducible. The objective of this study is to investigate the effect of viscosity ratio, interfacial tension and wettability on relative permeability during CO2-brine drainage. A multiphase lattice Boltzmann model (LBM) is employed to numerically measure pore-scale dynamics in CO2-brine flow in the sample of Berea sandstone. CO2/brine with interfacial tension from 30 to 45 mN/m and viscosity ratio from 0.05 to 0.17 (the range of values expected for typical storage reservoirs conditions) are carried out to systematically assess the influence on the relative permeability curves. Although CO2 storage in sandstone saline aquifers is predominantly water wet, there are contradictory results as to the magnitude of the contact angle and its variation with fluid conditions. Therefore, the range of wetting conditions is studied to gain a better insight into the effect of wettability on supercritical CO2 displacement. In this study, it is observed that interfacial tension variations play a trivial impact while both of viscosity ratio and wettability are likely to have a significant effect on relative permeability curves under representative condition of storage reservoirs. We also perform a near-wellbore scale geomechanics analysis to investigate the impact of relative permeability on CO2 injectivity. The result shows that water-wet condition facilitates the CO2 injection when there is no fracture induced.

Comparison of Intercept Methods for Correction of Steady-State Relative Permeability Experiments for Capillary End Effects

Summary Steady-state relative permeability experiments are performed by coinjection of two fluids through core plug samples. The relative permeabilities can be calculated using Darcy’s law from the stabilized pressure drop and saturation of the core if capillary end effects and transient effects are negligible. In most cases, such conditions are difficult to obtain. Recent works have presented ways to extrapolate steady-state pressure drop and average saturation measurements affected by capillary end effects collected at different rates to obtain correct relative permeabilities at correct saturations. Both the considered methods are based on linear extrapolations to determine intercepts. Gupta and Maloney (2016) derived their method intuitively and validated it with numerical and experimental data. Andersen (2021a) derived a method from fundamental assumptions and presented an intercept method in a different form where the saturation and relative permeabilities are found directly and uniquely from straightline intercepts. All system parameters, including saturation functions and injection conditions, appear in the model. In this work, the two methods are compared. It is proven theoretically that Gupta and Maloney’s method is correct in that it produces the correct saturation and pressure drops corrected for capillary end effects. Especially, a constant pressure drop was assumed and here proved to exist, as a result of capillary end effects in addition to the Darcy law pressure drop with no end effects. Their method assumes a well-defined end effect region with length xCEE, but this length can be defined almost arbitrarily. This choice has little impact on average saturation and pressure drop, however. They also assumed that for a defined end effect region, the average saturation was constant and equal to the slope in their saturation plot. It is shown that if the region is defined, the average saturation is indeed constant, but not given by the slope. The correct slope is predicted by the Andersen model. We also comment on theoretical misinterpretations of the Gupta and Maloney method. A few works have correctly calculated that the pressure drop over the end effect region is independent of rate, but not accounted for that its length is rate dependent. We show that the combined pressure drop is equal to a constant plus the Darcy pressure drop over the full core. Examples are presented to illustrate the model behaviors. Literature datasets are investigated showing that (a) apparently rate-dependent CO2-brine relative permeability endpoints can be explained by capillary end effects and (b) the intercept methods can be applied to correct shale relative permeabilities.

Effect of temperature on two-phase gas/oil relative permeability in unconsolidated sands

