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Spontaneous imbibition is an area of significant interest to the petroleum industry due to its large contribution to oil production in mature and fractured fields. This work discusses the physics behind the phenomenon of counter-current spontaneous imbibition: the key studies and experiments are reviewed along with how these projects influenced the understanding of the process. The work also simplifies the derivation of the semi-analytical solution of counter-current spontaneous imbibition (Schmid et al. 2011, 2016) and the equation by Schmid et al. (2012) to upscale the rate of spontaneous imbibition from the core to the field scales. Numerical applications of the solution for counter-current spontaneous imbibition, such as determination of relative permeability and capillary pressure, and oil recovery calculations are also discussed. The purpose of this work is to provide a clear and presentative overview of the main mathematical and theoretical concepts and their applications. The work compiles previous significant contributions to the topic and addresses development and applications of the semi-analytical solution, counter-current SI upscaling schemes, imbibition mechanisms and role of capillary backpressure.

Artificial Neural Networks (ANN) are trained to simulate two-phase capillary pressure and relative permeability data in bundles of capillary tubes with non-uniform arbitrary wettability conditions and cross-sectional shapes of different irregular convex polygons. All polygons with variable number of corners are randomly generated for a given range of inscribed radii, shape, and elongation factors. To generate the data for the training of ANNs, the minimization of Helmholtz free energy and Mayer-Stowe-Princen (MS-P) method are combined to find thermodynamically consistent threshold capillary pressures for two-phase flow. These capillary pressures are then used to determine the sequence of displacements in different capillary tubes. We calculate saturations and phase conductance at each quasi steady-state condition where no more displacements can be done for a given capillary pressure. The generated two-phase capillary pressure and relative permeability curves are then used for the training of ANNs. We test different designs of ANNs to find the optimal workflow for the training and predicting of petrophysical properties related to multiphase flow. In this work, we present the results of two different neural network structures. In the first structure, we use ANN to predict threshold capillary pressures of different capillary tubes during a drainage process (i.e., oil-to-water displacements). In the second structure, we predict capillary pressure and relative permeability curves for an arbitrary bundle of capillary tubes. The first structure of ANNs simulates a fixed property for a given capillary tube, whereas the second structure simulates time-series data format (i.e., for a given bundle of capillary tubes calculated properties vary with saturation). To do so, we have generated multi-phase flow properties for two large datasets consisting of 40,000 and 60,000 capillary tubes each. High-quality training datasets are critical in the training of high-fidelity ANN models. These models can then learn the impact of a wide variety of pore geometries (i.e., shape factors and elongations). Additionally, feature selection and preprocessing of the input data could significantly impact ANN's predictions. The multi-layer perceptron (MLP) neural network with three hidden layers with four outputs is adequate for predicting capillary pressure and relative permeability curves during drainage. This model is approximately an order of magnitude faster than conventional direct calculations using a desktop computer with four cores CPU. Such improvement in the speed of calculations becomes significant when dealing with larger models, more dimensions, and/or introducing pore connectivity in 3D.

Fluid flow in tight formations deviates significantly from that in conventional reservoirs due to the micro/nano pores and high confining pressure; non-linear flow occurs at low displacement pressure gradients. The effects of boundary layer and media deformation on fluid flow cannot be ignored. In this paper, a stochastic network model with anisotropic topology is firstly constructed to represent the complex structures of tight formations. Subsequently, a series of network models with different physical scales are generated to obtain the representative elementary volume (REV). Based on the representative network model, a pore network flow model coupling the boundary layer effect with media deformation is developed. Iterative methods are proposed to solve the strong nonlinear mathematical model. Microtube experiments with different radii and three corresponding representative networks with different distributions of throat radii are employed to verify the accuracy and reliability of the numerical results. After the validation, pore scale flow regularity considering the boundary layer effect and media deformation of tight formations is obtained. Furthermore, the factors influencing pore scale flow, such as the effective stress, aspect ratio, coordination number and fluid viscosity, are studied. The results show that pore scale flow velocity considering the boundary layer effect and media deformation is smaller than that without considering the two mechanisms. Nonlinear flow occurs at low displacement pressure gradients because of the boundary layer effect, and media deformation aggravates the nonlinear phenomenon. Similarly, the absolute permeability also decreases when the two mechanisms are considered. It is no longer constant when boundary layer effect is taken into consideration, which increases with increasing displacement pressure gradient and reaches a plateau when the displacement pressure gradient is large enough. The effects of different factors on pore scale flow considering boundary layer effect and media deformation differ from their roles in conventional flow network models. Although the absolute permeability increases with decreasing aspect ratio and increasing coordination number, the value is far smaller than that without considering the two mechanisms because they result in the compression of the effective flow space. Additionally, the absolute permeability no longer remains unchanged when the variation of fluid viscosity is included. This indicates that the absolute permeability considering the boundary layer effect is not only affected by the pore structures but also the fluid viscosity. The methodology developed in this work provides a novel way to study the effects of boundary layer and media deformation on pore scale flow. The results provide new insights into fluid flow in tight formations.

Rock permeabilities are typically calculated by applying some empirically derived relationships or expressions, which normally result in rough or erroneous values. Given advanced computing and smart techniques, rock samples acquired in boreholes or on outcrops can be imaged and broken down into small digital rocks. The renormalization group approach with isotropic block (RGAWIB) has been applied to calculate the permeability of digital rocks. The RGAWIB proposed by King can accurately derive the effective permeability if the pore structure is described correctly by the separated grid blocks. For King's method, the permeability of the grid block is assumed to be isotropic, which is not suitable for significant variance in neighboring permeabilities. In this study, we adopted discrete blocks with anisotropic permeability for the upscaling process of renormalization, which provided reasonable results for large perturbations of permeability in neighboring grid blocks. We assumed that the anisotropic block held different permeabilities in three orthogonal directions and calculated the effective permeabilities of idealized porous media and digital rocks by a renormalization group approach with anisotropic block (RGAWAB). Moreover, a permeability distribution method is presented in this paper. The original permeability distribution of an idealized porous media was calculated, along with the permeability distributions of the digital core data available in the literature in the x, y, and z directions using the method developed in this study. Then, we calculated the effective permeabilities of the digital rocks using RGAWAB in the x, y, and z directions, respectively. We compared the results with the absolute permeabilities calculated by the lattice Boltzmann method, which showed that the permeability calculation method was feasible for digital rocks.

In this study, a novel method to stochastically characterize the effective permeability of a fractured caprock (typically fine-grained sedimentary rock or natural mudstones) is presented. The method requires pressure monitoring data from above and below the caprock, which are used in combination with other readily-available data from laboratory and outcrop observations in a history-matching process that maintains the distribution of underlying fracture attributes to characterize the spatial variation in permeability of the caprock. A “best-fitting” geological model of caprock, representing a most-likely scenario, is selected from an ensemble of stochastic realizations generated using optimized parameters. The method is demonstrated using a representative, moderately permeable, heterogeneous caprock, as a reference “truth” to compare accuracy of caprock predicted using pressures from injection and post-injection phases. The accuracy of “best-fitting” caprock is assessed by studying its sensitivity to four variables, which are caprock thickness, leakage intensity, time length of available pressure history, and injection rate. Improved characterization of effective caprock permeability allows more confident prediction of flux through the sealing interval, over time. That information is useful in quantifying potential impacts of fluid migration, evaluating monitoring designs, and designing mitigation alternatives, should they be needed. It has value both during active injection and in building confidence that a site can be safely closed after injection is complete.

