Subsurface Multiphase Flow Research Articles

Enhancing subsurface multiphase flow simulation with Fourier neural operator

Accurate numerical modeling of multiphase flow in subsurface oil and gas reservoirs is critical for optimizing hydrocarbon recovery. However, traditional physics-based algorithms face substantial computational hurdles due to the need for fine grid resolution and the inherent geological heterogeneity. To overcome these challenges, data-driven surrogate models solving the flow governing partial differential equations (PDEs) offer a promising alternative to enhance the efficiency of hydrocarbon production operations. In this study, we employ the Fourier Neural Operator (FNO) to extract spectral information from the reservoir properties, thereby facilitating the solution of coupled porous flow PDEs. Our focus is on two-phase flow dynamics, specifically exploring how water injection enhances reservoir pressure and displaces oil. This scenario involves solving a set of nonlinearly coupled PDEs with highly heterogeneous coefficients. Numerical results demonstrate that the developed FNO accurately predicts the reservoir pressure distributions. We further observe that the FNO's zero-shot super-resolution capability is sensitive to abrupt local changes in the reservoir pressure near injection and production wells. To enhance its accuracy, we propose a multi-fidelity FNO model that exhibits better adaptability across various grid configurations. After moderate training on graphics processing units (GPUs), the FNO achieves a speedup of three orders of magnitude compared to traditional numerical PDE solvers. Our experiments confirm the FNO's potential to replace repetitive physics-based simulations, significantly advancing computational efficiency in the uncertainty quantification of reservoir performance.

A novel sequential-based hybrid approach incorporating physical modeling and deep learning for multiphase subsurface flow simulation

Multiphase subsurface flows are of great importance for both the sustainable utilization of resources and ecological protection. The simulation of multiphase flow is conventionally resolved using either physics-driven numerical discretization or data-driven machine learning strategy. Despite being perceived as distinct paradigms, their algorithmic-level synergy is expected to bring tremendous advantages. Within the implicit pressure and explicit saturation scheme, this study constructs deep learning model for pressure approximation using an ensemble of equal-probable permeability realizations and the corresponding pressure/velocity fields under randomized injection/production strategies. Specifically, this study proposes two network models, namely U-Net and Fourier Neural Operator, and empower them by physics-guided loss functions, which not only improve the training efficiency but also ensure the physical continuity of the velocity field and maintain the overall mass balance of the coupled system. Moreover, we advance the saturation front using a standard explicit solver under its strict stability condition. The results demonstrate that our hybrid approach performs strong adaptability and flexibility under different permeability and injection/production conditions enclosed in the model training set. For all test cases, we achieve less than 0.6% relative errors for both pressure and saturation solutions. More importantly, our well-trained hybrid solver only uses a fraction of second, which is several orders of magnitude faster than the traditional physics-driven numerical solvers. Our newly designed solution architecture provides a physically reliable technique for superfast multiphase subsurface flow field approximation, which is believed to be of great value for the challenging production optimization and uncertainty quantifications of subsurface resource utilizations.

Pore‐Scale Imaging of Multiphase Flow Fluctuations in Continuum‐Scale Samples

AbstractRepresentative elementary volumes (REVs) are an important concept in studying subsurface multiphase flow at the continuum scale. However, fluctuations in multiphase flow are currently not represented in continuum scale models, and their impact at the REV‐scale is unknown. Previous pore‐scale imaging studies on these fluctuations were limited to small samples with mm‐scale diameters and volumes on the order of ∼0.5 cm3. Here, we image steady‐state co‐injection experiments on a one‐inch diameter core plug sample, with nearly two orders of magnitude larger volume (21 cm3), while maintaining a pore‐scale resolution with X‐ray micro‐computed tomography. This was done for three total flow rates in a series of drainage fractional flow steps. Our observations differ markedly from those reported for mm‐scale samples in two ways: the macroscopic fluid distribution was less ramified at low capillary numbers (Ca) of 10−7; and the volume fraction of intermittency initially increased with increasing Ca (similar to mm‐scale observations), but then decreased at Ca of 10−7. Our results suggest that viscous forces may play a role in the cm‐scale fluid distribution, even at such low Ca, dampening intermittent pathway flow. A representative elementary volume study of the fluid saturation showed that this may be missed in smaller‐scale samples. Pressure drop measurements suggest that the observed pore‐scale fluctuations resulted in non‐Darcy like upscaled behavior. Overall, we show the usefulness of large field‐of‐view, high‐resolution imaging to bridge the gap between pore‐ and continuum‐scale multiphase flow studies.

