Three-phase Flow In Porous Media Research Articles

In-situ characterization of capillary pressure during three-phase flow in porous media

We characterize the pore-scale fluid distributions, phase connectivity, and local capillary pressures during three-phase flow in a water-wet Berea sandstone sample. In this investigation, we use a set of x-ray micro-tomography images acquired during three-phase core-flooding experiments conducted on a miniature core sample. We use several image analysis techniques to analyze the pore-scale fluid occupancy maps and use this information to develop several insights related to pore occupancy, oil and gas cluster distribution, and interfacial curvature during the gas injection process. The results of our investigation show that the large-, intermediate-, and small-sized pores are mostly occupied with gas, oil, and brine, respectively, which is consistent with the wetting order of the fluids (i.e., gas, oil, and brine are the nonwetting, intermediate wetting, and wetting phases, respectively). In addition, the connectivity analysis reveals that a significant amount of the gas phase was in the form of disconnected ganglia separated from the connected invading cluster. The presence of these trapped nonwetting phase clusters during the drainage process is presumably attributed to Roof snap-off and Haines jump events, as well as the anti-ripening phenomenon. Moreover, the average local oil-water capillary pressures are found to be greater than the gas-oil counterparts. This observation is then related to the relative location of the interfaces in the pore space and the threshold capillary pressures at which the various displacement events take place.

Uncertainty propagation and sensitivity analysis of three-phase flow in porous media using polynomial chaos expansion

In this study, polynomial chaos expansion (PCE) will be utilized to investigate propagation and evolution of uncertainty from uncertain model parameters to model outputs. Unknown PCE coefficients are calculated using probabilistic collocation method (PCM), which is a non-intrusive technique. The proposed approach is evaluated on a 2D reservoir under three-phase flow condition. By use of PCEs, dependent model outputs, such as well bottomhole pressure and production rates, are represented as functions of uncertain model parameters, including parameters defining the capillary pressure (Pc) and relative permeability (kr) curves. Accuracy, compatibility and efficiency of the proposed approach are compared with Monte Carlo (MC) method, which is considered as the reference case. Mean values, standard deviations and histograms for well bottomhole pressure and production rates estimated from the PCM-based PCE are closely matched to those obtained from MC method. This discloses the fact that the proposed approach can successfully restore the simulation model to represent propagation of uncertainty from uncertain model parameters toward model outputs and to perform sensitivity analysis (SA). Unlike the MC approach which requires an extremely large number of realizations to obtain accurate results, the PCM-based PCE requires to perform model evaluations only at the selected collocation points, thus the computational cost is significantly reduced. Subsequently, using the proposed PCE as the surrogate model of the reservoir, Sobol's sensitivity indices are calculated analytically. Results of SA reveal that those parameters defining Pc curves have negligible effect on the model outputs compared with those parameters defining kr curves, and thus may be ignored during history matching process. Moreover, it is observed that the effects caused by interactions between uncertain kr and Pc parameters have negligible contribution compared to the individual effect of each parameter.

Pore-scale study on interfacial force-induced residue mobilization under immiscible ternary fluids flow

Immiscible three-phase flow and the trapping/mobilizing mechanism are significant to many water and energy applications such as water infiltration, oily wastewater treatment, CO2 sequestration, and water-alternating-gas (WAG) for oil recovery enhancement. This work targets the ternary fluid system, namely water, gas, and oil, to uncover the significant role of interfacial forces in the transient flow behavior and trapped-phase mobilization. From both the lattice Boltzmann method (LBM) modeling and experimental observations, we firstly showed the deformation and mobilization process of the oil droplet when interacting with water droplet in air. The re-distribution of oil phase reveals the strong interfacial interactions at the water-gas-oil three-phase contact point (fluid-TPCP). For the more complicated three-phase flow in porous media, our visualization results also showed that the trapped oil phase, which initially adhered to rough surfaces or inside dead-end pores, was extracted by the pulling effect at fluid-TPCP during WAG injection. The influence of surface wettability conditions residue extraction efficiency was also discussed. This work provides insightful understandings of the interfacial forces in mobilizing the residues under immiscible three-phase flow in porous media.

