Relative Permeability Parameters Research Articles

Low salinity water flooding: estimating relative permeability and capillary pressure using coupling of particle swarm optimization and machine learning technique

The reservoir’s properties are required for proper reservoir simulation, which also involves uncertainties. Experimental methods to estimate the relative permeability and capillary pressure data are expensive and time-consuming. This study aims to determine the relative permeability and capillary pressure functions of a sandstone core in the presence and absence of clay during low-salinity water floods. The data were provided by automatic history matching the results from previously lab-reported studies through coupling a simulator with the particle swarm optimization algorithm. Correlations were proposed using multiple-linear regression for relative permeability and capillary pressure parameters at low-salinity conditions. They were validated against experimental results of no clay and clayey formation with regression of 95% and 97%. To assign one curve of relative permeability and capillary pressure to the grid cells of the simulator, averaging techniques were implemented. The effect of salinity and clay content on the obtained curves was investigated. Changing salinity from 42000 to 4000 ppm, the reduction in water relative permeability appeared to be higher than the oil relative permeability increment. Moreover, a noticeable shift in the relative permeability curves toward the highest saturations related to the clay content was observed. The proposed hybrid method could be a suitable tool to estimate the relative permeability and capillary pressure functions of the water-based EOR methods.

On the Identifiability of Relative Permeability and Foam Displacement Parameters in Porous Media Flow

AbstractThis study focuses on analyzing parameter identifiability in foam displacement models during two‐phase flow in porous media, with a particular emphasis on calibrating relative permeability and foam parameters. We employ the profile likelihood technique and Bayesian inference for identifiability analysis. Successful parameter estimation is demonstrated through steady‐state experiments for relative permeability and foam quality scan experiments when both types of experimental data are available and obtained from the same core sample. However, non‐identifiability issues arise when only foam quality scan data is accessible. Additionally, we investigated a standard practice that fits foam parameters using foam quality scan data obtained from one core sample and permeability values obtained from another core sample, but from the same reservoir. Our results show that this practice is ineffective in correctly estimating foam parameters, leading to misestimation of crucial foam model parameters. These findings underscore the importance of a mandatory relative permeability experiment on a representative core sample from the reservoir for accurate characterization of foam parameters. Without it, misestimation of foam model parameters hinders the proper understanding of foam effects on sweeping porous media.

Numerical study of exhaust chemical composition in a methane DBD plasma actuator under different operating conditions

In this paper, numerical simulations of a Dielectric-Barrier Discharge (DBD) plasma actuator are performed to predict its output chemical composition. The plasma actuator is cylindrical, with two coaxial electrodes and a quartz dielectric. The electrical discharge occurs in a pulsed manner around the quartz wall. This device is utilized for methane conversion in plasma-assisted combustion applications. The effects of voltage, frequency, temperature, and relative permeability parameters on methane conversion and some selected species concentrations were investigated. The results show that plasma discharging converts methane to hydrogen and heavier hydrocarbons such as C2H3, C2H4,C2H5, C2H6, and C3H8. Moreover, increasing the relative permeability coefficient and voltage had the greatest effect on methane conversion. Increasing the relative permeability from 2 to 6 increases the methane conversion by 43 % and also increases the H2 density by 57 %. The conversion rate of methane and the H2 density increase by 18 % with increasing the voltage from 6 to 8 kV. The partial conversion of methane to hydrogen and radical species benefits combustion applications in terms of flame stability and emissions reduction.

A Simulation of Core Displacement Experiments for the Determination of the Relative Permeability

Computations of the relative permeability curves were made through their representation by two functions for wetting and nonwetting phases. Each function contains one parameter that controls the shape of the relative permeability curves. The values of these parameters are chosen to minimize an objective function, that is represented as a weighted sum of the squared differences between experimentally measured data and the corresponding data calculated by a mathematical model simulating the experiment. These data comprise the pressure drop across core samples and the recovery response of the displacing phase. Two mathematical models are constructed in this study to simulate incompressible, one-dimensional, two-phase flow. The first model describes the imbibition process and the other describes the drainage process. The values of the relative permeability parameters are calculated by employing Rosenbrock optimization procedure. The reliability of this procedure has been confirmed by applying it to four displacement cases. The optimum values of the relative permeability parameters, which reflect the final shape of the relative permeability curves, are achieved at the minimum value of the objective function. All the above processes are be embodied in relative permeability package RPP which is constructed in this study using FORTRAN language.