An efficient workflow for meshing large scale discrete fracture networks for solving subsurface flow problems

A large percentage of subsurface hydrocarbon reservoirs are characterized as very complex due to presence of small to large scale fractures. Modeling of multi-physics processes like, environmental flow, CO2 sequestration, hydrocarbon flows, and so on, through such geologically complex reservoirs is challenging. Main challenges comes from the large scale variation in the fracture scales. Use of traditional modeling approaches, based on dual-porosity/dual permeability medium, to model such complex systems is complicated and results in incorrect flow patterns. Precise and efficient modeling of the fracture networks requires fractures to be represented as lower dimensional objects, which requires an efficient gridding technique. In last decade alone modeling of flow through discrete fracture systems has attracted attention from a number of researchers. As a result few new gridding and discretization techniques have been proposed to model flow through discrete fracture network systems (DFNs). DFN’s usually involve very high or very low angle fracture-fracture intersections and sometime presence of small to very large length scale fracture networks. In this article an efficient workflow for meshing of large scale complex DFN’s networks as lower dimensional objects is presented supported by quantitative results with aim of developing a software tool box, which could be coupled to a subsurface multi-phase flow simulator.

Smooth implicit hybrid upwinding for compositional multiphase flow in porous media

In subsurface multiphase flow simulations, poor nonlinear solver performance is a significant runtime sink. The system of fully implicit mass balance equations is highly nonlinear and often difficult to solve for the nonlinear solver, generally Newton(-Raphson). Although the physical problem is inherently nonlinear, discretization schemes introduce several strong nonlinearities that can cause Newton iterations to diverge or converge very slowly. This frequently results in time step cuts, leading to wasted iterations and computationally expensive simulations. Much literature has looked into how to improve the nonlinear solver through enhancements or safeguarding updates. In this work, we take a different approach; we aim to improve convergence with a smoother finite volume discretization scheme which is more suitable for the Newton solver.Building on recent work, we propose a novel total velocity hybrid upwinding scheme with weighted average flow mobilities (WA-HU TV) that is unconditionally monotone and extends to compositional multiphase simulations. Analyzing the solution space of a one-cell problem, we demonstrate the improved properties of the scheme and explain how it leverages the advantages of both phase potential upwinding and arithmetic averaging. This results in a flow subproblem that is smooth with respect to changes in the sign of phase fluxes, and is well-behaved when phase velocities are large or when co-current viscous forces dominate. Additionally, we propose a WA-HU scheme with a total mass (WA-HU TM) formulation that includes phase densities in the weighted averaging.The proposed WA-HU TV consistently outperforms existing schemes, yielding benefits from 5% to over 50% reduction in nonlinear iterations. The WA-HU TM scheme also shows promising results; in some cases leading to even more efficiency. However, WA-HU TM can occasionally also lead to convergence issues. Overall, based on the current results, we recommend the adoption of the WA-HU TV scheme as it is highly efficient and robust.