Thermal Enhanced Oil Recovery (TEOR) for heavy oil reservoirs involves the simultaneous flow of oil and steam, mimicking the gaseous phase with an elevation in the temperature. While implementing the TEOR process, reservoir performance prediction tools require the water/oil and gas/oil relative permeability data. Many studies reported the temperature effect on two-phase water/oil relative permeability despite knowing that steam or vapor is conventionally injected, mimicking the gaseous phase during heavy oil recovery. Thus, this requires the knowledge of temperature effect on two-phase gas/liquid relative permeability as well. However, limited studies are reported in the literature regarding the temperature dependency of relative permeability in gas/liquid systems; offer no census about its effects. The scarcity of such studies in the literature is due to the lack of systematic experimental studies and complications observed while conducting the higher temperature tests to mimic the thermal EOR. Hence, the objective of this study was to examine the temperature effect on two-phase gas/liquid relative permeability at varying temperatures from 64 to 132 °C using a systematic and reliable experimental process.In this study, Poly Alpha Olefin (PAO-100) was used as the oleic phase, deionized water as the immobile phase, and nitrogen gas as the displacing phase in a clean unconsolidated sandpack under the confining pressure around 1000 psi. Furthermore, Johnson-Neumann-Bossler (JBN) method was opted to interpret the two-phase gas/liquid relative permeability curves from the displacement data, i.e., cumulative oil production and pressure drop measured across the sandpack. The experimental observation suggests that irreducible water saturation and endpoint oil relative permeability are temperature independent. The residual oil saturation decreased with the increase in temperature and led to a higher endpoint relative permeability to gas. On the other hand, the oil relative permeability at equal saturation uplifted, suggesting the enhanced mobility of oil through pores with increasing temperature. On the other side, the gas relative permeability at equal saturation was temperature-insensitive other than at residual oil saturation. Also, the two-phase flow region increased with the rise in temperature as both the relative permeability curves shifted upwards, and the broader curve was observed. Hence, this study strongly suggests that the reservoir engineers or commercial reservoir simulators should account for the temperature effects on two-phase gas/oil relative permeability to efficiently predict heavy oil reservoir performance and management during the thermal enhanced oil recovery process (TEOR).

Laboratory Investigation of Impact of Slickwater Composition on Multiphase Permeability Evolution in Tight Sandstones

Summary Fracturing fluid filtrate that leaks off during injection is imbibed by strong capillary forces present in low-permeability sandstones and may severely reduce the effective gas permeability during cleanup and post-fracture production. This work aims to investigate the role fracturing fluid filtrate from slickwater has on rock-fluid and fluid-fluid interactions and to quantify the resulting multiphase permeability evolution during imbibition and drainage of the filtrate by means of specialized core laboratory techniques. Three suites of experiments were conducted. In the first suite of experiments, a fluid leakoff test was conducted on selected core samples to determine the extent of polymer invasion and leakoff characteristics. In the second suite, multigas relative permeability measurements were conducted on sandstone plugs saturated with fracturing fluid filtrate. A combination of controlled fluid evaporation and pulse decay permeability technique was used to measure liquid and gas effective permeabilities for both drainage and imbibition cycles. These experiments aim to capture dynamic permeability evolution during invasion and cleanup of fracturing fluid (slickwater). The final suite of experiments consists of adsorption flow tests to investigate, identify, and quantify possible mechanisms for adsorption of the polymeric molecules of friction reducers present in the fluid filtrate to the pore walls of the rock sample. Imbibition tests and observations of contact angles were conducted to validate possible wettability changes. Results from multiphase permeability flow tests show an irreversible reduction in endpoint brine permeability and relative permeability with increasing concentration of friction reducer. Our results also show that effective gas permeability during drainage/cleanup of the imbibed slickwater fluid is controlled to a large degree by trapped gas saturation than by changes in interfacial tension. Adsorption flow tests identified adsorption of polymeric molecules of the friction reducer present in the fluid to the pore walls of the rock. The adsorption friction reducer increases the wettability of the rock surface and results in the reduction of liquid relative permeability. The originality of this work is to diagnose formation damage mechanisms from laboratory experiments that adequately capture multiphase permeability evolution specific to a slickwater fluid system, during imbibition and cleanup. This will be useful in optimizing fracturing fluid selection.

Effects of temperature and CO2/Brine cycles on CO2 drainage endpoint phase mobility – implications for CO2 injectivity in deep saline aquifers

The coupled process of (seasonal) CO2 downhole temperature cycles and natural CO2/brine drainage-imbibition cycles is an inherent feature of large-scale CO2 injection schemes during the injection phase of a geologic storage site. Analysis of long-term field injection data shows that the effect of temperature cycles on injectivity is significant and cannot be explained by changes in CO2 properties alone, raising the question of whether CO2-rock properties such as relative permeability are also changing. We present the results of lab-scale coreflood experiments designed to measure CO2 drainage endpoint phase mobilities and relative permeabilities for cyclic CO2 displacing brine at representative reservoir drainage pressure/temperature conditions, using Basal Cambrian Sandstone (BCS) core samples from the storage reservoir of a large-scale (>1Mtpa) CO2 injection scheme in operation. The isothermal experiments are conducted at three temperatures: average seasonal low, average seasonal high, and reservoir. The measurements also incorporate the effects of repeated saturation cycles (or saturation hysteresis), between ∼100% brine saturation and irreducible brine saturation for the same core sample for up to 12 repetitive drainage-imbibition cycles. The results show that the CO2/brine two-phase flow characteristics change after each flooding cycle. CO2 drainage endpoint phase mobility increases as temperature increases, but the mobility increases cannot be fully explained by the decrease in CO2 viscosity and rock permeability changes alone. CO2 endpoint relative permeability (measured at about 0.20 ± 0.1) contributes marginally to the CO2 phase mobility changes with temperature and exhibits a weak inconsistent dependency on temperature. Field scale injectivity of CO2 can be optimised in large-scale CCS injection schemes design by exploiting the CO2 temperature-CO2/brine cycling-phase mobility functional relationship where CO2 phase mobility is enhanced at higher CO2 downhole temperatures. Field data show that this effect, though significant, may be weakened or even overridden by other temperature-dependent phenomena.