Based on the mechanical mechanisms of shear and tensile parting dilations, water injection into oil sand reservoirs prior to steam circulation can effectively establish inter-well hydraulic communication and create an expected initial steam chamber. To quantitatively evaluate the effectiveness of water injection, this paper defined some novel concepts including the effective permeability to injection water, hydraulic dilation area (HDA) as well as radius (HDR) incorporating longitudinal and lateral hydraulic dilation radii (HDRa and HDRb) for a more intuitive description of the hydraulic dilation behavior. An analytical model of hydraulic dilation area under water injection was established considering the interference effects of mudstone cap and base rocks, effective permeability to injection water, SAGD well geometry and operation parameters. The figures of analytical results are exhibited for evaluating the hydraulic dilation response under given geometry and flow properties and for finding an achievable path for improving the HDR and HDA through artificial operations for an operator. Major conclusions through an application on the wellpair A-2 in area A of Karamay Fengcheng oil field can be drawn that the HDR and HDA can be improved by increasing the injection pressure or decreasing the fluid viscosity and injection rate of unit well length. A higher effective permeability to injection water induced by a larger volumetric expansion is beneficial to the HDR and HDA. A larger wellbore radius, a closer distance between P well and base rock, and a closer well distance designed in the drilling process are advantageous to the HDR and HDA. The HDA and HDR are essentially controlled by the volumetric dilation resulting from pressure transfer capability and pressure interference by mudstones and SAGD wells. These findings provide an analytical approach for evaluating the efficiency of water injection, and offer some suggestions to improve the HDA by artificial operations for engineers.

Distinct from conventional reservoirs, shale formations have limited pore connectivity and unique pore spatial-distributions. Consequently, theoretical pore-network models developed for conventional formations are not representative of the pore topology within unconventional rocks. This paper presents a theoretical pore-network model, dendroidal model, based on the analysis of reconstructed pore-scale model extracted from Scanning Electron Microscope images. Dendroidal model is a semi-acyclic model, which characterizes the poor connectivity of void space without sacrificing the interaction between main flow paths. Dendroidal model infers pore-body distribution based on the hysteresis effect of isothermal adsorption/desorption measurements and characterizes pore-throat distribution using mercury injection capillary pressure data. The use of dual-compressibility model in pore-network model construction eliminates the effect of compressibility of both void space and matrix. Total organic carbon (TOC) content and minerology determine the composition of pore bodies and pore throats. The difference in mercury intrusion and extraction caused by trapping hysteresis and contact-angle hysteresis affects the stochastically distributed parameters, including pore-throat length, pore-throat cross-sectional morphology, coordination number and pore-body spatial distribution. We used shale core samples from Marcellus and Wolfcamp formations to validate the dendroidal models by calculating the absolute permeability without slippage effect. This newly developed pore-network model integrates aforementioned seven distinct types of experimental data to capture the realistic pore structures within shales.

Wettability is an important factor which controls oil recovery and fluids displacement efficiency in the porous media. Wettability alteration (WA) from strongly oil-wet towards water wet or neutral states is one of the most effective methods of oil recovery increment. Many studies have shown that nanofluid can change the wettability of rock surface towards a desirable state and base on literature structural disjoining pressure is the main mechanism of wettability alteration via nano-treatment. However, there is a lack of information regarding the impact of salinity on nanofluid performance in porous media. Therefore, in this work, the effects of salinity, nanofluid concentration and rock type (i.e. limestone and dolomite surfaces) on wettability alteration of oil wet carbonate substrates under ambient condition were investigated. For this purpose, various static and dynamic experiments including contact angle, imbibition and core flood tests have been performed. The results on contact angle measurements showed that by increasing nanoparticles and electrolyte concentration the wettability alteration from oil wet to water wet was significantly enhanced. Moreover, the wettability alteration of dolomite substrate is much more than that of limestone substrate. In the following, the impact of nanofluid on the spontaneous imbibition for strongly oil-wet carbonate cores was closely examined. Finding results showed an increase as much as 15% of oil recovery for nanofluid imbibition in comparison to that of formation brine. Final evaluation of the nanofluid treatment in terms of its effectiveness was measured by core flood experimental runs. Comparison of relative permeability curves before and after treating have outlined that after the treatment process, the relative permeability curve has shifted to the right and the water relative permeability has reduced from 0.43 mD to 0.23 mD at the residual oil saturation due to wettability alteration of rock surface from strongly oil wet to water wet state.

Relative permeability stress sensitivity studies reported in literature do not have a common conclusion with regards to end point saturations and their respective relative permeabilities. Moreover, there is lack of experimental results on stress sensitivity of pore fluid distribution, which is a key parameter for the behavior of relative permeability curves. This study extended core homogeneity to include similar porosity, permeability and NMR T2 distribution as well as examined NMR T2 distribution behavior with stress on artificial sandstone cores and the results used in explaining relative permeability stress sensitivity under net confining stresses of 5, 15 and 25 MPa. The effect of stress on displacement efficiency was also investigated. The bulk volume irreducible (BVI), which is the fraction of the bulk volume containing irreducible water, generally increased with stress. Meanwhile the free fluid index (FFI), which is the fraction of the bilk volume responsible for fluid flow, decreased with increased stress. NMR irreducible water saturation and irreducible water saturation obtained from relative permeability experiments both increased with stress. Irreducible water saturation was strongly related to the behavior BVI stress sensitivity. Residual oil saturation increased with increase in stress as a result of reductions in FFI pore volume. End-point oil relative permeability had a significant decrement with stress while water end-point relative permeability had a negligible decrement. The significant reduction in end-point oil relative permeability was due to reductions in pore radius evident in a corresponding reduction in FFI. Displacement efficiency decreased with increased stress indicating lower oil recovery on microscopic scale but end-point mobility ratio increased as stress increased. Relative permeability stress sensitivity could be tied to changes in BVI and FFI of NMR T2 distribution when changes in stress occur in petroleum reservoirs.

The main development method of tight oil was depletion development. It is determined that the seepage radius of tight reservoir is crucial to the layout and prediction development of tight oil development. Since the pore throat level of tight reservoirs was frequently nanoscale, the reservoir pressure propagation velocity was even faster than conventional medium high permeability. The fracture system in the tight oil reservoir, which is the main flow channel of oil flow to the direction of wellbore, is more sensitive to the sharp change in reservoir pressure. Hence, the stress-sensitive absolute permeability of the reservoir near the wellbore will fluctuate significantly during the depletion development phase, rather than a constant value. At present, the numerical simulation and graph method, which are commonly utilized in the regression and prediction of the depletion-developing seepage radius. Both do not consider the stress sensitivity phenomenon which caused by nanoscale pores of tight oil and the change of the permeability in the model. As a result, the prediction is not accurate and the model needs to be modified. Meanwhile, the percolation parameters at the scale of the tight oil permeability cannot be accurately obtained in using conventional experimental methods owing to the limitations of the accuracy of the experimental instruments. In this paper, the test of fluid permeability under overburden was carried out to verify the stress sensitivity of the tight core. The microscopic mechanism of nanoscale pore-throat stress sensitivity in tight reservoirs was analyzed from the perspective of tight reservoir mineral composition and nanopore characteristics by using Quantitative Evaluation of Minerals by Scanning Electron Microscopy (Qemscan) and MAPS micro-image splicing technology. Nanoscale pore network model was established with nano-CT scanning and the digital core seepage simulation of tight core was figured out. The accuracy of the digital core seepage simulation method was verified in comparison with the indoor over pressure liquid permeability test. The conventional reservoir model was modified by using the digital core seepage simulation result, and the new model has a high degree of confidence in predicting the tight oil seepage radius.

