Three-phase Relative Permeability Research Articles

An artificial-intelligence-based petrophysical property predictor for compositional volatile oil reservoir using three-phase production data

When considering multiphase flow scenarios, the interpretation of petrophysical properties poses significant challenges for production forecasts and reservoir modeling. The findings of the numerical modeling were therefore subject to uncertainty because characteristics like relative permeability and capillary pressure curve were hardly ever bound by interpretations. The uncertainty may result in inaccurate predictions of reservoir performance and skewed perceptions of the reservoir. Due to the difficulty in directly interpreting such property from the available field data and the expensive cost of coring, analyses or experimental measurements to determine relative permeability and capillary pressure were infrequently carried out. Such a gap would be filled by a straightforward yet rigorous method. In this study, we develop production projections for a wide range of three-phase compositional volatile oil reservoirs. Then, we used an artificial neural network to figure out how petrophysical characteristics and production data relate to one another. The artificial neural network model was adjusted, and the final trained model was tested blindly to determine how well it predicted permeability, multiphase relative permeability, and capillary pressure data. For the testing scenarios, consistency is seen between the predicted values and the original ones, despite some mispredictions being present. To provide production projections that can be compared to those from the reservoir model that include the initial petrophysical characteristic, the anticipated properties are then propagated into reservoir models. The comparison findings show that for 65/59/34 out of 74 testing scenarios, the reservoir model with artificial neural network-predicted features can anticipate oil/gas/water output with < 20% inaccuracy. With the developed artificial neural network tool, the reservoir engineers can evaluate the three-phase relative permeability surface from rate-transient data conveniently improving the accuracy of the relative permeability data implemented by history matching or from core experiments which sometimes are extremely expensive. The findings of this study can help for a better understanding of the relationships between three-phase rate-transient data and the relative permeability surface as well as the horizontal/vertical permeability.

Current methods for measuring three-phase relative permeability and its influencing factors

Current methods for measuring three-phase relative permeability and its influencing factors

Fundamentals-Based Alternative Addresses Issue With Three-Phase Permeability Model

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 205883, “Issue With Stone II Three-Phase Permeability Model and a Novel Robust Fundamentals-Based Alternative to It,” by Subodh Gupta, SPE, Heretech Energy. The paper has not been peer reviewed. _ The objective of this paper is to present a fundamentals-based, three-phase flow model consistent with observation that avoids the pitfalls of conventional models. Though the use of the Stone II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears counterintuitively to limit the flow of oil when water is present near its irreducible saturation. The novelty of the work presented in the complete paper is in the development of a model based on fundamentals of flow in fine channels that better explains observed results in the context of flow in porous media. Problem Definition Residual oil saturation (So) from retrieved cores from oil-drained chambers of steam-assisted gravity drainage (SAGD) reservoirs invariably shows values as low as 1 or 2%, whereas reservoir simulations using Stone II-based relative permeabilities (an industrywide favorite) predict significantly higher numbers (14–18%). In previous work, the author and others, in an attempt to remedy the situation, extended the oil-phase relative permeability in the presence of the water phase (krow) and oil-phase relative permeability in the presence of the gas phase (krog) curves all the way to water and gas saturation values less than unity; however, they discovered that, in the presence of water saturation (Sw) near the irreducible water saturation (Swi), the use of the Stone II formula for oil relative permeability still resulted in high residual So. Correct estimation of residual oil-phase saturation is even more important for solvent/steam mixed thermal recovery processes such as solvent-aided processes, where a small amount of solvent is added with steam in SAGD, and significantly more important for solvent-dominated processes, where a small amount of steam or heat is added with a large amount of solvent. A large amount of residual oleic-phase saturation and associated pessimistic solvent-recovery prediction will lead to erroneous economic assessment of these processes. The discrepancy in residual So, as the author and coauthors discovered in previous work, stems from a peculiarity of the Stone II formulation given by Equation 1 of the complete paper. To model this 1D problem numerically, a program developed by the author for his PhD thesis for modeling of moving front reservoir processes with dynamic gridding was modified and run with constant fluid properties for hexane and water at constant pressure and temperature. It also incorporated the three-phase relative permeabilities given by Equation 1 and Table 1 of the complete paper. The results are shown in Fig. 1.