Application of Gene Expression Programming (GEP) in Modeling Hydrocarbon Recovery in WAG Injection Process

Water alternating gas (WAG) injection has been successfully applied as a tertiary recovery technique. Forecasting WAG flooding performance using fast and robust models is of great importance to attain a better understanding of the process, optimize the operational conditions, and avoid high-cost blind tests in laboratory or pilot scales. In this study, we introduce a novel correlation to determine the performance of the near-miscible WAG flooding in strongly water-wet sandstones. We conduct dimensional analysis with Buckingham’s π theorem technique to generate dimensionless numbers using eight key parameters. Seven dimensionless numbers are employed as the input variables of the desired correlation for predicting the recovery factor of a near-miscible WAG injection. A verified mathematical model is used to generate the required training and testing data for the development of the correlation using a gene expression programming (GEP) algorithm. The provided data points are then separated into two subsets: training (67%) to develop the model and testing (33%) to assess the models’ capability. Conducting error analysis, statistical measures and graphical illustrations are provided to assess the effectiveness of the introduced model. The statistical analysis shows that the developed GEP-based correlation can generate target data with high precision such that the training phase leads to R2 = 92.85% and MSE = 1.38 × 10−3 and R2 = 91.93% and MSE = 4.30 × 10−3 are attained for the testing phase. The relative importance of the input dimensionless groups is also determined. According to the sensitivity analysis, decreasing the oil–water capillary number results in a significant reduction in RF in all cycles. Increasing the magnitudes of oil to gas viscosity ratio and oil to water viscosity ratio lowers the RF of each cycle. It is found that oil to gas viscosity ratio has a higher impact on RF value compared to oil to water viscosity ratio due to a higher viscosity gap between the gas and oil phases. It is expected that the GEP, as a fast and reliable tool, will be useful to find vital variables including relative permeability in complex transport phenomena such as three-phase flow in porous media.

Semi-analytic treatment of mixed hyperbolic–elliptic Cauchy problem modeling three-phase flow in porous media

This work provides a technical applied description of the residual power series method (RPSM) to develop a fast and accurate algorithm for mixed hyperbolic–elliptic systems of conservation laws with Riemann initial datum. The RPSM does not require discretization, reduces the system to an explicit system of algebraic equations and consequently of massive and complex computations, and provides the solution in a form of Taylor power series expansion of closed-form exact solution (if exists). Theoretically, convergence hypotheses are discussed, and error bounds of exponential rates are derived. Numerically, the convergence and stability of approximate solutions are achieved for systems of mixed type. The reported results, with application to general Cauchy problems, which rise in diverse branches of physics and engineering, reveal the reliability, efficiency, and economical implementation of the proposed algorithm for handling nonlinear partial differential equations in applied mathematics.

Analytical solution for one-dimensional three-phase incompressible flow in porous media for concave relative permeability curves

Three-phase flow in porous media may appear in different scenarios during the production life of a hydrocarbon reservoir. The simultaneous flow of different phases is modeled by relative permeability curves which are fundamental to petroleum production analysis and forecast. Laboratory experiments are the main source of data for relative permeability curves. Mathematical solutions for multiphase flow in porous medium are key for determining relative permeability curves from laboratory data, to check numerical reservoir simulation results and for screening an enhanced oil recovery technique. The complexity of reservoir modeling and the use of numerical optimization to history match the laboratory data have shown the importance of concave relative permeability curves. In this paper we present the analytical solution for one-dimensional incompressible immiscible three-phase flow in porous media, where the relative permeability functions are described by concave curves. The hyperbolic system of equations that results from mass conservation is solved by the method of characteristics. The results show close agreement to numerical solutions.