Semi-Implicit Finite Volume Procedure for Compositional Subsurface Flow Simulation in Highly Anisotropic Porous Media

Subsurface multiphase flow in porous media simulation is extensively used in many disciplines. Large meshes with non-orthogonalities (e.g., corner point geometries) and full tensor highly anisotropy ratios are usually required for subsurface flow applications. Nonetheless, simulations using two-point flux approximations (TPFA) fail to accurately calculate fluxes in these types of meshes. Several simulators account for non-orthogonal meshes, but their discretization method is usually non-conservative. In this work, we propose a semi-implicit procedure for general compositional flow simulation in highly anisotropic porous media as an extension of TPFA. This procedure accounts for non-orthogonalities by adding corrections to residual in the Newton-Raphson method. Our semi-implicit formulation poses the guideline for FlowTraM (Flow and Transport Modeller) implementation for research and industry subsurface purposes. We validated FlowTraM with a non-orthogonal variation of the Third SPE Comparative Solution Project case. Our model is used to successfully simulating a real Colombian oil field.

Contribution of dynamic capillary pressure to rainfall infiltration in thin homogeneous growth substrates

The use of green roofs to help mitigate storm water contributions to urban flooding has been gaining popularity but is hindered by the limited data on the performance of such roofs with regard to storm water runoff mitigation. The underlying issue stems from the inherent complexity of modeling subsurface multiphase flow. Modeling of this phenomena requires calculating the contributions of substrate microstructure characteristics, the influence of the wetting and non-wetting phases upon each other, and the effect of the microstructure on the wetting phase. Previously we have observed how the microstructure can affect detention, however the quantification of this relationship is still missing. In the present paper we present numerical simulations of wetting phase infiltration of a thin monodisperse packed bed in order to understand and quantify the impact of microstructure geometry on storm water infiltration of a green roof substrate. For a slightly hydrophilic case, (θ=82°), we find that a dominant mechanism underlying this relationship is the microstructure-induced dynamic behavior of the capillary pressure. We determine that at larger packing ratios (ratio of packed bed depth to particle size), the influence of hydraulic head diminishes and behaves conversely for thinner layers, particularly when larger pores are present. Indeed, thin beds composed of large particles can exhibit high flow velocities that in turn affect the capillary pressure within the substrate. We observe that the capillary pressure can shift from negative values denoting capillary suction to positive ones which cause valve-like blocking effects on the flow; dependent upon the flow velocity as determined by the microstructure. In particular, we find that the capillary pressure depends on the value of the pore-scale gravity-induced flow velocity, quantified through a characteristic Capillary number. The provided quantification of this relationship can be invaluable from a design perspective to understand the behavior of capillary pressure of different substrates under a variety of flow rates prior to testing substrate candidates. In addition, a comparison of the behavior of the dynamic component of capillary pressure to other works is undertaken. Flow homogeneity is also found to be linked to the flow velocity, and consequently to the microstructure.

Quantitative analysis of the influence of capillary pressure on geologic carbon storage forecasts case study: CO2-EOR in the Anadarko basin, Texas

Numerical models are a critical tool for forecasting subsurface multiphase flow associated with geologic carbon storage. The uncertainty of model results stems from many factors, including uncertainty in multiphase flow parameters. Specifically, relative permeability and capillary pressure relationships depend on both the rock properties and fluid properties, and the latter may be highly nonlinear as fluid temperature, and pressure conditions change. Forecasts of trapping mechanisms, phase behavior, and plume movement are impacted by choice of relative permeability and capillary pressure functions and how those functions are calibrated and constrained. In particular, one of the most neglected aspects of such simulations is meaningful capillary pressure processes. A primary goal of this study is to quantify the difference in forecasts for models that utilize capillary pressure functions calibrated with measured data from the results of models without such. Additionally, the relative permeability models developed here were derived from measured capillary pressure data. Those data were used to constrain saturation endpoints in the relative permeability curves and dictate how that relative permeability was distributed spatially. The main conclusions drawn from this analysis include (1) heterogeneity in relative permeability plays a significant role in simulated forecasts of CO2 migration, trapping mechanisms and storage capacity, as well as oil and water production, and (2) capillary pressure, and in particular, the magnitude of capillarity also plays a significant role in these processes. Conversely, if the magnitude of capillarity is small relative to in situ fluid pressures, it imparts insignificant effects on these processes.