Impact of Wettability Alteration on the Front Instability of Immiscible Displacement in Porous Media

AbstractWettability alteration that occurs as a result of changing the brine composition or using chemicals that lower the interfacial tension can significantly alter the mobility of nonaqueous liquid (NAPL)/water phases. Here, we show that including dynamic wettability alternation (moving from non‐water‐wet to water‐wet) or interpolating between two sets of relative permeability curves may create an unstable displacement of the residence‐fluid by the injected fluid. The instability occurs due to not only the viscosity ratio but also the new shape of relative permeability curves and their end‐point values. We perform a full factorial design on Corey relative permeability parameters to determine the most destabilizing factors when the viscosity ratio is one. The observations indicate that instability proliferates when the end‐point relative permeability to the NAPL phase of modified salinity brine increases, and their corresponding exponents decrease compared with high salinity brine (seawater or formation water). Besides, numerical simulations of such a displacement demonstrate that modified salinity water (MSW)'s breakthrough is accelerated by wettability change toward water‐wet compared with a non‐fingering analytical solution. This may result in a delayed mobilization of the NAPL phase in porous media. We also discuss the role of capillary pressure, heterogeneity, and secondary and tertiary injection of MSW in stabilizing the shock front.

Upscaled Dynamic Relative Permeability for Unstable CO2 Flow in Stratified Porous Media

In geologic porous media, layering is ubiquitous on all length scales ranging from sub-mm compositional laminations to km-thick formations. The current study presents a general framework for estimating the two-phase viscous limit dynamic relative permeability (k_{r} ) for non-communicating stratified sedimentary rocks. The approach is a two-stage upscaling taking into account the influence of nested heterogeneity at intra- and inter-layer scales. Sub-layer heterogeneities, promoting microflow instabilities in individual layers, are modelled by tuning input relative permeability parameters based on the viscosity contrast between fluids. Macroscopic flow instability at the domain scale is tackled by a new analytical solution for the saturation distribution in stratified media considering the complexities of frontal advance theory. For each layer, three flow stages are considered, each with its unique time-dependent behaviour. The overall solution is presented as a set of equations derived by overlapping of the solutions in different layers. The upscaled dynamic k_{r} is figured out by history matching. The practicality of the method is demonstrated in application to measurements collected from the Otway International Research Facility, Victoria, Australia. The results show the significant impact of layer separation on the upscaled endpoint saturations in addition to required modifications on the current k_{r} formulas. A comparison with conventionally modelled steady-state sweep highlights the inadequacy of steady-state upscaling for viscous limit flows. The applicability of the method to estimate k_{r} from the unsteady-state lab experiments conducted on heterogeneous cores is also discussed.

Immiscible/Near-Miscible relative permeability for confined fluids at high-pressure and high-temperature for a fractal reservoir

The complex interaction between fluids and solids in reservoirs includes interface slip, capillary confinement and the diffusion and mass transfer between CO2 and oil and results in intensely nonlinear flow complexity. This study proposes a relative permeability model that accommodates a fractal pore size distribution and honors these complex process interactions. The relative permeability to CO2 flooding, in the near-miscible region, is predicted through interpolation based on the Gibbs free energy (GFE). The thermodynamic phase behavior of the fluids in the nanopores is considered by applying critical shifts in the temperatures and pressures. A volume-translated Peng-Robinson equation of state is used to calculate the CO2 and n-alkane densities to high reservoir pressure. Fluid-based correlation and modified volumetric mixing rules are then used to extend the viscosity calculations to mixtures with heavy hydrocarbon components. Predictions from the proposed model better fit experimental observations relative to previous models similarly incorporating fractal theory. The nanopores are shown to increase the relative permeability of the non-wetting phase by decreasing the viscosity ratio of the two phases. Increasing key parameters that are related to the pore structure, e.g. the fractal dimension, Df, and critical pore radius, rc, increases the relative permeability of the non-wetting phase. The GFE-based interpolation contributes to the smooth and continuous change in the relative permeability parameters local to the critical point of the mixture, with the confined fluid more likely to be miscible at the same pressure than the bulk fluid. This model can be integrated with a compositional simulator to solve field-scale problems but accommodating the micro-scale physics of unconventional reservoirs.