Pore-Scale Imaging and Analysis of Wettability Order, Trapping and Displacement in Three-Phase Flow in Porous Media with Various Wettabilities

Three-phase flow in porous media is encountered in many applications including subsurface carbon dioxide storage, enhanced oil recovery, groundwater remediation and the design of microfluidic devices. However, the pore-scale physics that controls three-phase flow under capillary dominated conditions is still not fully understood. Recent advances in three-dimensional pore-scale imaging have provided new insights into three-phase flow. Based on these findings, this paper describes the key pore-scale processes that control flow and trapping in a three-phase system, namely wettability order, spreading and wetting layers, and double/multiple displacement events. We show that in a porous medium containing water, oil and gas, the behaviour is controlled by wettability, which can either be water-wet, weakly oil-wet or strongly oil-wet, and by gas–oil miscibility. We provide evidence that, for the same wettability state, the three-phase pore-scale events are different under near-miscible conditions—where the gas–oil interfacial tension is ≤ 1 mN/m—compared to immiscible conditions. In a water-wet system, at immiscible conditions, water is the most-wetting phase residing in the corners of the pore space, gas is the most non-wetting phase occupying the centres, while oil is the intermediate-wet phase spreading in layers sandwiched between water and gas. This fluid configuration allows for double capillary trapping, which can result in more gas trapping than for two-phase flow. At near-miscible conditions, oil and gas appear to become neutrally wetting to each other, preventing oil from spreading in layers; instead, gas and oil compete to occupy the centre of the larger pores, while water remains connected in wetting layers in the corners. This allows for the rapid production of oil since it is no longer confined to movement in thin layers. In a weakly oil-wet system, at immiscible conditions, the wettability order is oil–water–gas, from most to least wetting, promoting capillary trapping of gas in the pore centres by oil and water during water-alternating-gas injection. This wettability order is altered under near-miscible conditions as gas becomes the intermediate-wet phase, spreading in layers between water in the centres and oil in the corners. This fluid configuration allows for a high oil recovery factor while restricting gas flow in the reservoir. Moreover, we show evidence of the predicted, but hitherto not reported, wettability order in strongly oil-wet systems at immiscible conditions, oil–gas–water, from most to least wetting. At these conditions, gas progresses through the pore space in disconnected clusters by double and multiple displacements; therefore, the injection of large amounts of water to disconnect the gas phase is unnecessary. We place the analysis in a practical context by discussing implications for carbon dioxide storage combined with enhanced oil recovery before suggesting topics for future work.

Hybrid mathematical modelling of three-phase flow in porous media: Application to water-alternating-gas injection

Machine learning algorithms are extensively used to reduce the complexity of applied problems in various fields, including energy. Accurate prediction of the performance of water alternating gas (WAG) injection as an enhanced oil recovery (EOR) process is of great importance in the optimal management of hydrocarbon resources. In the current work, a hybrid mathematical model is proposed for the near-immiscible WAG injection process. We use data-driven sub-models, including least square support vector machine (LSSVM) and adaptive neuro-fuzzy inference system (ANFIS) in series with an empirical model (EM) and a first principle model (FPM) to study three-phase flow in porous media. The LSSVM and ANFIS sub-models predict the two-phase water-oil, gas-oil, and gas-water relative permeabilities. The outputs from these models are supplied to the empirical models (EMs) to estimate the three-phase relative permeabilities for oil, gas, and water phases. The model developed using LSSVM shows a better prediction performance in estimating the relative permeabilities, compared to that using ANFIS. The relative importance parameter analysis reveals that for the LSSVM sub-model, water saturation is the most influencing input parameter for the gas-water and oil-water systems while for the gas-oil system, gas saturation is the most important input parameter. Using the models proposed in this work, some hybrid models are developed to forecast the ultimate recovery factor (RF) in the testing phase. The predicted ultimate RF values are 92.0%, 91.6%, and 82.9% for the correlation-based EM-FPM, LSSVM-EM-FPM, and ANFIS-EM-FPM hybrid models, respectively, in comparison to the measured ultimate RF value of 93.6% after three cycles of water and gasinjection. Among the proposed hybrid models, the LSSVM-EM-FPM model significantly removes the non-linearity of the two-phase relative permeabilities. In general, the LSSVM-EM-FPM hybrid model possesses the same level of accuracy as that of the EM-FPM hybrid model, but with significantly less model complexity and non-linearity. Thus, the LSSVM-EM-FPM hybrid model can be used in demanding applications such as optimization and control of the WAG injection process, leading to a better resource management.