This study aimed to investigate the prediction method of permeability and its anisotropy of tight oil reservoir via precise pore-throat tortuosity characterization and “umbrella deconstruction” method combining the approaches of the field emission SEM imaging, high resolution image processing, fine and large-scale mathematical statistics, nonlinear regression and other technical means. In this paper, the authors proposed the new calculation model of pore-throat tortuosity, the absolute permeability and the permeability anisotropy based on the improved deep understanding of reservoir. Results of the prediction on the tight oil reservoir of “YANCHANG” formation in Ordos Basin show that the errors of the new method in this paper are the smallest among the total five methods, respectively 0.023 × 10−3μm2 and 0.090 × 10−3μm2; the average values of other four methods were 0.090 × 10−3μm2 and 0.108 × 10−3μm2, respectively. The predicted results have higher accordance with the measured results, which proved the practicality of the new method. The samples has the highest permeability at the angle of 0°(180°/360°) and the permeability values are equal to 0.25 × 10−3μm2. Similarly, the sample has the lowest permeability at the angle of 22.5°(202.5°), 90°(270°), and 112.5°(292.5°), the permeability values are all equal to 0.06 × 10−3μm2. At the same time, the calculation of permeability anisotropy results shows that the anisotropy of tight oil reservoirs is very significant, and the permeability value in one direction is obviously higher than which in other directions. It is concluded that the precise description of pore throat geometry, especially the calculation of pore-throat tortuosity parameter, is one of the most important parameters affecting the prediction accuracy of permeability theoretically. Meanwhile, there are dominant seepage channels, which would play a very important guiding role in the prediction of hydrocarbon accumulation and seepage capacity. The conclusion will provide a more rigorous theoretical basis for the rapid and accurate evaluation of the physical properties of unconventional reservoirs.

Oil-water relative permeability is not only the basis for studying the oil-water two-phase flow characteristics, but also one of the indispensable parameters for the reservoir numerical simulation and production dynamic analysis. Waxy oil has obvious viscosity-temperature characteristics and wax precipitation phenomenon, resulting in complex and diverse factors affecting the relative permeability. Presently, no systematic investigation on the oil-water relative permeability and displacement efficiency of wax oil reservoir exists, especially using live oil as experimental oil. In this paper, the accurate wax appearance temperature (WAT) and necessary aging time of experimental oil and cores were determined using ultrasonic detection and spontaneous imbibition methods, respectively. Subsequently, the viscosity, wettability, relative permeability and displacement efficiency of live oil and crude oil were compared and analyzed at different temperatures. Finally, the influencing factors of live oil-water relative permeability and displacement efficiency, namely, solution gas, temperature, permeability, wettability, water injection parameters and wax precipitation were comprehensively analyzed and studied. Experimental results showed that the WAT, wettability and viscosity of live oil are different from those of crude oil, thereby causing the difference in relative permeability and displacement efficiency of live oil and crude oil. When the temperature is above the WAT, the dominate influencing factor is oil viscosity, while the effect of core permeability is not obvious. When the temperature drops below the WAT, the precipitated wax not only causes a sharp increase in the oil viscosity, but also forms a wax film on the surface of flow channel to transform the rock wettability from hydrophilicity to lipophilicity. Furthermore, the wax film narrows the flow channel and the wax particles block the small pore throats. All these changes caused by wax make the relative permeability and displacement efficiency before and after the wax precipitation very different. The effect of permeability becomes significantly because of the physical deposition and pore throat plugging. Similarly, the displacement efficiency of different water injection parameters is the result of the interaction of multiple mechanisms. This investigation not only provides a systematic and reliable measuring method for the oil-water relative permeability and displacement efficiency of waxy live oil reservoirs, but also improves our understanding of the multiphase flow mechanisms in waxy oil reservoir.

Enhanced liquid treatment magnifies the difference of fluid flow velocity between borehole and inter-well zones. The flow velocity will influence the relative permeability and change the percolation law in the oil-water two-phase flow. In this study, we conduct three group experiments with different permeability using 15 artificial cores. The unsteady-states measurement method is used to test the relative permeability curve at different velocities. We found that relative permeability would be affected by the testing velocity based on the experimental results. A new relative permeability equation considering flow velocity is established, which indicates that higher oil recovery can be obtained by an early enhanced liquid treatment. There is also a critical velocity with different permeability. If the flow rate (vw) of the enhanced liquid treatment is larger than the critical velocity, the treatment will improve the oil recovery. On the contrary, if the vw of the enhanced liquid treatment is larger than the critical velocity, the treatment will reduce the oil recovery. We summarize the new relative permeability equation and implement it to the numerical simulation model. The new simulator is validated with the three-parallel sand-pack experiment and the actual China offshore oilfield model. The new simulator could predict oil production accurately after enhanced liquid treatment.

Multiphase displacement in tight sandstone is fundamental and critical for tight oil production. Micropores dominate the pore space in tight sandstone. Microscopic mineral components in micropores substantially influence the multiphase displacement behavior. Pore size distribution exhibits a self-similar or fractal property, similar to inorganic mineral grains. Utilizing fractal theory eases the rebuilding of the flowing space and calculation of relative permeability. As an improvement of previous work, we successfully extended the 3D intermingled fractal model (3D IFM). The extended 3D IFM can evaluate multiphase flow behavior in tight sandstone, considering fractal characteristics of pore size distribution and mineral grain distribution. The fractal information of pores and mineral properties are obtained by scalable scanning electron microscopy (SEM) and energy dispersive spectroscopy(EDS) images, respectively. This method is useful and reliable for calculating relative permeability and residual saturation. The method is also successfully used to evaluate the influence of oil-water viscosity ratio, mineral components and formation depth on multiphase displacement behavior, proving its convenience and potential in rapidly evaluating multiphase displacement behavior in tight sandstone.

Aquifer strength is one of the main parameters in surface water separation facilities design. The material balance method is a common approach to calculate the aquifer strength and water influx in mature reservoirs which are in the second half of their lives. However, this method could not be used for green and newly developed reservoirs. In this type of reservoirs, the suitable vertically and laterally distance between aquifer and perforation intervals in the development wells is a main question which depends on future aquifer behavior. In this study, a methodology has been presented to estimate aquifer properties using water pressure data and also well testing data in a newly developed giant gas field in Middle East. The numerical sector model is used to match simulated water pressure data with actual MDT (Modular Dynamic Tester) data. The water relative permeability for each rock type and vertical-horizontal permeability relationship have been determined in history matching process. The tuned model can be used for the prediction of the aquifer performance and also the water production in future development wells.

Proper characterization of multi-phase flow in porous media is of significant importance in selecting and optimizing the performance of a given oil reservoir. The main factors influencing the characterization of multi-phase flow in porous media include: microscopic pore structure, movable fluid saturation, nonlinear seepage characteristics and clay minerals composition, and etc. However, it is very difficult to quantitatively study the multi-phase flow process in porous media, because there is no clear relationship between the oil production rate and the physical parameters of oil reservoir, particularly in low permeability reservoirs. Furthermore, on-going research activities has led to the discovery that it has been a challenge to tell why two oil reservoirs with the same degree of permeability (i.e. low permeability) have far different production performances. In an attempt to comprehend this challenge, a concept of global mobility by Li and Horne (2005, 2006) derived from the Li-Horne model was proved to be a new approach for evaluating the seepage capacity in imbibition system, because it can unify oil and water phase mobility into one model and take many static and dynamic physical parameters into accounts. In this paper, the global mobility concept is applied and verified to characterize the mobility of a multi-phase flow and evaluate the production performance from core to field scale. Comparisons between the global mobility concept and other characterization methods were conducted based on various flooding experiments and field data tests from rock/oil/water systems and rock/oil/polymer systems with different porosities and permeabilities. The results showed that there is a linear relationship between the global mobility and the production performance which is better than the other methods, and the application range of the global mobility was extended. In addition, a convenient and empirical approach was proposed to obtain the global mobility with relative permeability data. Its feasibility has been preliminarily proved through five case studies, and the demonstration is that the global mobility could be an effective parameter to characterize a two-phase flow in porous media and evaluate the production performance for field application.