Impact of sub-core scale heterogeneity on CO2/brine multiphase flow for geological carbon storage in the upper Minnelusa sandstones

This study aims at understanding effects of sub-core scale petrophysical heterogeneity on CO2-brine multiphase flow properties during CO2 injection in samples of the Minnelusa Formation in Wyoming, representing differing lithofacies. Unsteady-state CO2-brine drainage tests were performed on a core sample from a dune deposit with laminated bedding and poorly sorted grain distribution. To highlight the role of low-porosity and low-permeability bedding layers (LLBL) on CO2 migration during CO2 injection, a contrasting coreflooding experiment was conducted on a sample of well-sorted sandstone collected from an interdune deposit. Assisted history matching was used to estimate the corresponding core-scale relative permeability curves, a procedure that reveals heterogeneity-dependent behavior. The simulated brine production from the optimal history matching case suggests that the main variation in multiphase flow properties could be attributed to internal permeability structures, i.e. sub-core scale LLBL, leading, in turn, to capillary pressure heterogeneity. CO2 sweep efficiency and distribution in heterogeneous Eolian sandstone are hard to estimate based solely on the limited number of coreflooding experiments, due to LLBL properties variability. Consequently, sensitivity analyses for the properties of sub-core scale LLBL on core-scale brine production were conducted using the developed model. Analyses indicate that the residual brine saturation and thickness of LLBL have a more significant effect on bulk brine production, whereas the impact of CO2 end-point relative permeability of LLBL on bulk brine production is negligible. In addition, comparison results show that ignoring the sub-core scale heterogeneity (e.g. sub-core scale relative permeability) during CO2 injection can create significant uncertainties in storage and fluid flow displacement in simulated results, due to important flow effects and thereby physically insightful responses. Overall, this study provides us with a deeper understanding of core-scale CO2-brine multiphase flow properties for CO2 geological storage in heterogeneous sandstones and gained us insights into CO2-brine multiphase flow upscaling in heterogeneous geological models. Our approach needs to be incorporated in upscaling procedures to avoid smearing key small-scale features, relevant to multiphase flow behaviour.

Further Insights into the Performance of Silylated Polyacrylamide-Based Relative Permeability Modifiers in Carbonate Reservoirs and Influencing Factors.