On the relationship between capillary pressure, saturation, and interfacial area for three-phase flow in water-wet porous media

We encounter three-phase flow in porous media within a range of settings, such as enhanced oil recovery, geologic CO2 sequestration, and groundwater remediation. While an abundance of studies has been performed on the behavior of two fluid phases (e.g. oil/water or air/water) in porous media, relatively little information exists for three-phase flow systems (e.g. oil/water/air). This work explores the relationships between capillary pressure (Pc), saturation (S) and fluid-fluid interfacial area (a) for water-wet three-phase flow systems where water is the wetting phase, oil is the intermediate-wet phase, and air (or gas) is the non-wetting phase. Specifically, we examine whether the Pc-S-a relationships exhibit hysteresis during drainage and imbibition cycles. We present data collected via x-ray microtomography resulting in high-resolution three-dimensional images of the fluid configurations for varying degrees of saturation. Among the findings of the study (based on the available data), we highlight that (1) the Pc-S-a relationship is non-hysteretic for both the oil-water fluid pair, and the air-oil fluid pair, and (2) that this same relationship is independent of the initial water saturation at the point of air injection. This finding suggests that both the oil-water and air-oil fluid pairs in a three-phase system can be adequately described by the thermodynamics-based theory originally proposed by Hassanizadeh and Gray (1993), as is the case for the equivalent two-phase system.

Determination of contact angles for three-phase flow in porous media using an energy balance

HypothesisWe define contact angles, θ, during displacement of three fluid phases in a porous medium using energy balance, extending previous work on two-phase flow. We test if this theory can be applied to quantify the three contact angles and wettability order in pore-scale images of three-phase displacement. TheoryFor three phases labelled 1, 2 and 3, and solid, s, using conservation of energy ignoring viscous dissipation (Δa1scosθ12-Δa12-ϕκ12ΔS1)σ12=(Δa3scosθ23+Δa23-ϕκ23ΔS3)σ23+Δa13σ13, where ϕ is the porosity, σ is the interfacial tension, a is the specific interfacial area, S is the saturation, and κ is the fluid–fluid interfacial curvature. Δ represents the change during a displacement. The third contact angle, θ13 can be found using the Bartell-Osterhof relationship. The energy balance is also extended to an arbitrary number of phases. FindingsX-ray imaging of porous media and the fluids within them, at pore-scale resolution, allows the difference terms in the energy balance equation to be measured. This enables wettability, the contact angles, to be determined for complex displacements, to characterize the behaviour, and for input into pore-scale models. Two synchrotron imaging datasets are used to illustrate the approach, comparing the flow of oil, water and gas in a water-wet and an altered-wettability limestone rock sample. We show that in the water-wet case, as expected, water (phase 1) is the most wetting phase, oil (phase 2) is intermediate wet, while gas (phase 3) is most non-wetting with effective contact angles of θ12≈48° and θ13≈44°, while θ23=0 since oil is always present in spreading layers. In contrast, for the altered-wettability case, oil is most wetting, gas is intermediate-wet, while water is most non-wetting with contact angles of θ12=134°±~10°,θ13=119°±~10°, and θ23=66°±~10°.

A compressible viscous three-phase model for porous media flow based on the theory of mixtures

In this paper we focus on a general model to describe compressible and immiscible three-phase flow in porous media. The underlying idea is to replace Darcy’s law by more general momentum balance equations. In particular, we want to account for viscous coupling effects by introducing fluid-fluid interaction terms. In [Qiao, et al. (2018) Adv Water Resour 112: 170–188] a water-oil model based on the theory of mixtures was explored. It was demonstrated how the inclusion of viscous coupling effects could allow the model to better capture flow regimes which involve a combination of co-current and counter-current flow. In this work we extend the model in different aspects: (i) account for three phases (water,oil,gas) instead of two; (ii) deal with both the compressible and incompressible case; (iii) include viscous terms that represent frictional forces within the fluid (Brinkman type). A main objective of this work is to explore this three-phase model, which appears to be more realistic than standard formulation, in the context of petroleum related applications. We first provide development of stable numerical schemes in a one-dimensional setting which can be used to explore the generalized water-oil-gas model, both for the compressible and incompressible case. Then, several numerical examples with waterflooding in a gas reservoir and water alternating gas (WAG) experiments in an oil reservoir are investigated. Differences and similarities between the compressible and incompressible model are highlighted, and the fluid-fluid interaction effect is illustrated by comparison of results from the generalized model and a conventional model formulation.