Recently, exploration operations for gas wells target deep reservoirs, where the temperature and pressure are very high. High temperature (more than 200 °C) and pressure (more than 5500 psi) result in degrading the complex organic molecules into dry gas or gas condensate. During gas production the reservoir pressure will decrease below the gas dew point and form a condensate bank near to the borehole. Condensate banking has been branded to cause serious drop in the gas effective permeability, gas productivity and results in formation damage. Numerous techniques have been adapted to mitigate gas condensate banking effects in gas wells. These approaches include the injection of solvents and chemicals to alter formation wettability to minimize condensate blockage. Other methods include acids injection, fracturing treatments, and drilling horizontal wells. These methods will lower the rate of pressure drop and permit the production of a single phase gas. This paper critically reviews the causes and instants of condensate banking in gas reservoirs. The developed models that capture and enumerate this phenomenon, and the most adapted mitigation techniques in accordance to the leading conditions are thoroughly discussed. The most successful agents for enhancing condensate production are reported and their effects on the condensate behavior is identified. Furthermore, novel and new technique for permanent condensate removal is presented in this paper. This review will fill the gap in the area of condensate removal treatments by critically analyzing and summarizing the techniques proposed in the literature.

We study the impact of explicitly including hysteresis effects (HEs) for relative permeabilities in numerical simulations of enhanced oil recovery approaches grounded on the application of Water Alternate Gas (WAG) injection protocols. Our work explores the significance of hysteresis exhibited by the relative permeability of the non-wetting and/or intermediate wetting phases on the results of reservoir simulations performed within a black-oil modeling approach. We consider four diverse strategies that can be employed to model relative permeabilities of fluid phases under WAG scenarios implemented in a water-wet system following primary waterflooding. The effects of all these modeling strategies are assessed in terms of field oil efficiency (FOE) and gas oil ratio (FGOR) evaluated at the total production lifetime of the reservoir, as compared against a base case where only waterflooding is applied to promote oil recovery. Two of these strategies are implemented and used in typical commercial black-oil reservoir simulators and either neglect hysteresis or consider it only for the gas phase. We then examine a procedure where only hysteresis for relative permeability of the oil phase is considered. Finally, we explicitly consider hysteresis of both non- and intermediate-wetting phases. Our results generally show that including HEs yields an increased FOE and a decreased FGOR. This is consistent with the observation that when injection well controls are set at an optimum value, a non-negligible portion of the domain is associated with saturation paths corresponding to three-phase flow conditions, where saturation history can play a significant role. As compared against a base case where waterflooding is considered as the sole strategy for oil recovery, including hysteresis on three-phase relative permeabilities in the numerical simulations of WAG promotes an increased net present value. We also analyze the impact on reservoir simulation responses of the main WAG injection parameters, i.e., (i) injection rate of gas and water, and duration of (ii) WAG cycles, and (iii) primary waterflooding.

Representative capillary pressure and relative permeability curves for reservoir rock types are important inputs for a dynamic reservoir simulator. The current study proposes a third-step approach to generate representative capillary pressure and relative permeability curves of reservoir rock types from nuclear magnetic resonance (NMR) log. First, reservoir electrofacies were identified by integration of conventional well logs and NMR log parameters. Employing cluster analysis reservoir rocks were classified into six electrofacies (EF) with reservoir quality being increased from EF1 to EF6. In the second step, the NMR T2-distribution arrays were converted to synthetic drainage capillary pressure curves and the results were validated by available laboratory measured mercury injection capillary pressure curves (MICP). Finally, the relative permeability curves were generated from the NMR-derived MICP data by using the Wyllie and Gardner equations for each individual electrofacies. Comparing the results with laboratory data indicates the effective role of electrofacies control in generating high accuracy capillary pressure and relative permeability curves. The results of this study show that the application of NMR log can further be extended through the generation of drainage capillary pressure and relative permeability data in the framework of electrofacies clustering.

Application of multi-fractured horizontal wells has led to significant progress in the development of tight oil reservoirs. However, oil production rapidly decreases and the estimated ultimate recovery is still low when the well is in production and approaching depletion. Water huff-n-puff is regarded as a useful measure to improve oil recovery due to oil-water imbibition and drainage. Additionally, complex fracture networks consisting of natural fractures (NF) and hydraulic fractures can significantly enhance oil recovery in the process of water huff-n-puff after multi-stage hydraulic fracturing. However, there is a non-flowing thin film on the solid-liquid wall surface in the pore-throats of the matrix, and the so-called boundary layer effect (BLE) is quite significant at the nano-scale. This effect reduces the effective flow space and effective permeability of the reservoir, leading to production damage. To date, few numerical simulation studies have considered the impact of the BLE and complex fracture networks in water huff-n-puff process simulation studies. In this study, the process of water huff-n-puff is evaluated considering complex fracture networks and formation damage in a matrix. The embedded discrete fracture model (EDMF), validated by local grid refinement (LGR), is applied to describe the distribution of hydraulic fractures and NF. The well performance considering the BLE is analyzed by a vectorization programming. The results show that the BLE reduces production and accelerates the production decline, so the BLE should be considered in reservoir simulations and productivity evaluations of water huff-n-puff processes. A certain degree of natural fracture development is conducive to improving the sweep efficiency of the water huff-n-puff, which could significantly improve oil recovery compared to depletion. By considering the impact of the BLE in water huff-n-puff simulations in tight oil reservoirs, it is possible to accurately evaluate the well performance and provide a theoretical basis for the optimization of water huff-n-puff.

Numerical investigations were carried out with special attentions on the inlet and outlet behaviors of foam flow process in a homogeneous porous media with confined entrance and exit boundaries. The Stochastic Bubble Population (SBP) balance model, which usually involves two parameters of the bubble generation rate Kg and the maximum bubble density n∞ for bubble number prediction, was employed to study the dynamic foam generation and development process in porous media. With introduction the Kfp parameter to take into account the foam phase relative permeability reduction effect, the control equations of the two-phase flow process in a two-dimensional computational domain were solved with the IMPES algorithm and the inlet and outlet behavior of the foam displacement process were scrutinized based on detailed analysis of the bubble density, water phase pressure and water phase saturation distributions in porous medium. Numerical results showed a clear entrance effect of higher water saturation, lower pressure gradient and developing bubble density in the inlet region of the porous media in the transient foam displacement process, whereas the confined exit results in elevating water saturation and decreasing pressure gradient towards the outlet of the core. Parametric studies on Kg, n∞, Kfp and inlet & outlet sizes D indicate higher bubble generation rate could remarkably suppress the entrance region in the foam seepage process, while the higher maximum bubble number did not lead to obvious change of the foam flow behavior in the inlet and outlet region, although it could produce higher absolute values of bubble density and pressure drop along the core. With lower Kfp values, the strong foam flooding behavior could be properly predicted with much higher pressure drop and lower water saturation. Two dimensional numerical results at various inlet and outlet sizes clearly show the confined geometry effect on foam flow characteristics with smaller sizes corresponding to longer inlet and outlet regions. Computational domain and numerical results were validated through comparisons with corresponding experimental setup and CT measurement results. It is observed that, the numerical simulation could reproduce not only qualitatively but also quantitatively the experimentally obtained water saturation distribution and pressure drop result. It is concluded that the mechanistic stochastic bubble population model could be reasonably employed on prediction of the inlet and outlet behavior in the transient foam flow process in the homogeneous porous media.