Real‐Time Imaging Reveals Distinct Pore‐Scale Dynamics During Transient and Equilibrium Subsurface Multiphase Flow

AbstractMany subsurface fluid flows, including the storage of CO2 underground or the production of oil, are transient processes incorporating multiple fluid phases. The fluids are not in equilibrium meaning macroscopic properties such as fluid saturation and pressure vary in space and time. However, these flows are traditionally modeled with equilibrium (or steady‐state) flow properties, under the assumption that the pore‐scale fluid dynamics are equivalent. In this work, we used fast synchrotron X‐ray tomography with 1 s time resolution to image the pore‐scale fluid dynamics as the macroscopic flow transitioned to steady state. For nitrogen or decane, and brine injected simultaneously into a porous rock, we observed distinct pore‐scale fluid dynamics during transient flow. Transient flow was found to be characterized by intermittent fluid occupancy, whereby flow pathways through the pore space were constantly rearranging. The intermittent fluid occupancy was largest and most frequent when a fluid initially invaded the rock. But as the fluids established an equilibrium the dynamics decreased to either static interfaces between the fluids or small‐scale intermittent flow pathways, depending on the capillary number and viscosity ratio. If the fluids were perturbed after an equilibrium was established, by changing the flow rate, the transition to a new equilibrium was quicker than the initial transition. Our observations suggest that transient flows require separate modeling parameters. The time scales required to achieve equilibrium suggest that several meters of an invading plume front will have flow properties controlled by transient pore‐scale fluid dynamics.

Monitoring and surveillance of subsurface multiphase flow and well integrity

With maturing oil fields, there is an increasing focus on improving the oil recovery factor and pushing the envelope towards a 70% target. This target is indeed very challenging and can be reached by fully understanding the reservoir characteristics before using an enhanced oil recovery method. These include reservoir heterogeneities, displacement efficiency, horizontal sweep, vertical sweep due to flow behind the casing, and the presence of conductive faults or fractures. Therefore, a proper surveillance should be performed to evaluate the injectant plume front, reservoir conformance, well connectivity, and the assessment of well integrity, which can be crucial for the success of the project and its future development. This paper discusses a special downhole logging technique including a set of conventional multiphase sensors alongside high precision temperature (HPT) and high-definition spectral noise logging (SNL-HD). It was run for an injector and producer pair near the wellbore area to provide complete assessment of the integrity issues that might impair the lateral sweep of injectants into the target layer. The operation was carried out with a tool string that contained no mechanical parts and was not affected by downhole fluid properties. It was also conducted under both flowing and shut-in conditions to identify flow zones, to check fracture signatures and to provide multiphase fluid velocity profiles. The results of the survey allowed for in-depth assessment of borehole and behind casing flow, confirming lateral continuity, and allow for better well planning and anticipation of possible loss of well integrity. Combining the behind casing flow assessment with borehole multiphase flow distribution can be used for production optimization by sealing unwanted water contributing zones that might impair production in the future.

Iterative Ensemble Kalman Filter and genetic algorithm for automatic reconstruction of relative permeability curves in the subsurface multi-phase flow

Relative permeability curves are one of the main factors that control the behavior of multi-phase flow in underground energy resources. The incorrect selection of relative permeability curves can lead to inaccurate predictions of the reservoir's future behavior. Accurate prediction of the reservoirs transient behavior is therefore vital as it influences subsequent political and management decisions. In this study, two different algorithms, namely GA (Genetic Algorithm) and Iter EnKF (Iterative Ensemble Kalman Filter), were used to estimate the optimal set of relative permeability curves aiding Corey's three-phase relative permeability correlation. A synthetic reservoir model was used as a benchmark to compare the accuracy and efficiency of the utilized algorithms. Sensitivity analysis was conducted over the type of cost function used within the optimization algorithm. Graphical results, such as time-evolved reservoir parameters, saturation maps, and mismatch of the relative permeability curves were used for comparison purposes. The comparison study unveiled that oil recovery is the best option to be included in the cost function with a mean AARD (Average Absolute Relative Deviation) of around 6%. Nonetheless, the inherent non-uniqueness of the problem showed that the best optimal case based on the mismatch analysis might not necessarily represent the true relative permeability curves. Overall, parameters such as “oil recovery” and “cumulative gas production” better captured the evolution of the well and reservoir state variables with time, probably due to the consideration of the history of production at each data point. Finally, a comparison between GA and Iter EnKF showed that the difference between the optimal solutions obtained using these two algorithms is almost insignificant. Computational time analysis showed that both algorithms have almost the same running time for small population sizes while Iter EnKF leads to lower computation times for population sizes larger than 50.