An Integrated Assisted History Matching and Embedded Discrete Fracture Model Workflow for Well Spacing Optimization in Shale Gas Reservoirs

Abstract Optimum well spacing is an essential element for the economic development of shale gas reservoirs. We present an integrated assisted history matching (AHM) and embedded discrete fracture model (EDFM) workflow for well spacing optimization by considering multiple uncertainty realizations and economic analysis. This workflow is applied in shale gas reservoirs of the Sichuan Basin in China. First, we applied the AHM to calibrate ten matrices and fracture uncertain parameters using a real shale gas well, including matrix permeability, matrix porosity, three relative permeability parameters, fracture height, fracture half-length, fracture width, fracture conductivity, and fracture water saturation. There are 71 history matching solutions obtained to quantify their posterior distributions. Integrating these uncertainty realizations with five-well spacing scenarios, which are 517 ft, 620 ft, 775 ft, 1030 ft, and 1550 ft, we generated 355 cases to perform production simulations using the EDFM method coupled with a reservoir simulator. Then, P10, P50, and P90 values of gas estimated ultimate recovery (EUR) for different well spacing scenarios were determined. In addition, the degradation of EUR with and without well interference was analyzed. Next, we calculated the NPVs of all simulation cases and trained the K-nearest neighbors (KNN) proxy, which describes the relationship between the net pressure value (NPV) and all uncertain matrix and fracture parameters and varying well spacing. After that, the KNN proxy was used to maximize the NPV under the current operation cost and natural gas price. Finally, the maximum NPV of 3 million USD with well spacing of 766 ft was determined.

The Application of Integrated Assisted History Matching and Embedded Discrete Fracture Model Workflow for Well Spacing Optimization in Shale Gas Reservoirs with Complex Natural Fractures

An appropriate well spacing plan is critical for the economic development of shale gas reservoirs. The biggest challenge for well spacing optimization is interpreting the subsurface uncertainties associated with hydraulic and natural fractures. Another challenge is the existence of complex natural fractures. This work applied an integrated well spacing optimization workflow in shale gas reservoirs of the Sichuan Basin in China with both hydraulic and natural fractures. The workflow consists of five components: data preparation, reservoir simulation, estimated ultimate recovery (EUR) analysis, economic calculation, and well spacing optimization. Firstly, the multiple realizations of thirteen uncertain parameters of matrix and fractures, including matrix permeability and porosity, three relative permeability parameters, hydraulic fracture height, half-length, width, conductivity, water saturation, and natural fracture number, length, and conductivity, were captured by the assisted history matching (AHM). The fractures were modeled by the embedded discrete fracture model (EDFM) accurately and efficiently. Then, 84 AHM solutions combining with five well spacing scenarios from 517 ft to 1550 ft would generate 420 simulation cases. After reservoir simulation of these 420 cases, we forecasted the long-term gas production for each well spacing scenario. Gas EUR degradation and well interference would imply the critical well spacing. The net present value (NPV) for all scenarios would be calculated and trained by K -nearest neighbors (KNN) proxy to better understand the relationship between well spacing and NPV. In this study, the optimum well spacing was determined as 793 ft, corresponding with a maximum NPV of 18 million USD, with the contribution of hydraulic fractures and natural fractures.

Simulation and analysis of dynamic wettability alteration and correlation of wettability-related parameters during smart water injection in a carbonate core