The large-scale hydraulic fracturing technology is commonly employed to significantly improve oil recovery in shale. An exceptional phenomenon from many field tests is worthy of attention that the majority of fracturing fluid (mainly water) does not return to the surface during hydraulic fracturing, but flows into shale matrix. As a consequence of this phenomenon, oil-water two-phase flow would happen. However, the fluid transportation in nano-pores is different from that of the conventional sandstone reservoirs. To understand oil-water two-phase flow in shale, an integrated pore network model (PNM) framework including network construction and flow simulation is developed. In the network construction, combined with a pore-size distribution (PSD) curve of shale system, a shale multiscale random pore network model is proposed, where organic pores and inorganic pores can be distinguished appropriately. In the flow simulation, considering that the traditional Hagen-Poiseuille equation may not be applicable in shale system, new bulk fluid and corner film flow models with slip length in various geometric pores (circular, square, equilateral triangle) are developed using the computational fluid dynamic (CFD) method. Through the quasi-static simulation technique, we estimate the flow properties in shale including capillary pressure and relative permeability. Simulation results confirm the slip effect would significantly affect oil-water two-phase flow in shale. And then, influences of shale pore structure on two-phase flow are further investigated. Through coupling network construction and two-phase flow simulation, we believe our work could shed light on the further research for multi-phase transportation in shale.

Accumulation of gas-condensates in near wellbore regions, and consequently, the reduction of gas production rates, is a well-known phenomenon in most gas reservoirs all around the globe. In this study, the injection of CO2 in “huff-n-puff” (HnP) mode and its potential advantages of removing accumulated gas-condensates are thoroughly investigated. A compositional simulator was used to capture the near wellbore fluid flow physics causing the condensate dropout under various wellbore/field operational conditions. The severity of condensate blockage was evaluated using detailed sensitivity and uncertainty analyses of various key static and dynamic influencing parameters such as porosity, permeability, fluid composition, boundary flux, and flowing bottomhole pressure. Under various scenarios of condensate blockage, studies related to effectiveness and optimization of CO2 slug-size, soaking-time, and flowback rate are conducted. As a proof of concept, it is observed that miscibility of CO2 in condensates, and near wellbore re-vaporization of accumulated liquids, are two of the main mechanisms of removing the condensate blockage. Because of these two mechanisms an improvement in effective permeability to gas can be expected. It is also concluded that CO2 is relatively more effective in removing near wellbore condensates as compared to far-field regions. Finally, based on various optimization analyses, a viable approach to adopt HnP CO2 injection scheme is suggested.

Enhanced oil recovery by low-salinity waterflooding (LSW) has been shown to result from the combined effect of various physical mechanisms. In this study, laboratory experiments were designed in such a way that only fines migration mechanism remains active. Then, experimental observations and detailed characterizations of core plugs and produced fluids (water and oil) were used to analyze the effect of fines migration-induced formation damage on displacement efficiency. In the first set of experiments, core plugs of Berea and Obernkirchener sandstones were subjected to single-phase injections of water at salinities 40, 30, 20, 10, 5, 2.5, 0.5 and 0 g/L NaCl. An order-of-magnitude decrease in permeability was observed for both core plugs and was associated with an increase in fines concentration in the produced water. SEM-EDS images of the produced fines showed that kaolinite is mobilized as the salinity is reduced. SEM images of the pores before and after injection also showed fines retention and blockage. In the second set of experiments, two-phase LSW was performed on a pair of core plugs comparable to those in the first set of experiments. Kaolinite migration results were consistent with those of single-phase LSW. The two-phase LSW experiments showed 50% reduction in water relative permeability and 3% increase in oil recovery. Because no wettability alteration mechanism was active, the increase in oil recovery is attributed solely to enhanced displacement due to fines migration.

Understanding the relative permeability characteristics of coal in a gas-water system is crucial for coalbed methane development. Due to a lack of experimental information on the gas-water relative permeability of coal, the relative permeability of the low-rank coals in the Erlian Basin in the north of China was investigated under different conditions using the unsteady-state method. The studied coals are dominated by huminite with high moisture content, volatile yield, and low ash yield. The pore sizes of the coals feature a bimodal pattern distribution with a higher left peak of approximately 10–100 nm and a relatively lower right peak of approximately 10000 nm. The measurement of mercury intrusion-extrusion hysteresis also suggests that ink bottle-shaped pores are possibly developed within the coals. The results from relative permeability tests with methane (CH4) and water depend on the pore structure, coal wettability, confining pressure, and pressure difference in the coal. The results show that a definite correlation does not exist between relative permeability and porosity in the low-rank coal. However, macropore porosity rather than the whole range of the porosity is the most likely property affecting the water relative permeability, whereas the effect of pore size on gas relative permeability varies along with a broader range. It has been observed that the low-rank coal with higher water wettability exhibits lower water relative permeability, narrower two-phase span, higher gas relative permeability, and irreducible water saturation. With the increase in the confining pressure, both the methane and water relative permeabilities decrease, while the ratio of relative permeability (krw/krg) increases. This suggests that the confining pressure has less influence on water relative permeability than that on gas. As the pressure difference increases under the same effective stress, the residual water saturation in the low-rank coals decreases, and the associated two-phase span increases. Water relative permeability obviously increases above the crossover point water saturation, whereas gas relative permeability increases below the crossover point water saturation.

Despite the differences between petrophysical static (PSRTs) and dynamic rock types (PDRTs), previous indices were unable to distinguish between them. FZI-Star (FZI*) and PSRTI are recently developed petrophysical dynamic and static rock typing indices, respectively. Considering the importance of rock typing in reservoir characterization and the need for reliable and user-friendly techniques, in this study we attempt to further verify the performance of FZI* and PSRTI by comparing them with FZI, Winland r35, and MFZI using data belonging to a heterogeneous carbonate reservoir from the Asmari Formation. The experimental data set includes 10 primary drainage mercury injection, 29 water-oil, and 45 gas-oil capillary pressure tests for PSRTs prediction in conjunction with 52 water-oil and 51 gas-oil relative permeability data for PDRTs. Moreover, we investigated the correlation between various indices and several petrophysical attributes. We defined these attributes as the integrals of mercury injection capillary pressure, mercury injection threshold capillary pressure, measured r35, capillary pressure, and relative permeability curves along with residual saturations. The results showed that our indices are able to successfully identify static and dynamic rock units with higher accuracy than other indices. Among the other existing methods, Winland r35 was the only one that showed an acceptable outcome; while, FZI, and MFZI underperformed in identifying the existing rock types. Using the experimental data we also propose the empirical equations that can be used to model capillary pressure and relative permeability characteristics of rocks.