Issue with Stone-II three phase permeability model, and a novel robust fundamentals-based alternative to it

The objective of this paper is to present a fundamentals-based, consistent with observation, three-phase flow model that avoids the pitfalls of conventional models such as Stone-II or Baker's three-phase permeability models.While investigating the myth of residual oil saturation in SAGD with comparing model generated results against field data, Gupta et al. (2020) highlighted the difficulty in matching observed residual oil saturation in steamed reservoir with Stone-II and Baker's linear models. Though the use of Stone-II model is very popular for three-phase flow across the industry, one issue in the context of gravity drainage is how it appears to counter-intuitively limit the flow of oil when water is present near its irreducible saturation.The current work begins with describing the problem with existing combinatorial methods such as Stone-II, which in turn combine the water-oil, and gas-oil relative permeability curves to yield the oil relative permeability curve in presence of water and gas. Then starting with the fundamentals of laminar flow in capillaries and with successive analogical formulations, it develops expressions that directly yield the relative permeabilities for all three phases. In this it assumes a pore size distribution approximated by functions used earlier in the literature for deriving two-phase relative permeability curves. The outlined approach by-passes the need for having combinatorial functions such as prescribed by Stone or Baker.The model so developed is simple to use, and it avoids the unnatural phenomenon or discrepancy due to a mathematical artefact described in the context of Stone-II above. The model also explains why in the past some researchers have found relative permeability to be a function of temperature. The new model is also amenable to be determined experimentally, instead of being based on an assumed pore-size distribution. In that context it serves as a set of skeletal functions of known dependencies on various saturations, leaving constants to be determined experimentally.The novelty of the work is in development of a three-phase relative permeability model that is based on fundamentals of flow in fine channels and which explains the observed results in the context of flow in porous media better. The significance of the work includes, aside from predicting results more in line with expectations and an explanation of temperature dependent relative permeabilities of oil, a more reliable time dependent residual oleic-phase saturation in the context of gravity-based oil recovery methods.

A Three-Phase Relative Permeability Model for Heavy Oil Emulsion System

Chemical flooding is important and effective enhanced oil recovery processes are applied to improve the recovery of heavy oil reservoirs. Emulsification occurs during chemical flooding processes, forming an oil-in-water (O/W) emulsion system. In this work, the heavy oil emulsion system is characterized as a three-phase (continuous oil phase, dispersed oil phase, and continuous water phase) system. Based on a capillary tube model, a new relative permeability model is proposed to describe the flow of the emulsion system in porous media quantitatively, considering the physicochemical properties of emulsions and the properties of porous media. A resistance factor is derived in this model to describe the additional resistance to the emulsion flow caused by the interaction between dispersed oil droplets and the pore system. Three dimensionless numbers related to the emulsion porous flow process were proposed and their different effects on the three-phase relative permeability are investigated. To validate the reliability of the proposed model, a one-dimensional O/W emulsion–oil displacement experiment is simulated. The maximum absolute error between the simulated results and experimental data is no more than 10%, and the new model can be used to describe the flow behavior of heavy oil emulsions in porous media.