We have previously used surface chemistry analysis techniques to optimize the functionalization of carbonate rocks with a silylated polyacrylamide-based relative permeability modifier (RPM). The RPM is expected to selectively reduce the permeability to water in a hydrocarbon reservoir setting, resulting in a reduction in the amount of produced water while maintaining the production of oil/gas. This study will focus on using core flooding techniques with brine/crude oil under reservoir conditions (i.e., 1500 psi pore pressure and 60 °C temperature) to understand the impact of a silylated polyacrylamide-based RPM on the fluid transport properties in carbonate rocks. The effects of RPM concentration, brine salinity, rock permeability, and pore structure on permeability characteristics were studied. Scanning electron microscopy (SEM) combined with energy dispersive spectroscopy (EDX) provided visual images of the polymer adsorbed onto the rock surfaces and confirmed the attachment of the polymer on the surface of the rock pore space after treatment. The relative percentage of Si increased from 1.65 to 13.55%, and the relative percentage of N increased to 4.54%. Core flooding showed that increasing the PAM-co-AA (poly acrylamide-co-acrylic acid partial sodium salt) concentration resulted in residual resistance factors for oil (RRFoil) and brine (RRFbrine) that were greater than 1. However, there was a modest decrease in the disproportionate permeability reduction (DRP) ratio (RRFbrine/RRFoil) from 1.75 to 1.60 when the polymer concentration was increased from 0.05 to 0.1 wt %. Furthermore, the RRFbrine values decreased slightly from 120 to 62 with increasing salinity (i.e., 1–10% NaCl) because of electrostatic shielding caused by charged ions in brine and the RPM. The cross-over points of relative permeability in these four samples shifted to the right because of the larger decrease in relative water permeability compared with relative oil permeability. End-point relative permeability to water in sample C-5 decreased by 80%, showing a reduction greater than that in the sample C-2 (i.e., 74%). Kr curves indicated a stronger formation damage in sample C-1, C-2, and C-4 than in sample C-5. Rock samples with a higher initial permeability exhibited a higher RRFbrine to RRFoil ratio (i.e., 3.05) under similar test conditions. This can be attributed to a larger pore radius, which was verified by nuclear magnetic resonance (NMR) measurements. Furthermore, a detailed mechanism has been proposed to understand the effects of the RPM on fluid transport in porous carbonate cores. In this study, SEM–EDX and NMR measurements combined with core flooding tests provide insights into the performance of silylated polyacrylamide-based RPMs and benefit its future implementation in carbonate reservoirs.

Predicting the CO2 Footprint in Saline Aquifers: A Numerical-analytical Hybrid Model

In this study, we present a hybrid framework in which we combine pore-scale lattice Boltzmann (LB) simulations with a macroscopic analytical model for predicting CO2 plume migration and its residual trapping in saline aquifers. These integrated methods combine the flexibility of a pore-scale simulation method, allowing for implementing the micro-scale properties such as wettability, with the efficiency of an analytical method, for a quick estimation of the CO2 plume extension and its residual trapping during the injection and post-injection stages. The LB model is adopted to perform two-phase flow simulations of CO2/brine in the microstructure of a rock sample of Tuscaloosa sandstone taken from the Cranfield site in Mississippi. Employing the pore-scale LB simulations, we estimate pore-scale properties such as connate brine saturation, CO2 residual saturation, and CO2 end-point relative permeability. Subsequently, these parameters have been used in the analytical model for predicting the macro-scale behavior of CO2 plume during the injection and post-injection periods. To gain a better insight into the effect of wettability on the footprint of CO2 plume and its residual trapping, we run pore-sale simulations in different samples under various wetting conditions and calculate the pore-scale properties as a function of wettability. Thus, incorporating the pore-scale simulation results into the analytical model helps us evaluate the effect of pore-scale properties such as wettability on storage efficiency. We believe that this approach provides an appropriate tool for the estimation of storage efficiency in CO2 sequestration projects.

Robust Multiobjective Nonlinear Constrained Optimization with Ensemble Stochastic Gradient Sequential Quadratic Programming-Filter Algorithm

Summary As the crucial step in closed-loop reservoir management, robust life-cycle production optimization is defined as maximizing/minimizing the expected value of a predefined objective (cost) function over geological uncertainties (i.e., uncertainties in the reservoir permeability, porosity, endpoint relative permeability, etc.). However, with robust optimization, there is no control over downside risk defined as the minimum net present value (NPV) among the individual NPVs of the different reservoir models. Yet, field operators generally wish to keep this minimum NPV reasonably large to try to ensure that the reservoir is commercially viable. In addition, the field operator may desire to maximize the NPV of production over a much shorter time period than the life of the reservoir under the limitation of surface facilities (e.g., field liquid and water production rates). Thus, it is important to consider multiobjective robust production optimization with nonlinear constraints and when geological uncertainties are incorporated. The three objectives considered in this paper are; to maximize the average life-cycle NPV, to maximize the average short-term NPV, and to maximize the minimum NPV of the set of realizations. Generally, these objectives are in conflict; for example, the well controls that give a global maximum for robust life-cycle production optimization do not usually correspond to the controls that maximize the short-term average NPV of production. Moreover, handling the nonlinear state constraints (e.g., field liquid production rates and field water production rates for the bottom-hole pressure controlled producers in the robust production optimization) is also a challenge because those nonlinear constraints should be satisfied at each control steps for each geological realization. To provide potential solutions to the multiobjective robust optimization problem with state constraints, we developed a modified lexicographic method with a minimizing-maximum scheme to attempt to obtain a set of Pareto optimal solutions and to satisfy all nonlinear constraints. We apply the sequential quadratic programming filter with modified stochastic gradients to solve a sequence of optimization problems, where each solution is designed to generate a single point on the Pareto front. In the modified lexicographic method, the objective is always considered to be the primary objective, and the other objectives are considered by specifying bounds on them to convert them to state constraints. The temporal damping and truncation schemes are applied to improve the quality of the stochastic gradient on nonlinear constraints, and the minimizing–maximum procedure is applied to enforce constraints on the normal state constraints. The main advantage that the modified lexicographic method has over the standard lexicographic method is that it allows for the generation of potential Pareto optimal points, which are uniformly spaced in the values of the second and/or third objective that one wishes to improve by multiobjective optimization.