Low salinity/Smart water injection (LSWI) is a promising enhanced oil recovery (EOR) method, where manipulating the injected water compositions helps in recovery from oil reservoirs via alteration of the rock wettability towards a more water-wet state. In this paper, the experimental data of LSWI in a carbonate core sample have been simulated and matched. The experimental results of oil recovery by injection of four different waters were examined, and the relative permeability curves were adjusted using a dynamic wettability alteration approach. Moreover, results of drainage and imbibition tests used to approximate the corresponding capillary pressures. True effective mobility (TEM) functions were also derived to evaluate the two-phase flow characteristics of the systems. Relative permeability and capillary pressure parameters showed strong correspondence with the injected salinity, and correlations were proposed for estimating the unknown parameters in other similar studies with different salinities. The trend of wettability alteration by LSWI was investigated, and it was concluded that the wettability does not linearly change with salinity, but rather it is non-linearly correlated with the logarithm of the total injected salinity. Injection of seawater (SW) did not significantly change the wettability and flow efficiency of the system compared to formation water (FW). However, dilution of SW to the salinity of 5000 ppm seemed to be the critical threshold below which the effect of LSWI had become substantially more pronounced. The results of this study can be helpful in optimizing and upscaling similar smart water applications, predicting the wettability-related parameters and two-phase flow characteristics at different injected salinities, and also block-to-block modelling in which the effect of the capillary pressure in the fracture network is also considered. Additionally, the non-linear relationship of the wettability-related parameters with salinity is particularly considerable for modifying the common modelling approaches of wettability alteration by LSWI in commercial simulators.

Surrogate‐Based Joint Estimation of Subsurface Geological and Relative Permeability Parameters for High‐Dimensional Inverse Problem by Use of Smooth Local Parameterization

AbstractThis paper introduces an efficient surrogate model with the aim of accelerating joint estimation of subsurface geological properties and relative permeability parameters for high‐dimensional inversion problems. We fully replace the high‐fidelity model with a set of subdomain linear models through integrating model linearization with smooth local parameterization where the Gaussian geological parameters and non‐Gaussian facies indicators are locally parameterized. These subdomain linear models with smooth local parameterization, referred to as SLM‐SLP, are constructed in each subdomain individually using only a few high‐fidelity model simulations. An adaptive scheme, that is, weighting smooth local parameterization (WSLP), is introduced as well to mitigate the negative effects of inappropriate domain decomposition schemes by adaptively optimizing the domain decomposition strategy. The computational advantages of the proposed algorithm are demonstrated on a synthetic non‐Gaussian facies model and a real‐world high‐dimensional Gaussian model. The amount of computational cost has been drastically reduced while reasonable accuracy remains. Specifically, SLM‐SLP only needs 220 fidelity simulations to optimize 302 parameters. Compared to ensemble smoother with multiple data assimilation (ES‐MDA), SLM‐SLP effectively and efficiently mitigates the ensemble collapse problem in the course of uncertain quantification.

Thermal enhanced oil recovery in deep heavy oil carbonates: Experimental and numerical study on a hot water injection performance

Currently, thermal methods of enhanced oil recovery are based on the use of heat transfer mediums (steam, hot water) and in-situ combustion, which are the most efficient methods in the development of heavy oil reservoirs. In this study, experimental and numerical modeling was carried out to estimate the efficiency of hot water injection to engage in the active development of high-viscosity oil reserves in a deep carbonate reservoir. There is a limited amount of published experimental studies on carbonates, in comparison with sandstones, shale, or oil sands. Oil-bearing formations at depths of 1100–1500 m require technology that can achieve sufficiently high fluid temperature (250–300 °C) in the bottom-hole zone to be successful. The performance of the implemented technique on a field greatly depends on the quality of the experimental data and numerical simulation. Particularly, the hydrodynamic model, reaction kinetics, and operational parameters are crucial parameters for future upscaling.The hot water injection experiment was conducted using a medium pressure combustion tube assembly on the reservoir rock model made of consolidated carbonate samples. Moreover, a new numerical model was constructed to simulate the experiment with a reproduction of the fluid models, properties of the oil and rock samples, and full geometry of the core holders where chemical interactions occur. What makes this model authentic is the calibration of reaction kinetics called “aquathermolysis” to hot water injection process, which replicate the most prevalent thermal process during the interaction of hot water and hydrocarbons.A close correlation between experimental and numerical results was obtained in terms of cumulative water and oil recovery and temperature profiles. The developed numerical model reflects the dynamics of oil displacement at different rates of water injection. According to experimental and numerical simulations, thermal effects reduce viscosity with a proportionate increase in oil recovery. The achieved recovery factor for the experiment was 63%. Lastly, a good match of cumulative gases (CH4, H2, H2S, CO2, and HMWG) was obtained for the hot water injection experiment. Adapted fluid model, relative permeability, kinetic model, and operational parameters are necessary for the upscaling to the field. The improved efficiency of oil displacement at this site is confirmed by numerical simulation.