Bayesian Optimization for Field-Scale Geological Carbon Storage

We present a framework that couples a high-fidelity compositional reservoir simulator with Bayesian optimization (BO) for injection well scheduling optimization in geological carbon sequestration. This work represents one of the first at tempts to apply BO and high-fidelity physics models to geological carbon storage. The implicit parallel accurate reservoir simulator (IPARS) is utilized to accurately capture the underlying physical processes during CO 2 sequestration. IPARS provides a framework for several flow and mechanics models and thus supports both stand-alone and coupled simulations. In this work, we use the compositional flow module to simulate the geological carbon storage process. The compositional flow model, which includes a hysteretic three-phase relative permeability model, accounts for three major CO 2 trapping mechanisms: structural trapping, residual gas trapping, and solubility trapping. Furthermore, IPARS is coupled to the International Business Machines (IBM) Corporation Bayesian Optimization Accelerator (BOA) for parallel optimizations of CO 2 injection strategies during field-scale CO 2 sequestration. BO builds a probabilistic surrogate for the objective function using a Bayesian machine learning algorithm—the Gaussian process regression, and then uses an acquisition function that leverages the uncertainty in the surrogate to decide where to sample. The IBM BOA addresses the three weaknesses of standard BO that limits its scalability in that IBM BOA supports parallel (batch) executions, scales better for high-dimensional problems, and is more robust to initializations. We demonstrate these merits by applying the algorithm in the optimization of the CO 2 injection schedule in the Cranfield site in Mississippi, USA, using field data. The optimized injection schedule achieves 16% more gas storage volume and 56% less water/surfactant usage compared with the baseline. The performance of BO is compared with that of a genetic algorithm (GA) and a covariance matrix adaptation (CMA)-evolution strategy (ES). The results demonstrate the superior performance of BO, in that it achieves a competitive objective function value with over 60% fewer forward model evaluations.

Computational fluid dynamic simulation of multi-phase flow in fractured porous media during water-alternating-gas injection process

Naturally fractured reservoirs (NFRs) are among major oil and gas producing reservoirs that are commonly targeted for various enhanced oil recovery (EOR) techniques, particularly water-alternating-gas (WAG) injection. Production from NFRs is complicated due to the flow communication between the matrix and fractures in such porous media. The implementation of WAG injection in NFRs features inherent complexities not only related to the three-phase flow, saturation history, and cycle-dependent hysteresis of the individual phases, but also the fracture-matrix communication, fingering, and early breakthrough of the injected phases particularly during gas injection processes. This paper provides the key results on the computational fluid dynamics (CFD) simulation of WAG injection in a fractured system. We evaluate the impacts of hysteresis, fracture characteristics (aperture, orientation, and fracture density in the network), and the three-phase relative permeability of available phases during the WAG injection. The CFD model simulates an immiscible WAG injection, and the CFD results are compared to the experimental data in a strongly water-wet sand-pack. Similar to the experiments, we simulate Maroon crude as the oil phase, and synthetic brine, and pure CO2 at 100 °C and atmospheric outlet pressure. The CFD results are in excellent agreement with the experimental data. The absolute relative error is less than 12% for predicting the ultimate oil recovery factors (RFs) in water flooding (WF) and gas injection (GI) cycles. Including the three-phase hysteresis significantly increases the accuracy of the WAG process simulation, while excluding hysteresis underestimates the instantaneous RFs at each cycle (especially GI cycles) and the ultimate RF by 4%. We also analyze the fracture pattern and configuration; adding fractures to the system increases the system effective permeability, leading to more contact between the injecting fluid and trapped oil, and consequently higher oil recovery. Connecting a vertical fracture to the horizontal fracture enhances the recovery through strong connections between the vertical and horizontal blocks. An increase in the fracture aperture from 0.5 to 3 mm increases the RF from 50% to 59%. The fracture inclination angle from 30° to 90° increases the ultimate RF by only 2%. Including gravity forces in vertical model orientation results in overall improvement in RF through engaging both matrix and fracture media in all cycles. As the permeability contrast between the matrix and fracture media decreases, the flow communication between the two regions increases, which improves the recovery performance of the WAG process. Our simulation results can help to further understand the effect of various parameters and operational conditions on WAG injection performance in fractured reservoirs.