The application of the yield approach to study slurry migration in drill cuttings waste underground disposal

The underground disposal of drill cuttings waste is a common practice for the gas/oil industry to achieve zero-discharge sustainable development. In this study, a numerical modeling approach was developed to simulate the slurry flow for underground disposal of drill cuttings waste. The modeling approach was coupled with and implemented in the well-known general purpose subsurface multiphase flow simulator, TOUGH2. The new modeling approach treats the slurry flow behavior in subsurface systems as Bingham plastic liquid, with a linear relationship representing the yield stress and the concentration of the gelatinizer in the slurry. In addition, the precipitation-dissolution process was taken into account for solid-aqueous phase changes of the water-slurry mixture under and over the threshold pressure. The model has been verified by the analytical solution of a transient flow of single-phase Bingham fluid, and has further been tested by modeling field-scale injection of drill cutting wastes into a multi-layered geological formation in Texas. A hypothetical model has also been used to conduct sensitivity analysis of the impact of slurry density, injection depth and injection pattern on the storage formation performance. The results revealed that the effect of injection volume is greater than the mass on pressure buildup. In addition, a short period of intermittent reinjection can lead to an earlier formation breakdown due to particle sedimentation and reduce the storage capacity. The developed model can be used to evaluate the prediction of slurry transport, storage capacity, pressure distribution, and the formation breakdown time in a drill cuttings waste disposal project.

Wetting Behavior of Shale Rocks and Its Relationship to Oil Composition

The wettability of shale oil reservoirs is an important petrophysical property to determine subsurface multiphase flow and residual oil saturation. While a few studies have been undertaken to under...

Prediction of Relative Air Permeability of Porous Media With Weibull Pore Size Distribution

AbstractModeling convective air movement in unsaturated porous media requires appropriate characterization of the relative air permeability (RAP). Adopting Assouline et al. (1998, https://doi.org/10.1029/97WR03039) water retention function that is based on the Weibull pore size distribution, this study was conducted to derive seven new predictive RAP models. These 7 new models, together with another 3 models developed by Assouline et al. (2016, https://doi.org/10.1002/2015WR018286), were then compared with data from 30 disturbed soil samples to investigate their predictive RAP performances. The model and data comparison results showed that the modified Burdine, modified Mualem, and modified Alexander and Skaggs relative permeability models proposed by Yang and Mohanty (2015, https://doi.org/10.1002/2014WR016190) had the highest accuracy for the RAP prediction among the 10 investigated models, which indicated that the tortuosity and connectivity exponent of water phase should be smaller than that of air phase for the disturbed soil samples. The modified Burdine, modified Mualem, and modified Alexander and Skaggs models were then the suggested RAP parameterizations for the subsurface multiphase flow numerical simulation.

Insights into the wettability alteration of CO2-assisted EOR in carbonate reservoirs