CO2 injectivity behaviour under non-isothermal conditions – Field observations and assessments from the Quest CCS operation

Commercial-scale deployment of Carbon Capture and Storage (CCS) as a viable greenhouse gas (GHG) emissions reduction technology requires that the CO2 be continuously injected at predictably significant and cost-efficient rates into geological formations (e.g. deep saline aquifers).The Quest CCS operation (located in Alberta, Canada) is a fully integrated carbon capture, transport and storage facility operated by Shell Canada. Quest continuously captures and stores about 1.1 Mt of CO2 per year, and it’s expected to continue until 2040. Quest is a dedicated geological storage project (no EOR component) with multiple injectors and monitoring wells. Injection operations started in August 2015 and by mid-October 2018, more than 3.45 Mt of CO2 has been stored using only 2 out of 3 planned injection wells. To date Quest has observed significant injectivity variability relating to seasonal variation in injected CO2 and bottom-hole temperatures.The high-resolution time-series data from the Quest operations gathered over the first 3 years of CO2 injection indicate the standard models of CO2 injectivity leave out some important physics. Prior to the start of injection, theoretical CO2 injectivity at the CO2 injector wells was initially modelled and calculated to decrease by ∼5% - 8% with decreasing CO2 bottom-hole temperature within the temperature range 20 °C–60 °C at the wellbore largely due to increased fluid viscosity at lower temperatures. However, field observations made to date at the Quest CCS site indicate an inverse relationship between CO2 injectivity and bottom-hole temperature, where injectivity increases of up to 10% due to colder CO2 have been observed in the bottom-hole temperature range of 21 °C–33 °C. This paper presents the field observations of injectivity compared to the theoretically expected and modelled 3D isothermal and non-isothermal conditions of injectivity at various CO2 bottom-hole temperatures, together with an assessment of the dominant controlling mechanisms and parameters that could influence CO2 injectivity under non-isothermal conditions. The assessment results indicate that the seasonal CO2 injectivity correlating inversely with bottom-hole temperature (BHT), cannot be explained by CO2 PVT behaviour under non-isothermal conditions. The inverse correlation is driven by near-wellbore permeability (k), relative permeability (kr) and (non-darcy) dynamic skin factor parameters varying in an inverse relationship with bottom-hole temperature through reversible temperature-driven mechanism(s) such as fluid flow regime changes, fluid-rock interactions and thermally-induced micro-fractures leading to increases in dynamic injectivity at lower CO2 bottom-hole temperatures.A full understanding of the non-isothermal processes and their relative impacts on CO2 injectivity are not only crucial for successful deployment of CCS projects but can also have wider beneficial applications in CO2-EOR modelling and operations cost optimisation.

Large scale modeling and assessment of the feasibility of CO2 storage onshore Abu Dhabi

Carbon Capture and Storage has become a widely recognized viable means to exterminate anthropogenic gases from the atmosphere. One major setback is finding the best storage candidate. Initial comparison of geologic structures in the Emirate of Abu Dhabi has identified saline aquifers as potential sites for the storage of carbon dioxide necessitating the need for detailed assessments. Therefore, we present in this study the results of feasibility studies to determine the prospects of long term injection of CO2 into the proposed aquifers. The aquifers assessed are the Simsima, Dammam, UER and Shuaiba formations. The assessment criteria employed include the estimation of storage capacities, prediction of plume migration, contribution of trapping mechanisms to storage and sensitivity analysis to different reservoir parameters. Geologic models of the aquifers have been created by combining information from wells, seismic, logs and numerical models have been made by upscaling the respective geologic models. The analytical estimates of storage capacities indicate capacities of 5 GT, 1.7 GT, 8 GT and 960 MT for the Simsima, Dammam, UER and Shuaiba aquifers respectively. Dissolution is the dominant trapping mechanism at early and late times via diffusion and convection respectively. The sensitivity analysis implied that the effect of salinity and relative permeability parameters is vital in the final deployment of the storage projects. The results presented here suggests good potential candidates exists for the long-term storage of CO2 onshore Abu Dhabi.