Integrated characterization of wormhole network by use of a modified pressure-gradient-based (PGB) sand failure criterion and ensemble-based history matching during CHOPS processes

In this paper, a damped iterative ensemble Kalman filter (IEnKF) technique has been developed and integrated with a recently modified pressure-gradient-based (PGB) sand failure criterion to implicitly and inversely characterize the dynamic wormhole network during cold heavy oil production with sand (CHOPS) processes. With an improved upscaling process, not only has a microscopic PGB sand failure criterion been properly upscaled to the grid-scale simulation, but also it can be dynamically, implicitly, and inversely determined. Then, such a sand failure model together with three-phase relative permeability is validated and applied to reproduce wormhole network in a laboratory experiment conditioned to its sand production profile. Good agreements between the observed and simulated cumulative production profiles including oil, gas, and sand have been achieved with satisfactory convergence by integrating the ensemble-based history matching method. The simulated wormhole network has shown its great similarity to the experimental observations, while the convergence of the ensemble-based history matching algorithm is greatly improved with a widespread of initial ensembles in each grid. Furthermore, deviations between the observed and updated production profiles can be significantly minimized by dividing the entire production period into three sequential stages, each of which has its distinct relative permeability curves due to the major effect (i.e., foamy oil flow, sand failure, and slurry flow) on its multiphase flow behaviours, respectively. By integrating the ensemble-based sand failure model with the damped-IEnKF method, the dynamic wormhole network during a CHOPS process can be accurately characterized with satisfactory convergence, demonstrating its robustness and practicality of dynamically and inversely simulating the preferential wormhole network. Such an ensemble-based sand failure model can be seamlessly incorporated with any commercial reservoir simulators under various conditions. • A hybrid IEnKF-PGB technique is developed to characterize wormhole network for CHOPS wells. • Good agreements between the observed and simulated cumulative production profiles are achieved. • Simulated wormhole network shows its great similarity to the experimental observations. • Dividing the production period into three stages minimizes deviations between observed and updated production profiles. • This hybrid technique is robust and can be seamlessly coupled with any reservoir simulators.

Parallel Implementation of the Deterministic Ensemble Kalman Filter for Reservoir History Matching

In this paper, the deterministic ensemble Kalman filter is implemented with a parallel technique of the message passing interface based on our in-house black oil simulator. The implementation is separated into two cases: (1) the ensemble size is greater than the processor number and (2) the ensemble size is smaller than or equal to the processor number. Numerical experiments for estimations of three-phase relative permeabilities represented by power-law models with both known endpoints and unknown endpoints are presented. It is shown that with known endpoints, good estimations can be obtained. With unknown endpoints, good estimations can still be obtained using more observations and a larger ensemble size. Computational time is reported to show that the run time is greatly reduced with more CPU cores. The MPI speedup is over 70% for a small ensemble size and 77% for a large ensemble size with up to 640 CPU cores.

Assessment of two-phase relative permeability hysteresis models for oil/water, gas/water and gas/oil systems in mixed-wet porous media