Wettability of oil-brine‑carbonate system is an important petro-physical parameter, which governs subsurface multiphase flow and residual oil saturation. CO2-assisted EOR techniques have been identified as cost-effective and environmentally friendly means to unlock remaining hydrocarbon resources from carbonate reservoirs. While wettability alteration appears to be one of the main mechanisms during CO2-assisted EOR implementation, the controlling factor(s) of wettability alteration at molecular level remains unclear. We thus hypothesized that excess of H+ as a result of water uptake of CO2 increases hydrophilicity of oil-brine‑carbonate systems. More specifically, the surface charge properties will be alterated to more positive due to the increase of H+ in the brine. To test this hypothesis, we measured oil contact angles on calcite surfaces in the presence of non‑carbonated brine, carbonated brine, and acidic brine (pH = 3). We also performed surface complexation modelling to examine how the surface chemistry controls over wettability of oil/brine/carbonate system using PHREEQC. Our contact angle results show that both carbonated brine and acidic brine gave a contact angle of 24° and 22°, respectively, while non‑carbonated brine gives a contact angle of 73° in 1 mol/L CaCl2 brines. Same trend was also observed in synthesized formation brine, showing that non‑carbonated formation brine yielded a contact angle of 69° while both acidic formation brine and carbonated formation brine gave a contact angle of 37°. Experimental results show that both carbonated brine, and acidic brine significantly decreased contact angle compared to non‑carbonated brine, suggesting a strong water-wet system. Surface complexation modelling shows that for both carbonated water and acidic water, >CaOH2+ dominates surface charges at calcite surfaces, and NH+ governs surface charges on oil surfaces. Together, these two processes increase repulsive forces thus hydrophilicity. Our study sheds light on the significant influence of excess H+ due to water uptake of CO2 on oil-brine‑carbonate system wettability thus enhancing hydrocarbon recovery in carbonate reservoirs.

Relative permeability for water and gas through fractures in cement.

Relative permeability is an important attribute influencing subsurface multiphase flow. Characterization of relative permeability is necessary to support activities such as carbon sequestration, geothermal energy production, and oil and gas exploration. Previous research efforts have largely neglected the relative permeability of wellbore cement used to seal well bores where risks of leak are significant. Therefore this study was performed to evaluate fracturing on permeability and relative permeability of wellbore cement. Studies of relative permeability of water and air were conducted using ordinary Portland cement paste cylinders having fracture networks that exhibited a range of permeability values. The measured relative permeability was compared with three models, 1) Corey-curve, often used for modeling relative permeability in porous media, 2) X-curve, commonly used to represent relative permeability of fractures, and 3) Burdine model based on fitting the Brooks-Corey function to fracture saturation-pressure data inferred from x-ray computed tomography (XCT) derived aperture distribution results. Experimentally-determined aqueous relative permeability was best described by the Burdine model. Though water phase tended to follow the Corey-curve for the simple fracture system while air relative permeability was best described by the X-curve.

Excess H+ Increases Hydrophilicity during CO2-Assisted Enhanced Oil Recovery in Sandstone Reservoirs

CO2-assisted enhanced oil recovery appears to be a cost-effective and an environmentally friendly means to unlock remaining oil resources from sandstone reservoirs. While wettability alteration due to water uptake of CO2 has been identified as one of the primary mechanisms to govern subsurface multiphase flow and thus residual oil saturations, few works have been done to explore the leading factor of wettability alteration and fewer works have looked beyond the quantitative characterization of this physical process. We hypothesized that water uptake of CO2 provides excess H+ which decreases electrostatic bridges of an oil–brine–sandstone system, thus increasing hydrophilicity. To test our hypothesis, we conducted three sets of contact angle measurements in non-carbonated and carbonated brines using muscovite substrates at the pressure of 3000 psi and temperature of 25 °C. Moreover, we performed a geochemical study to quantify how excess H+ governs electrostatic bridges in the oil–brine–muscovite system bearing basal charged clays. Our contact angle measurements show that non-carbonated water gave a contact angle of 118°, whereas carbonated brine gave a contact angle of 30°, implying a strong hydrophilic system. Geochemical modeling demonstrates that excess H+ substantially substitutes exchangeable cations (>Na) embedded in muscovite, thus decreasing electrostatic bridges between oil–brine–muscovite. This work provides a first quantitative investigation on how water uptake of CO2 depresses the ion-exchange process between oil–brine–muscovite, thus leading to wettability alteration.