Experimental and theoretical quantification of the relationship between electrical resistivity and hydrate saturation in porous media

An equivalent resistivity model is proposed and validated to determine hydrate saturation based on the experimentally measured resistivity. Experimentally, hydrate with different saturations is formed in an artificial sandpack to measure pressure, temperature, and resistivity as a function of time. The resistivity evolution includes induction of nucleation, large-scale hydrate nucleation, and hydrate rearrangement. Theoretically, a mathematical model on the basis of the parallel circuit principle is developed to quantify the relationship between resistivity and hydrate saturation by taking sand skeleton, temperature, brine salinity, and formation tortuosity into account. The formation tortuosity is expressed as a function of water relative permeability which can be determined by incorporating the existing semi-empirical models. In addition, the cementation exponent and saturation index in the Archie formula are empirically obtained by nonlinearly regressing the experimental measurements, while the sand skeleton resistivity, the correlation coefficient of formation tortuosity, and hydrate saturation index are introduced and determined in the equivalent resistivity models. It is found that the equivalent resistivity models are in a better agreement with the experimental measurements, while the Archie formula introduces an obviously larger error at higher hydrate saturation. Furthermore, it is recommended to use the dynamic porosity expressed as a function of hydrate saturation when characterizing the electrical properties and three-phase flow in porous media. Also, the equivalent resistivity models are found to have a less dependence on the accuracy of porosity compared with the Archie’s formula.

Mathematical modeling and simulation of water-alternating-gas (WAG) process by incorporating capillary pressure and hysteresis effects

Mathematical modeling and simulation of three-phase flow in porous media involves complexities related to the three-phase relative permeability, capillary pressure, and hysteresis effects that are cycle-dependent. Extensive theoretical studies are available in the literature, simulating immiscible and miscible water-alternating-gas (WAG) processes; however, the simulation of recovery behaviors and mechanisms of near-miscible WAG is overlooked. Also, a majority of WAG simulation studies lack the cycle-dependent three-phase hysteresis that appears in the relative permeability and capillary pressure models. In this paper, we study a three-phase flow modeling of near-miscible WAG process for EOR implication, using implicit pressure explicit saturation (IMPES) method. The mathematical model simulates a WAG case study in a strongly water-wet Berea sandstone core, using synthetic oil and brine at 38 °C and 12.7 MPa. Three cycles of water flooding (WF) and gas injection (GI) are used in the WAG operation. The recovery data from our mathematical model is in excellent agreement with the corresponding experimental data. The absolute relative error is less than 1.7%, while estimating the ultimate oil recovery factor in the WF and GI stages of all three cycles. We also study the effects of influential variables such as injection rate, WAG ratio, slug size, crude oil viscosity, and core absolute permeability on the WAG performance. The WAG ratio of 1 is found to be better than 0.5 and 2 cases. Although the absolute permeability changes the breakthrough recovery performance of the individual stages, it does not significantly affect the ultimate recovery of near-miscible WAG. Increasing the injection rate decreases the recovery factor. This effect is more pronounced in the GI cycles. Also, the ultimate recovery factor is reduced by 20% upon an increase in the viscosity of the in-situ oil. The findings of this research work can help to better understand the near-miscible WAG injection at various scenarios/conditions in terms of operational conditions and rock and fluid characteristics for the purposes of WAG design, operation, and optimization.

The Inverse Coefficient Problem for Equations of Three-Phase Flow in Porous Medium

The identification task of the absolute permeability is considered under conditions isothermal three-phase flow in porous medium. The identification process is carried out by known values of the flow rate on a single well. The resulting permeability field is used to calculate the flow rate at the following moments of time. The proposed approach is tested to solve the model problem. The influence of time and number of the flow rate measurements on the identification results is investigated.