Accurate determination of relative permeability curves and their hysteresis is vital for reliable prediction of the performance of oil and gas reservoirs under enhanced recovery processes. Two out of the three available approaches to simulate three-phase relative permeability hysteresis are based on two-phase hysteresis. A few options (e.g., Carlson, Killough and Jargon models) are available in commercial reservoir simulators to account for hysteresis in relative permeability curves under two-phase flow. These models are based on the assumptions of water-wet state of the rocks, while most of the reservoir rocks are mixed-wet. As a result the aim of the present work is to evaluate the performance of these hysteresis models for mixed-wet systems. In addition to the above models, more recent ones such as Beattie et al., Kjosavik et al., Spiteri et al. are also evaluated by coupling an in-house MATLAB code with the Eclipse simulator. The assessments of models are performed by comparing their predictions with those of previously reported comprehensive set of experimentally measured relative permeabilities for different two-phase systems. All possible two phase fluid/fluid systems i.e. oil/water, gas/water and gas/oil are considered. The interfacial tension in the case of oil/gas system is extra low (i.e. 0.04 mN.m−1) and it represents near-miscible condition. It is concluded that hysteresis models developed by Killough and Carlson are unable to accurately predict hysteresis effect on relative permeability in oil/gas system under extra low IFT and mixed-wettability. However, either of Killough and Carlson models could provide satisfactory results in gas/water and oil/water systems, respectively. Beattie et al. model that is not used in Eclipse gave a better fit to experimental data in oil/gas system, but it couldn't provide a suitable fit with experimental data in the cases of gas/water and oil/water systems. For different fluids systems, Kjosavik et al. model results were approximately close to the Killough model during the imbibition process and Beattie et al. during the drainage process. Even the results of the best models in each category of the two phase systems are not very satisfactorily. This study highlights the lack of a versatile hysteresis model to capture the hysteresis effect in all possible two phase systems for the mixed-wettability. As a result it is vital that modified or even novel hysteresis models in the case of mixed-wet system be developed.

Pore-scale numerical prediction of three-phase relative permeability in porous media using the lattice Boltzmann method

Three immiscible fluids systems are often encountered in energy and environmental disciplines, especially in the oil exploration field. It is essential to enhance oil recovery (EOR) by identifying the three-phase fluid flow mechanism of oil-gas-water system in complex geological structures. In the present study, a lattice Boltzmann (LB) color gradient model for three immiscible fluid flow in three-dimensional porous media is employed and validated using five benchmarks (i.e., the multiphase spinodal decomposition; the multiphase Young-Laplace test; the liquid lens; contact angles and 3D channel layered three-phase fluid flow). The effects of wettability, viscosity ratio (M) and capillary number (Ca) on the relative permeability curves are analyzed in detail. When the wetting condition is enhanced, the results indicate that the relative permeability of non-wetting phase raises while that for the wetting phase exhibits a decline. When M is not equal 1, the relative permeability of high viscosity phase is significantly increased, while the other two phases are less affected. Meanwhile, the maximal value of relative permeability does not exceed unity because of the low porosity in the porous medium. For the influence of Ca, simulation results indicate the relative permeability shows weak sensitivity to Ca.

Prediction of three-phase relative permeabilities of Berea sandstone using lattice Boltzmann method

Three-phase flows through a pore network of Berea sandstone are studied numerically under critical interfacial tension conditions. Results show that the relative permeability of each fluid increases as its own saturation increases. The specific interfacial length between wetting and nonwetting fluids monotonously decreases with increasing the saturation of intermediate-wetting fluid, while the other two specific interfacial lengths exhibit a nonmonotonous variation. As the wetting (nonwetting) fluid becomes less wetting (nonwetting), the relative permeability of wetting fluid monotonously increases, while the other two relative permeabilities show a nonmonotonous trend. Due to the presence of a spreading layer, the specific interfacial length between wetting and nonwetting fluids always stabilizes at a low level. As the viscosity ratio of wetting (nonwetting) to intermediate-wetting fluids increases, the relative permeability of wetting (nonwetting) fluid increases. With the viscosity ratio deviating from unity, the phase interfaces become increasingly unstable, leading to an increased specific interfacial length.

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.

A New Way of Compositional Simulation without Phase Labeling

SummaryCurrent relative permeability models rely on labeling a phase as “oil” and “gas” and cannot therefore capture accurately the effect of compositional variations on relative permeabilities and capillary pressures in enhanced oil recovery processes. Discontinuities in flux calculations caused by phase labeling problems not only cause serious convergence and stability problems but also affect the estimated recovery factor owing to incorrect phase mobilities.We developed a fully compositional simulation model using an equation of state (EoS) for relative permeabilities (kr) to eliminate the unphysical discontinuities in flux functions caused by phase labeling issues. The model can capture complex compositional and hysteresis effects for three-phase relative permeability. Each phase is modeled separately based on physical inputs that, in part, are proxies to composition. Phase flux calculations from one gridblock to another are also updated without phase labels. The tuned kr-EoS model and updated compositional simulator are demonstrated for simple ternary cases, multicycle three-phase water-alternating-gas (WAG) injection, and three-hydrocarbon-phase displacement with complex heterogeneity. The approach improves the initial estimates and convergence of flash calculations and stability analyses, as well as the convergence in the pressure solvers. The new compositional simulator allows for high-resolution simulation that gives improved accuracy in recovery estimates at significantly reduced computational time.