Effect of the Flow Rate on the Relative Permeability Curve in the CO2 and Brine System for CO2 Sequestration

The relative permeabilities of CO2 and brine are important parameters that account for two-phase flow behavior, CO2 saturation distribution, and injectivity. CO2/brine relative permeability curves from the literature show low endpoint CO2 permeability values and high residual brine saturation values. These are the most distinguishing aspects of the CO2/brine relative permeability from oil/water and gas/oil. In this study, this aspect is investigated experimentally by employing a wide range of CO2 injection flow rates. As a result, all the measurements align with previous studies, having low endpoint relative permeability and high residual brine saturation values. They have obvious relationships with the changes in CO2 flow rates. As the CO2 flow rate increases, the endpoint relative permeability increases, the residual brine saturation decreases, and they converge to specific values. These imply that a high CO2 injection flow rate results in high displacement efficiency, but the improvement in efficiency decreases as the flow rate increases. The reasons are identified with the concept of the viscous and capillary forces, and their significance in the CO2 injection into a reservoir is analyzed.

Analytical modeling and correction of steady state relative permeability experiments with capillary end effects – An improved intercept method, scaling and general capillary numbers

Steady state relative permeability experiments are performed by co-injection of two fluids through core plug samples. Effective relative permeabilities can be calculated from the stabilized pressure drop using Darcy’s law and linked to the corresponding average saturation of the core. These estimated relative permeability points will be accurate only if capillary end effects and transient effects are negligible. This work presents general analytical solutions for calculation of spatial saturation and pressure gradient profiles, average saturation, pressure drop and relative permeabilities for a core at steady state when capillary end effects are significant. We derive an intuitive and general “intercept” method for correcting steady state relative permeability measurements for capillary end effects: plotting average saturation and inverse effective relative permeability (of each phase) against inverse total rate will give linear trends at high total rates and result in corrected relative permeability points when extrapolated to zero inverse total rate (infinite rate). We derive a formal proof and generalization of the method proposed by Gupta and Maloney (2016) [SPE Reserv. Eval. Eng. 19, 02, 316–330], also extending the information obtained from the analysis, especially allowing to calculate capillary pressure. It is shown how the slopes of the lines are related to the saturation functions allowing to scale all test data for all conditions to the same straight lines. Two dimensionless numbers are obtained that directly express how much the average saturation is changed and the effective relative permeabilities are reduced compared to values unaffected by end effects. The numbers thus quantitatively and intuitively express the influence of end effects. A third dimensionless number is derived providing a universal criterion for when the intercept method is valid, directly stating that the end effect profile has reached the inlet. All the dimensionless numbers contain a part depending only on saturation functions, injected flow fraction and viscosity ratio and a second part containing constant known fluid, rock and system parameters such as core length, porosity, interfacial tension, total rate, etc. The former parameters determine the saturation range and shape of the saturation profile, while the latter number determines how much the profile is compressed towards the outlet. End effects cause the saturation profile and average saturation to shift towards the saturation where capillary pressure is zero and the effective relative permeabilities to be reduced compared to the true relative permeabilities. This shift is greater at low total rate and gives a false impression of rate-dependent relative permeabilities. The method is demonstrated with multiple examples. Methodologies for deriving relative permeability and capillary pressure systematically and consistently, even based on combining data from tests with different fluid and core properties, are presented and demonstrated on two datasets from the literature. The findings of this work are relevant to accurately estimate relative permeabilities in steady state experiments, relative permeability end points and critical saturations during flooding or the impact of injection chemicals on mobilizing residual phase.