Dynamic optimization of thermodynamically rigorous models of multiphase flow in porous subsurface oil reservoirs

In this paper, we consider dynamic optimization of thermal and isothermal oil recovery processes which involve multicomponent three-phase flow in porous media. We present thermodynamically rigorous models of these processes based on 1) conservation of mass and energy, and 2) phase equilibrium. The conservation equations are partial differential equations. The phase equilibrium problems that are relevant to thermal and isothermal models are called the UV and the VT flash, and they are based on the second law of thermodynamics. We formulate these phase equilibrium problems as optimization problems and the phase equilibrium conditions as the corresponding first order optimality conditions. We demonstrate that the thermal and isothermal flow models are in a semi-explicit differential-algebraic form, and we solve the dynamic optimization problems with a previously developed gradient-based algorithm implemented in C/C++. We present numerical examples of optimized thermal and isothermal oil recovery strategies and discuss the computational performance of the dynamic optimization algorithm in these examples.

A multiphase level set approach to motion of disconnected fluid ganglia during capillary-dominated three-phase flow in porous media: Numerical validation and applications

We present a multiphase level set (MLS) approach to capillary-controlled, three-phase displacement in porous media, and use it to simulate displacements of disconnected fluid ganglia surrounded by two other fluid phases (i.e., double displacements), which are important pore-scale mechanisms for oil recovery and CO2 storage. After a comprehensive model validation on several new benchmark cases, including 3-D simulations of double displacements in a straight angular tube, we show two new applications of the MLS method. First, we simulate three-phase capillary pressure curves for gas invasion along constant oil saturation paths in sandstone. The results show significant oil redistribution by double displacements, which leads to fluctuations of gas/oil capillary pressure due to oil volume preservation, whereas oil/water capillary pressure increases mostly monotonically, yet the pressure level is lower than in the corresponding two-phase oil/water system. Further, gas/water capillary pressure is lower when mobile oil is present in the sample. The second application demonstrates the suitability of MLS method to describe foam dynamics both with and without oil present in the pore space. MLS method successfully describes well-known foam interfacial properties, and it also captures the rise of displacement capillary pressure when adding gas bubbles between continuous gas and water inside a pore channel.

A comparative study of explicit high-resolution schemes for compositional simulations

PurposeThis paper aims to numerically study the compositional flow of two- and three-phase fluids in one-dimensional porous media and to make a comparison between several upwind and central numerical schemes.Design/methodology/approachImplicit pressure explicit composition (IMPEC) procedure is used for discretization of governing equations. The pressure equation is solved implicitly, whereas the mass conservation equations are solved explicitly using different upwind (UPW) and central (CEN) numerical schemes. These include classical upwind (UPW-CLS), flux-based decomposition upwind (UPW-FLX), variable-based decomposition upwind (UPW-VAR), Roe’s upwind (UPW-ROE), local Lax–Friedrichs (CEN-LLF), dominant wave (CEN-DW), Harten–Lax–van Leer (HLL) and newly proposed modified dominant wave (CEN-MDW) schemes. To achieve higher resolution, high-order data generated by either monotone upstream-centered schemes for conservation laws (MUSCL) or weighted essentially non-oscillatory (WENO) reconstructions are used.FindingsIt was found that the new CEN-MDW scheme can accurately solve multiphase compositional flow equations. This scheme uses most of the information in flux function while it has a moderate computational cost as a consequence of using simple algebraic formula for the wave speed approximation. Moreover, numerically calculated wave structure is shown to be used as a tool for a priori estimation of problematic regions, i.e. degenerate, umbilic and elliptic points, which require applying correction procedures to produce physically acceptable (entropy) solutions.Research limitations/implicationsThis paper is concerned with one-dimensional study of compositional two- and three-phase flows in porous media. Temperature is assumed constant and the physical model accounts for miscibility and compressibility of fluids, whereas gravity and capillary effects are neglected.Practical implicationsThe proposed numerical scheme can be efficiently used for solving two- and three-phase compositional flows in porous media with a low computational cost which is especially useful when the number of chemical species increases.Originality/valueA new central scheme is proposed that leads to improved accuracy and computational efficiency. Moreover, to the best of authors knowledge, this is the first time that the wave structure of compositional model is investigated numerically to determine the problematic situations during numerical solution and adopt appropriate correction techniques.