Crude-oil recovery processes with a voidage replacement ratio (VRR = injected volume/produced volume) less than 1 combine solution gas drive mechanisms and viscous crude-oil displacement. Previous laboratory and field studies have shown that a VRR less than 1 for a period of time is optimal for recovery of some viscous and heavy crude oils that form emulsions and/or bubbly oil in situ. This study extends understanding of the effect of VRR to recovery of live, less-viscous crude oils from sands. The crude oil used is roughly 28 °API, has a dead-oil viscosity of 26 cP, a live-oil viscosity of 0.41 cP, and an asphalt content of 2.1 wt%. It is found in the laboratory that the final crude-oil recovery (70.5%) using a 0.01 PV/h depletion rate and VRR equal to 0.7 is more than 8% greater than recovery with VRR equal to 1 (65.1%). Recovery using a 0.001 PV/h depletion rate with VRR equal to 0.7 (79.1%) was nearly the same as the sum of oil recoveries for solution gas drive (VRR = 0, 24.5%) plus waterflooding (VRR = 1, 53.4%). For these two depletion rates, the oil recovery obtained using VRR equal to 0.7 is more favorable than VRR = 1 (waterflooding). Relative permeability was inferred from experimental results. Substantial critical gas saturations (8.1–16.1%) also contributed to oil production. A concave shape of the oil/water relative permeability curve indicated an emulsion-like effect that also promoted recovery when the VRR was less than 1.

Asphaltene deposition in oil reservoirs is a contentious issue affecting both well and reservoir productivity. Though the phenomenon has been previously studied in several laboratory experiments, the uniformity aspects of the asphaltene deposit are usually overlooked. We have previously developed an experimental workflow to create a uniform deposit of asphaltene inside the core sample. In this study, the impact of this uniform deposit on fluid flow is quantified through imbibition, corefloods and relative permeability experiments. In addition, the lab results are used in a field scale simulation to investigate the impact of deposition on field performance. The results exhibit a shift in the wettability state where a reduction in both water imbibition rate and capacity are observed after deposition. Besides, up to 25% reduction in absolute permeability is detected. Results of pressure drop experiments across the core conducted on the exposed rocks indicate a change in the wetting characteristics, with the exposed rocks becoming more mixed/intermediate wet and varying with the change in the initial brine saturation in the rock. Subsequently, the relative permeability set is affected where a shift in the oil residual saturation, a downgrade in the oil curve and an upgrade in the water curve are observed. Upscaling this new data to field scale indicated a loss of more than half of the well productivity and an earlier breakthrough if waterflooding is implemented.

The objective of Low Salinity Water Flooding (LSWF) is to improve oil recovery. While a significant number of laboratory tests have been carried out to investigate the impact of LSWF, field scale modelling is often reported in the form of sector models with relatively coarse cells. This paper assesses the impact of simulating flow at very fine scales and informs on the properties that should be captured at the coarse scale to avoid numerical errors. We have found that the weighting function that is used to control changes to fluid mobility combines with numerical and physical diffusion to induce a retardation/acceleration effect. This is a physical effect rather than part of a chemical reaction. In this study, numerous simulations of LSWF have been carried out at the reservoir scale to investigate flow behaviour for various salt concentration (salinity) weighting functions and dispersion coefficients. We have examined the effective salinity range over which the weighting function is applied as well as considering various shapes. Dispersion was varied to represent physical and numerical effects. These have been compared to analytical solutions from fractional flow theory. We also observed that the fractional flow of the oil bank will be same for both the secondary and tertiary flooding. We point out the relative importance of various parts of the relative permeability curves. An important finding of this work is that by spreading the salinity front through dispersion and setting a low value at which salinity impacts mobility, we saw the injected low salinity front advance more slowly while the high salinity front of formation water moves more quickly. This is an effective retardation effect. We related this to an effect equivalent to adsorption in the fractional flow theory and could measure it in a similar way. We were also able to develop a prediction of the effect using the analytical solution to the advection-diffusion equation. The outcome is that we can estimate a corrective term for the flow behaviour in situations where the dispersion is quite strong, particularly in numerical simulations. We consider that this enable corrections to be made for numerical dispersion effects in field scale models.

Relative permeability of multiphase flow through porous media plays a vital role in the petroleum industry, especially in enhanced oil recovery (EOR) processes. In this study, models were developed based on a combination of Least-Square Support Vector Machine and Couple Simulated Annealing (CSA-LSSVM) algorithm to predict oil-water relative permeability in sandstone and carbonate porous media. Comparing the model to thousands of experimental data resulted in overall squared correlation coefficients (R2) of 0.9866 and 0.9965, and minimum squared errors (MSEs) of 0.0014 and 0.000143 for Kro and Krw, respectively. In addition, Model predictions were found to agree excellently with experimental data. The results of CSA-LSSVM model were compared with some of the well-known mathematical equations including the Purcell, Burdine, Brooks and Corey, Corey, and some empirical correlations for predicting the oil-water relative permeability in a heterogeneous carbonate core sample. The models developed in this study outperform the mathematical equations and empirical correlations yielding an overall squared correlation coefficients of 0.9987 and 0.9994, and minimum squared errors of 0.0003 and 0.0049 for Kro and Krw, respectively. Finally, leverage value was introduced to analyze the whole dataset from which 19 points were diagnosed as possible outlier experimental data.

Digital Rock Physics (DRP) is a field that makes use of recent advances in imaging technology and computational methods to determine several rock properties by running numerical simulations on 3D rock images. In this work, DRP tools were used in a novel multi-scale approach that combined micro and macro computations to determine permeability for comparison with lab experiments of 2 different samples at 2 different sizes; 0.5 inch diameter and the standard 1.5 inch diameter. The Lattice Boltzmann Method (LBM) was used to perform micro-scale computations on subvolumes of images at high-resolution images. This was done to determine the permeability, and extract porosity-permeability trends. Then, a macro-scale computational grid was set to have porosity and permeability values from the micro-scale simulations in order to compute the upscaled effective permeability which could then be compared to experimental results. The workflow was first applied to a standard Silurian Dolomite to validate it and then applied to a carbonate sample from an Abu Dhabi reservoir that exhibited a higher level of heterogeneity.

Asphaltene deposition in surface facilities, wellbore and near wellbore region poses a chronic problem during oil production processes. It reduces permeability significantly by blocking pore throats as well as wettability alteration toward oil-wet. In this study, near wellbore damage due to asphaltene deposition is addressed. A numerical approach has been followed to investigate the impacts of asphaltene deposition in near wellbore region using an Iranian crude oil sample. An IMPEC (Implicit Pressure and Explicit Compositions) compositional simulator has been developed in cylindrical coordinates. Three mechanisms of asphaltene damage including porosity reduction, permeability reduction and wettability alteration are taken into account, and the impact of each mechanism is individually discerned. It is assumed precipitated asphaltene is a pure dense liquid and it is determined by LLE calculation using PR-EoS. The reduction in permeability is correlated with porosity reduction using a power law relation. To model wettability alteration, instantaneous wettability dependent properties (relative permeability, capillary pressure and residual saturations) are determined by a weight averaging between before/after deposition state. By assuming porous media is a bundle of capillary tubes, a weight factor is suggested which is sensitive to asphaltene particle size and their orientation on the surface and calculated dynamically during the simulation. Furthermore, sensitivity analysis is done to investigate the effect of model parameters. It is found that the wettability alteration is the main cause for the reduced production rate. Wettability alteration could reduce oil production even up to several times more than porosity and permeability reduction. The results also reveal that at early time of production, most deposition occurs in the vicinity of the well but as time elapses, the maximum deposition point expands gradually to farther areas from the wellbore.