Improving Water-oil Relative Permeability Parameters Using New Synthesized Calcium Oxide and Commercial Silica Nanofluids

This paper addressed the application of new hydrophobic synthesized calcium oxide (CaO) and silicon dioxide (SiO2) nanofluids to low permeability carbonate porous media. Crude oil and plugs were selected from one of oil reservoirs in the west of Iran. The main goal of this paper is comparing the results of improving water-oil relative permeability parameters in low permeability plugs of carbonate cores in the presence of new synthesized CaO and SiO2 nanofluids. All the experiments were performed at a temperature of 40 °C and at a nanoparticle concentration of 45 ppm. The experimental approaches were designed into two main steps: 1) the effects of both nanoparticles on the changes in interfacial tension (between oil and brine) and oil viscosity 2) the effects of both nanoparticles on wettability (qualitatively) and relative permeability parameters. SiO2 and CaO decreased interfacial tension from 46.414 mN/m to 41.772 mN/m and 32.860 mN/m respectively. Moreover, SiO2 and CaO decreased oil viscosity from 9.90 cP to 8.61 cP and 8.01 cP respectively. Based on the obtained results in the core flood experiments, although CaO and SiO2 nanofluids decreased effective water permeability, effective oil permeability and ultimate oil recovery increased. Moreover, it was seen that the CaO nanofluid improved oil flow in carbonate cores more than the commercial SiO2 flooding. Finally, it was seen that both nanoparticles change the wettability from oil-wet to water-wet (qualitatively).

Suitability of ionic solutions as a chemical substance for chemical enhanced oil recovery – A simulation study

Surfactant flooding is one of the important methods applied in chemical enhanced oil recovery (CEOR). Toxicity, high cost, and degradation at harsh conditions are the main issues that face companies during surfactant flooding process. Ionic liquids (ILs), known as liquid organic salts at ambient condition, have been suggested as alternative chemicals due to their superiority over the conventional surfactants. In this paper, we report simulation of core flooding experiments conducted using ionic liquid (Ammoeng 102) on Berea sandstone core samples to study efficiency of the IL on oil recovery. The core flooding experiments were published elsewhere (BinDahbag et al., 2014, 2015). The experiments were simulated using surfactant flood model (SFM), accessible in CMG STARS software. The measured oil recovery and pressure drop were utilized to history match the core flood experiments. First scenario was simulated by injecting 20 wt% salinity brine (83% sodium chloride, NaCl, and 17% calcium chloride, CaCl2) into a core sample initially saturated with 26% irreducible water saturation (Swirr) of the same brine to recover 43% of the original oil in place (OOIP) followed by the ionic solution flooding to recover more than 5% of the OOIP. To study the effect of Swirr on oil recovery using ionic solution, the second scenario was simulated similar to the first one in terms of the injected liquids and sequence except the irreducible water saturation (34% compared to 26%). About 38% of the OOIP was produced during brine flooding whereas more than 6% of the OOIP oil was recovered during ionic solution flooding. To study the effect of brine salinity on oil recovery, a third scenario similar to first one except salinity of brine (10% instead of 20 wt%) was simulated. The result for the third scenario shows recovery of 53% of the OOIP throughout brine flooding followed by 2% incremental recovery during the ionic solution flooding. The results demonstrate that the effect of irreducible water saturation is important during brine flooding stage; however, it is insignificant during ionic solution flooding stage for the runs conducted in this study. In addition, low salinity brine flooding results in higher oil recovery, however, ionic solution flooding was more efficient at higher salinity environment. Simulation of all scenarios showed an acceptable agreement between the experimental and simulation oil recoveries. However, the simulation pressure drops were not matched with the experiments. This may be possible by including the well parameters into the sensitivity analysis. Nevertheless, this has not been conducted in order to isolate the impact of well parameters on the estimated relative permeability parameters.

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.

Three-Phase Relative Permeability and Capillary Pressure Models With Hysteresis and Compositional Consistency

SummaryNew coupled three-phase hysteretic relative permeability and capillary pressure models have been developed and tested for use in compositional reservoir simulators. The new formulation incorporates hysteresis and compositional consistency for both capillary pressure and relative permeability. This approach is completely unaffected by phase flipping and misidentification, which commonly occur in compositional simulations. Instead of using phase labels (gas/oil/solvent/aqueous) to define hysteretic relative permeability and capillary pressure parameters, the parameters are continuously interpolated between reference values using the Gibbs free energy (GFE) of each phase at each timestep. Models that are independent of phase labels have many advantages in terms of both numerical stability and physical consistency. The models integrate and unify relevant physical parameters, including hysteresis and trapping number, into one rigorous algorithm with a minimum number of parameters for application in numerical reservoir simulators. The robustness of the new models is demonstrated with simulations of the miscible water-alternating-gas (WAG) process and solvent stimulation to remove condensate and/or water blocks in both conventional and unconventional formations.