A hybrid assimilation scheme for characterization of three-phase flow in porous media

ABSTRACTIn this study, ensemble Kalman filter (EnKF) is first applied to estimate absolute and relative permeabilities jointly under three-phase flow condition in the porous media. By assimilating historical data, absolute permeability field is adjusted progressively towards its reference. However, assimilation process does not improve the estimation of all relative permeability parameters, and some of them are poorly estimated at the end of assimilation. To improve the estimation of the relative permeability curves, we propose a new hybrid approach in which the estimation process of the absolute and relative permeabilities is separated. In this approach, gridblock permeabilities are again estimated within the EnKF framework in the inner loop. While, at each assimilation cycle, relative permeability parameters are updated in the outer loop using genetic algorithm so as to minimize the new proposed objective function. The proposed technique is validated in a synthetic two-dimensional reservoir model under three-phase flow condition. The hybrid approach results in monotonic reduction of the root-mean-squared error between the updated and the true permeability fields as well as accurate estimation of the relative permeability curves. Furthermore, the hybrid approach is compared against EnKF in terms of accuracy of the estimated model parameters, quantification of uncertainty, computational cost and quality of history-match.

Characterization of three-phase flow in porous media using the ensemble Kalman filter

In this study, the ensemble Kalman lter is used to characterize threephase flow in porous media through simultaneous estimation of three-phase relative permeabilities and capillary pressures from production data. Power-law models of relative permeability and capillary pressure curves are used and the associated unknown parameters are estimated by assimilating the measured historical data. The estimation procedure is demonstrated on a twin numerical setup with two di erent scenarios, in which a synthetic 2D reservoir under three-phase flow is considered. In the rst scenario, all the endpoints are assumed to be known and only the shape factors are estimated during the assimilation process. In the second, all the endpoints and shape factors are estimated by assimilating observed data. Accurate estimation of the unknown model parameters is achieved by assimilating oil, water, and gas production rates of the producers and bottom-hole pressureof the injector. Moreover, sensitivity analysis of the observations with respect to the parameters de ning the relative permeabilities and capillary pressures shows that for the most sensitive parameters, better estimation and lower uncertainty are obtained at the end of the assimilation process.

A Robust Methodology To Simulate Water-Alternating-Gas Experiments at Different Scenarios Under Near-Miscible Conditions

Summary Three-phase flow in porous media during water-alternating-gas (WAG) injections and the associated cycle-dependent hysteresis have been subject of studies experimentally and theoretically. In spite of attempts to develop models and simulation methods for WAG injections and three-phase flow, current lack of a solid approach to handle hysteresis effects in simulating WAG-injection scenarios has resulted in misinterpretations of simulation outcomes in laboratory and field scales. In this work, by use of our improved methodology, the first cycle of the WAG experiments (first waterflood and the subsequent gasflood) was history matched to estimate the two-phase krs (oil/water and gas/oil). For subsequent cycles, pertinent parameters of the WAG hysteresis model are included in the automatic-history-matching process to reproduce all WAG cycles together. The results indicate that history matching the whole WAG experiment would lead to a significantly improved simulation outcome, which highlights the importance of two elements in evaluating WAG experiments: inclusion of the full WAG experiments in history matching and use of a more-representative set of two-phase krs, which was originated from our new methodology to estimate two-phase krs from the first cycle of a WAG experiment. Because WAG-related parameters should be able to model any three-phase flow irrespective of WAG scenarios, in another exercise, the tuned parameters obtained from a WAG experiment (starting with water) were used in a similar coreflood test (WAG starting with gas) to assess predictive capability for simulating three-phase flow in porous media. After identifying shortcomings of existing models, an improved methodology was used to history match multiple coreflood experiments simultaneously to estimate parameters that can reasonably capture processes taking place in WAG at different scenarios—that is, starting with water or gas. The comprehensive simulation study performed here would shed some light on a consolidated methodology to estimate saturation functions that can simulate WAG injections at different scenarios.