On the prediction of three-phase relative permeabilities using two-phase constitutive relationships

The predictions of two recent and two classical mathematical models are compared with experimentally measured three-phase relative permeabilities. Experimentally determined constitutive relationships in two-phase systems were used as model input parameters to numerically predict relative permeabilities (kr) in three-phase systems. Then the estimated results were compared with experimental three-phase permeabilities measured along decreasing water saturation/decreasing oil saturation/increasing gas saturation (DDI) paths. The results of the individual models to each of the three fluids involved (water, oil, and gas) were analyzed in detail. The simulated results showed that the Total Differential (TD) compatible model overestimates significantly both the global mobilities as well as the relative phase permeabilities in the three-phase system. There was improvement in the prediction with the TD compatible model when experimental data were used to locally impose the global mobility and fractional water and gas fluxes in the ternary diagram. Globally, the best prediction of the measured kr values was obtained with the so-called mechanistic model. However, its numerical implementation requires a preliminary calibration of the relative phase permeabilities in a three-phase system against experimental data along one DDI path to quantify the required six characteristic coefficients. In contrast to the TD compatible model, which by construction does not exhibit any numerical instabilities, elliptic zones in the water-oil (NAPL)-gas ternary diagram were identified in the mechanistic model.

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.

Characterization of Multiphase Flow in CHOPS Processes Using a Systematic Framework

Summary Cold heavy oil production with sand (CHOPS) technique has successfully improved oil recovery from heavy oil reservoirs due to high permeability channels resulted from sand failure and foamy oil flow enhancing heavy oil movability. However, impacts of the sand failure and the foamy oil flow on multiphase fluid flow features are still not properly understood. In this paper, an effective and systematic framework has been proposed to characterize the multiphase fluid flow and determine the three-phase relative permeability of CHOPS processes. A recently developed sand failure criterion and a relative permeability model have been integrated with a reservoir simulator to simulate the CHOPS process. The unknown parameters involved in the systematic framework are intelligently determined by an iterative ensemble smoother (IES) algorithm, which also enables sensitivity analysis on CHOPS production profiles. Subsequently, the proposed framework is tested through a laboratory CHOPS experiment. We obtained not only fairly history-matched production data (i.e., cumulative oil, gas, and sand production), but also satisfactorily converged three-phase relative permeability curves by iteratively assimilating production profiles of the CHOPS experiment. It has also been found that using two sets of three-phase relative permeability is capable of representing the segment-type nature of the multiphase flow and reproducing the transition stage on the production profiles. Furthermore, the comparison between two sets of three-phase relative permeability indicates that the sand failure phenomenon yields a reduced residual oil saturation and an increased oil/gas relative permeability. In addition, the sensitivity analysis demonstrates that the segment-type nature of production profiles results from the variation of key impact factors dominating the multiphase fluid flow in CHOPS processes. Overall, the proposed systematic framework can not only reproduce the physical phenomena of sand failure and foamy oil, but also provide a convenient tool to characterize the multiphase flow in CHOPS processes.