Performance of Relative Permeability and Two-Phase Flow Parameters Under Net Effective Stress in Water Wet Porous Media: A Comparative Study of Water–Oil Versus Silica Nanofluid–Oil

While studies on the stress sensitivity of relative permeability using conventional fluids have varying and inconclusive results, the effect of stress on relative permeability using nanofluids has not been reported. In this study, the effect of net effective stress on relative permeability and two-phase flow parameters using conventional and nanofluid was investigated. Nanoparticle retention in pores was examined by changes in nuclear magnetic resonance transverse relaxation time distribution. Nanoparticle deposition affected big pores more than small pores. As net effective stress was increased during water flooding, end-point oil and water saturations increased and end-point oil relative permeability decreased. Nanofluid–oil relative permeability showed contrasting results depending on whether the sample had adsorbed nanoparticles prior to relative permeability measurements. For the sample that had adsorbed nanoparticles prior to subsequent stress increments, the effect of stress was dominated by the effect of nanoparticle adsorption. However, the effect of stress took precedence over nanoparticle adsorption in samples that had no nanoparticle deposition prior to relative permeability experiments. A comparison of water–oil and nanofluid–oil relative permeabilities showed similar initial water saturations and end-point oil relative permeability changes but differing residual oil saturations and end-point water relative permeability. Mobility ratio increased in water flooding as stress increased but decreased after an initial increase in nanofluid flooding. Displacement efficiency decreased with increased stress for both water and nanofluid flooding. The results provide insights into the effect of stress on relative permeability using conventional fluids and silica nanofluid.

A systematic investigation into the flowback cleanup of hydraulic-fractured wells in unconventional gas plays

This paper conducts an extensive investigation into fracture cleanup efficiency by considering several pertinent parameters instantaneously over a wide practical range. Injection, shut-in and production stages of the fracturing operation were simulated for 32 sets consisting of 113,072 runs. To perform such a large number of simulation runs, a computer code was utilised to routinely read input data, implement the simulation runs and produce output data. In each set (which consists of 4096 runs), instantaneous impacts of twelve different parameters (i.e., fracture and matrix permeability, Brooks matrix capillary pressure (Pc) parameters, and Brooks-Corey relative permeability parameters) were investigated. To sample the domain of variables, full factorial experimental design (two-level FFS) was employed. The linear surface methodology was used to map the simulation output, which is the loss in gas production (GPL), compared to the clean case (i.e., 100% clean-up) after three production periods of 10, 30 and 365 days.The impact of various combinations of fracture fluid injection volume, fracture length, shut-in soaking time, matrix permeability variation range and drawdown on GPL were studied in different sets. Additionally, more simulation sets were performed to capture the impact of hysteresis, layering and mobile formation water on the clean-up efficiency.Results indicated that in line with some literature data, factors that controlled the mobility of FF inside the fracture had the most significant impact on cleanup efficiency. It was also noted that injecting high volumes of FF, into very tight formations significantly delayed clean-up and impaired gas production. The effect of varying other parameters such as extending soaking time or increasing pressure down in such a case delivered negligible GPL improvement. Introducing hysteresis made clean-up slightly faster in all production periods.The impact of the gravity segregation was discussed in this study. Considering the layered systems, it was indicated that in the top layer, the fracture mobility coefficients were more important than the ones in the bottom layer whist capillary pressure seems to become more important in deeper layers compared to the top layers.Additionally, a slower clean-up was observed for sets with larger initial water saturation compared to those cases with immobile water saturation due to the detrimental effect of mobile water on gas production. In some cases, with significantly high values of water saturation, using chemicals (which IFT reducing agents) to reduce Pc could reduce GPL and improve cleanup efficiency.These findings contribute to the further understanding of the fracture fluid cleanup process and provide practical guidelines to achieve economically successful hydraulic fracturing operations, which are popular but expensive for tight and ultra-tight reservoirs.