This paper provides an integrated approach to simulate gas-water relative permeability in nanoscale porous media with interfacial effects using fractal theory. The calculation results with present model considering the interfacial effects match the laboratory results very well. The characteristics of relative permeability were analyzed under different values of Hydrogen bond ( ∏ h ), Double layer repulsive force ( ∏ e ), Long-range van der Waals force ( ∏ w ) and Short-range structure repulsive force ( ∏ s ). The result shows that the interfacial effects can promote the fluid flow in the nanoporous media and the relationship is as follows: ∏ h > ∏ e > ∏ w > ∏ s . ∏ h and ∏ e improve spreading obviously, which are accounted for more than 70%.Then the ∏ w affects spreading accounts for 1/5 nearly. In addition, the analysis of fractal dimension on relative permeability is carried out to indicate that the gas-water relative permeability decreases with the increase of the fractal dimension. While the capillary force has impact on relative permeability slightly. The new insight and theoretical basis could be obtained for CO2 geological storage and shale gas extraction from nanoscale porous media.

The combination of low salinity water with gas in the form of water alternating CO2 injection (CO2-LSWAG) is a promising EOR method that could simultaneously benefit from gas mobility control and also rock wettability alteration to more water-wet as consequence of geochemical interaction between rock and reservoir fluids. This paper aims to investigate the EOR potential of CO2-LSWAG under miscible conditions in a sandstone oil reservoir by coupling fluid flow and geochemical modeling. The wettability alteration of the rock surface was described by a series of relevant geochemical reactions between rock and low salinity water in a compositional simulator. The concept of ion equivalent fraction was used as the wettability index during CO2-LSWAG injection. It consists mainly of the effects of ion exchange and clay properties on oil-water relative permeability functions. Also, the effect of calcite mineral dissolution was studied as result of interaction with low salinity water and CO2 gas using relevant geochemical reactions. Results showed that salinity difference between injected and formation water triggers ion exchange processes between water and rock. Also, the rate of calcite dissolution increased due to the CO2 partitioning into the aqueous phase. The calcite dissolution caused the increase of calcium ions in the reservoir leading to more water-wet condition. However, results indicated that the rate of calcite dissolution decreased far from the injection well most likely due to reduced interaction time between low salinity water with dissolved CO2 and the reservoir rock. The oil recovery results showed that CO2-LSWAG is capable of producing incremental oil as much as 10% of the initial oil in place on top of high salinity CO2-WAG. The results of this numerical study support the potential application of CO2-LSWAG as an efficient EOR method in sandstone reservoirs.

The rate of gas production from coal seam gas reservoirs is highly dependent on coal lithotype, cleat attributes and multiphase flow in cleats. In this paper, we explore and categorize the wettability, roughness data, sorption capacity, and the flow in bright and dull coal lithotypes. The roughness measured on the wall surface of coal fractures indicates different values for each lithotype. Multiphase flow through rough-walled fractures is measured and the pressure variation and relative permeability data are compared for samples from bright and dull bands. Finally, microfluidic experiments are conducted to visualize and analyze the flow in the bright and dull bands. A flow scenario is investigated in which gas is transported through coal regions that have parallel and adjacent lithotypes. It is visualized that the production from these regions can be 53% less than the production from dull band regions. Herein, the impact of coal lithotypes properties on displacement efficiency in coal seams is discussed.

An experimental study was conducted to investigate two-phase and three-phase relative permeability behavior in a multi-phase flow, which involved a typical Canadian bitumen. A series of isothermal core flood experiments were conducted on an unconsolidated core composed of cleaned Athabasca sand matrix and relative permeabilities of the involved phases were determined. Drainage and imbibition processes for two-phase water/oil flow and oil saturation reversal in a three-phase oil/water/gas flow, which is encountered in a typical air injection process were examined. A history matching technique was used to determine relative permeabilities for two-phase water/oil and gas/liquid systems. A strong hysteresis was observed in both wetting phase and nonwetting phase relative permeabilities. The endpoint relative permeability of oil was higher than the end-point relative permeability of water by two orders of magnitude in two-phase water/oil experiments. Similar end-point relative permeability ratio was observed in two-phase liquid/gas experiments. Using the determined relative permeabilities for two-phase flows, Stone's first and second model and Baker's interpolation model were used to predict the fluid production in the three-phase flow. Despite showing a satisfactory prediction for liquid production, all models showed a significant deviation for produced gas at the early stages of the three-phase flow experiment.

Hydraulic fracturing is a method of reservoir stimulation that enhances the effective permeability of tight unconventional reservoirs such as shale oil and gas. In typical hydraulic fracturing treatments, millions of gallons of water are pumped under pressure into rock formations deep below the earth's surface. Proppant particles such as sand are injected as part of the fracturing slurry to hold the hydraulic fractures open, or propped, after high-pressure water injection has ceased. Propped hydraulic fractures provide a conduit for long-term hydrocarbon production, thus being essential to commercial oil and gas production from shale reservoirs. The distribution of the proppant particles can be useful in understanding effectiveness of hydraulic fracturing treatments. It can also help identify both, unstimulated and under-stimulated zones within the reservoirs of interest. These proppant particles can be found in drilling fluid return or in cores, which can be sampled from subsurface. In this study, we highlight the design and development of artificial neural network based workflow that helps identify where proppant particles are located and classifies proppant and various particles of interest. In this study, these particles are limited to naturally occurring calcite or other minerals from subsurface rocks. Various features of interest that help with the classification process have been conceptualized and defined. This method has been verified using controlled test cases and validated using actual samples from subsurface. The designed ANN classifier has also been benchmarked with other classification methods including k-nearest neighbor, naive-Bayes classifiers and Support vector machines. A workflow to process samples from subsurface and quantify proppant distribution for future test programs including potential real time applications has been proposed. Based on this workflow, we share proppant distribution from a Permian Basin case study. We have also compared proppant distribution using our proposed method with results from an independent workflow on a similar dataset, which does not utilize machine learning.

Ensemble data assimilation methods are among the most successful techniques for assisted history matching. However, these methods suffer from sampling errors caused by the limited number of ensemble members employed in practical applications. A typical consequence of sampling errors is an excessive loss of ensemble variance. In practice, the posterior ensemble tends to underestimate the uncertainty range in the parameter values and production predictions. Distance-based localization is the standard method for mitigating sampling errors in ensemble data assimilation. A properly designed localization matrix works remarkably well to improve the estimate of gridblock properties such as porosity and permeability. However, field history-matching problems also include non-local model parameters, i.e., parameters with no spatial location. Examples of non-local parameters include relative permeability curves, fluid contacts, global property multipliers, among others. In these cases, we cannot use distance-based localization. This paper presents an investigation on several methods proposed in the literature that can be applied to non-local model parameters to mitigate erroneous loss of ensemble variance. We use a small synthetic history-matching problem to evaluate the performance of the methods. For this problem, we were able to compute a reference solution with a very large ensemble. We compare the methods mainly in terms of the preservation of the ensemble variance without compromising the ability of matching the observed data. We also analyse the robustness and difficulty to select proper configurations for each method.