Simultaneous Interpretation of Three-Phase Relative Permeability and Capillary Pressure for a Tight Carbonate Reservoir From Wireline Formation Testing

AbstractIn this paper, techniques have been developed to interpret three-phase relative permeability and water–oil capillary pressure simultaneously in a tight carbonate reservoir from numerically simulating wireline formation tester (WFT) measurements. A high-resolution cylindrical near-wellbore model is built based on a set of pressures and flow rates collected by dual packer WFT in a tight carbonate reservoir. The grid quality is validated, the effective thickness of the WFT measurements is examined, and the effectiveness of the techniques is confirmed prior to performing history matching for both the measured pressure drawdown and buildup profiles. Water–oil relative permeability, oil–gas relative permeability, and water–oil capillary pressure are interpreted based on power-law functions and under the assumption of a water-wet reservoir and an oil-wet reservoir, respectively. Subsequently, three-phase relative permeability for the oil phase is determined using the modified Stone II model. Both the relative permeability and the capillary pressure of a water–oil system interpreted under an oil-wet condition match well with the measured relative permeability and capillary pressure of a similar reservoir rock type collected from the literature, while the relative permeability of an oil–gas system and the three-phase relative permeability bear a relatively high uncertainty. Not only is the reservoir determined as oil-wet but also the initial oil saturation is found to impose an impact on the interpreted water relative permeability under an oil-wet condition. Changes in water and oil viscosities and mud filtrate invasion depth affect the range of the movable fluid saturation of the interpreted water–oil relative permeabilities.

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.

Detailed Assessment of Compositional and Interfacial Tension Effects on the Fluid Behaviour During Immiscible and Near-Miscible CO2 Continuous and WAG Displacements

This study seeks to improve numerical simulations of the key physics occurring in CO2 enhanced oil recovery (CO2-EOR) processes, with a particular focus on the transition from immiscible to miscible displacements. In the previous work, we have investigated interactions between compositional effects and the underlying heterogeneities of the flow field in near-miscible floods (Wang et al. in Transp Porous Media 129(3):743–759, 2019a). In this current study, we have further analysed the effects of reduction in interfacial tension (IFT) on the flow behaviour, as motivated by the study on the film-flow mechanism previously presented by Sorbie and van Dijke (SPE improved oil recovery symposium, Society of Petroleum Engineers, 2010). We identify two clear mechanisms of oil recovery that may occur in near-miscible CO2 (or other gas) injection processes, which we denote, MCE, as oil stripping or conventional compositional effects, and MIFT as lower IFT oil film-flow effects. The latter MIFT effects are described by an enhanced hydrocarbon relative permeability in the near-miscible three-phase relative permeabilities (3PRP). Various combinations between the MCE and MIFT mechanisms were tested by numerical simulations to evaluate the impact of each mechanism on the flow behaviour, i.e. their separate and joint effects on quantities such as the local oil displacement efficiency, phase flow vectors and the ultimate oil recovery. When acting in combination, the oil stripping and IFT effects can greatly improve the local displacement performance even when viscous fingering flow occurs. Viscous fingering is well known to lead to bypassed oil in the “non-preferential” flow paths between the main fingers. We show that the remaining oil in these non-preferential flow paths (i.e. bypassed oil) can be efficiently recovered by the combined MCE and MIFT mechanisms, but only with the application of water alternating gas (WAG). In contrast to oil stripping effects, the IFT effect is not dependent on continuous contact between oil and CO2. Instead, the remaining oil is mobilized by gas as the IFT is reduced and can be efficiently produced by subsequent water injection. This MIFT mechanism has much less impact in cases with continuous CO2 injection compared to its efficiency in WAG. This is because during continuous injection, gas fingers are dominant in the preferential flow paths, and therefore the local displacement efficiency is very good, but only in these preferential routes. On the other hand, WAG is able to make full use of the IFT effects because of its relatively stable displacing front, which allows the MIFT mechanism to contribute. In this study, the effects of using different three-phase relative permeability methods were investigated and, as expected, different methods yielded different results. However, an important observation is that when IFT effects (MIFT) were included, there was much less difference in the final oil recovery using the different 3PRP models; our analysis shows why this is the case.