Effect of electrical double layer and ion exchange on low salinity EOR in a pH controlled system

Wettability of an oil/brine/sandstone system is an important petro-physical parameter, governing subsurface multi-phase flow and residual oil saturations. While how edge-charged clays (e.g., kaolinite) contribute to low salinity effect has been extensively investigated, few work have been done on basal-charged clays (e.g., illite, smectite, and chlorite), and few have look beyond the application of the low salinity effect in reservoirs bearing basal-charged clays. We thus integrated atomic force microscopy (AFM) (at a given pH = 7), disjoining pressure calculations, together with surface complexation modelling to understand the importance of basal-charged clays during low salinity water flooding in sandstone reservoirs. We found that low salinity effect can take place without pH increase, confirming that electrical double layer is at least one of the mechanisms to yield low salinity effect, which can be interpreted using disjoining pressure isotherm, whereas ion exchange between oil and basal charged clays leads to an opposite effect at a given pH. However, ion exchange likely favors low salinity effect without controlling pH due to the chemical reaction: >Na + H+ = >H + Na+, which in return decreasing the electrostatic bridges between NH+/clays, COOCa+/clays. Knowing the contribution of EDL and ion exchange on oil/brine/basal-charged clays interaction, the potential of low salinity effect in sandstone reservoirs can be quantified.

Reduced-Order Modeling of Subsurface Multi-phase Flow Models Using Deep Residual Recurrent Neural Networks

We present a reduced-order modeling technique for subsurface multi-phase flow problems building on the recently introduced deep residual recurrent neural network (DR-RNN) (Nagoor Kani et al. in DR-RNN: a deep residual recurrent neural network for model reduction. ArXiv e-prints, 2017). DR-RNN is a physics-aware recurrent neural network for modeling the evolution of dynamical systems. The DR-RNN architecture is inspired by iterative update techniques of line search methods where a fixed number of layers are stacked together to minimize the residual (or reduced residual) of the physical model under consideration. In this manuscript, we combine DR-RNN with proper orthogonal decomposition (POD) and discrete empirical interpolation method (DEIM) to reduce the computational complexity associated with high-fidelity numerical simulations. In the presented formulation, POD is used to construct an optimal set of reduced basis functions and DEIM is employed to evaluate the nonlinear terms independent of the full-order model size. We demonstrate the proposed reduced model on two uncertainty quantification test cases using Monte Carlo simulation of subsurface flow with random permeability field. The obtained results demonstrate that DR-RNN combined with POD–DEIM provides an accurate and stable reduced model with a fixed computational budget that is much less than the computational cost of standard POD–Galerkin reduced model combined with DEIM for nonlinear dynamical systems.

PH effect on wettability of oil/brine/carbonate system: Implications for low salinity water flooding

Wettability of oil/brine/carbonate system is a critical parameter to govern subsurface multi-phase flow behaviour, thus remaining oil saturation and ultimate oil recovery in carbonate reservoirs. Despite the fact that salinity level, ionic strength, oil composition and rock chemistry (e.g., limestone and dolomite) have been extensively investigated, few work has been done regarding the effect of pH on oil/brine/rock interaction, thus wettability.We thereby measured contact angles at two different pH (pH = 3 and 8) in the presence of either 1 mol/L Na2SO4 or 1 mol/L CaCl2 using a crude oil with acid number of 1.7 and base number of 1.2 mg KOH/g. Moreover, we performed a geochemical modelling study in light of the diffuse double layer to understand how pH controls the number of surface species at interfaces of oil/brine and brine/carbonate. Our results show that pH scales with oil/brine/carbonate wettability, demonstrating that pH is one of the controlling factors to govern the system wettability. Further, our results suggest that pH (6.5–7.5) likely triggers an oil-wet system, which is favourable for low salinity water flooding, but pH < 5 usually exhibits a water-wet system, which explains why low salinity effect is not always observed in carbonate reservoirs. This also confirms that CO2 flooding, carbonated water flooding, and CO2 huff-and-puff EOR very likely renders a strongly water-wet system due to H+ adsorption on the interface of oil/brine and brine/carbonate as a result of CO2 dissolution.