Foam mobility in porous media is governed by bubble texture, foam trapping, bubble generation, and bubble coalescence. Published reports showed that foam mobility is dominated by foam trapping in the transient flow regime or low capillary pressures (Pc), while bubble coalescence dominates foam flow in the steady state regime or higher Pc. An efficient foam model is expected to capture all these pore scale phenomena. However, most of the available models do not adequately account for foam trapping behavior because their model parameters are usually determined from coreflood experiments at steady state flow regimes. Hence, they are unsuitable for simulating transient foam flow behavior. Some mechanistic population balance models incorporate the effect of foam trapping on gas mobility through the relative permeability (Kr) function such that the Kr of the flowing foam is a function of only the flowing foam saturation. However, a constitutive equation is required to predict the flowing foam fraction. Some of the variables in this equation are also obtained from experimental data at steady state, while there is no known experimental method to measure other variables. In this paper, a novel coreflood method is presented that allows flowing foam fraction to be measured directly at different Pc and water saturations during foam flow. A consolidated porous medium was treated like a bundle of capillaries of various sizes, by modifying the surfactant alternating gas (SAG) method of foam injection. An electrical resistivity tool monitored in-situ saturation changes while a high resolution pressure transducer measured the pressure drop across rock samples. Multiple SAG cycles generated a data array of trapped and flowing foam as a function of water saturation and capillary pressure, which was then used to generate Pc and Kr curves. The Pc and Kr curves exhibit behavior that are consistent with established physics of foam flow in porous media. The measured Pc curves also compared well with porous plate Pc measurements, which thus validates the accuracy of the methodology in treating a consolidated porous medium as a bundle of capillaries. The measured foam limiting capillary pressure values also showed a good trend with those reported in the literature. The critical water saturation for foam was much higher than the connate water saturation measured from the porous plate method. Finally, it was shown that this method has a strong potential to be implemented at a field scale.

Gas-condensate flow around the wellbore is quite different from conventional gas oil flow. This is mainly due to complicated velocity effects on relative permeability in these very low interfacial tension systems. In the current study, it has been proposed that the desirable velocity effect on gas-condensate relative permeability is the result of inertial force. Having said that, inertial number, which is the ratio of inertial force over capillary force, could be a better candidate compared to capillary number when somebody deals with the modeling of gas-condensate relative permeability. A generalized correlation was obtained for gas-condensate relative permeability with applying this new approach. The results are promising. This approach is not only needs less core data, but also it is much simpler and even more accurate compared to previously developed equations using capillary number.

In the present study, spontaneous imbibition experiments, steady-state permeability measurements, and numerical simulation were integrated to quantify the changes in the effective water permeability, capillary pressure, and water relative permeability curves due to the polymer adsorption of the spontaneously imbibed fracturing fluid. The effect of the nonionic surfactant and core bedding plane on the fluid spontaneous imbibition volumes were also investigated. The researchers considered the impact of the spontaneous imbibition of a friction reducer fluid in tight sand and shale core samples. Three comparative systematic spontaneous imbibition experiments were conducted for each of the core samples using brine, anionic friction reducer fluid, and brine again. The core sample water permeability before and after the imbibition experiment was measured using a constant rate steady-state permeability apparatus. The polymer adsorption from the spontaneously imbibed fracturing fluid significantly reduced the brine spontaneous imbibition volumes in tight sand samples and in shale samples, though to a lesser degree. Moreover, the effective water permeability was decreased because of the polymer adsorption effect. Therefore, the polymer adsorption during hydraulic fracturing reduces the fluid leak-off into the formation and also the fluid flowback. The nonionic surfactant increased the fluid spontaneous imbibition volumes in both tight sand and shale samples. Thus, adding a nonionic surfactant to the friction reducer pad fluid during hydraulic fracturing leads to enhance both of the fluid leak-off and fluid flowback. The results also showed that the effect of polymer adsorption on the imbibition rates is less when the rock-fluid contact surface is parallel to the bedding plane. The imbibition potentials and imbibition capillary pressure curves were calculated before and after polymer adsorption. The polymer adsorption led to a slight increase in the capillary pressure; moreover, the tight sand samples had higher capillary pressure than the shale samples. The imbibition water relative permeability curves were calculated using ECLIPSE commercial simulator. The polymer adsorption significantly reduces the water relative permeability curves for tight sand samples and in less degree for shale samples.

This paper presents a new three-phase relative permeability model for use in chemical flooding simulators. Numerical simulation test cases are presented to illustrate the continuity of the new relative permeability model. Comparisons are made with a three-phase relative permeability model that has been widely used in chemical flooding simulators for decades. These comparisons show the old model has numerical discontinuities that are not physical in nature and that can lead to oscillations in the numerical simulations. The proposed model is simpler, has fewer parameters and requires less experimental data to determine the relative permeability parameters compared to the original model. Simulations using the new model showed excellent agreement with ASP coreflood data.

Most modern production data type curve (PDTC) techniques, which are used in the estimation of reservoir and well productivity parameters such as permeability, drainage radius and skin, were originally developed with the assumption of Darcy flow (i.e. laminar flow, with pressure gradient proportional to the fluid superficial velocity, in accordance with Darcy's law) of a single-phase fluid. Two-phase conditions, e.g. in a gas condensate reservoir (GCR) operating below dewpoint pressure, introduce nonlinearities into the diffusivity equation, making the use of single-phase techniques questionable, and potentially producing erroneous parameter estimates. A common approach to linearizing the system is by the use of pseudovariables which account for the two-phase effects in addition to the pressure-dependence of fluid properties. In this study, GCR production data generated using homogeneous fine-grid compositional simulation models, were first analysed using a well-known conventional (single-phase) modern PDTC technique, namely the Blasingame type curves for radial flow around a vertical well in a circular drainage area. The conventional techniques were then modified using an equivalent single phase concept, which was employed in the computation of two-phase pseudovariables for use with the single-phase PDTC. To compute these two-phase pseudovariables, pressure-saturation/kr relationships are required. These were determined using a technique, which employs fluid component weight fractions and gas fractional flow of a fluid with constant fixed total composition. Sensitivities were conducted on reservoir fluid richness (maximum liquid dropout from 1% to 42%), relative permeability curves, degree of reservoir undersaturation and well operating pressures, to examine their impact on production decline response and subsequent conventional PDTC analysis, as well as their impact on the effectiveness of the equivalent single-phase based approach used in this study. The paper first highlights the impact of two-phase flow conditions in GCRs on conventional PDTC analysis, in terms of the quality of the type curve match (TCM) and estimates of permeability, drainage radius and skin. Then it is shown that, in GCR analysis where the impact of two-phase effects are important, significant improvements can be obtained, both in the quality of the TCM and subsequent parameter estimates, through the use of pseudovariables computed using equivalent single phase concepts. The results also identify conditions under which, depending on the fluid richness and/or the degree of undersaturation, two-phase effects, although present, may not significantly impact the quality of interpretation of long-term production data from GCRs, using conventional single-phase PDTC techniques.

Multiphase seepage characteristics are vital factors for improving the recovery efficiency of natural gas hydrate (NGH) via stepwise depressurization. However, the difficulties to experimentally construct real and natural hydrate-bearing sediments in a laboratory hinder the study of the association between multiphase seepage and the development of NGH. In this study, an optimized simulation model based on the features of fine shaly silt sediment in the Shenhu area of the South China Sea is proposed to analyze the influence of seepage characteristics on hydrate exploitation induced by stepwise depressurization. Multiple perspectives, including the intrinsic permeability, gas and water relative permeability, porosity, and permeability anisotropy of the reservoir are regarded as sensitive parameters of the hydrate production. The exploitation economy of fine hydrate-bearing sediment was evaluated by introducing the Ste number, gas-water ratio (GWR), and sensitivity analysis. The results demonstrate that the contribution of sensible heat to hydrate exploitation in reservoirs with poor seepage characteristics is limited; the effects of the abovementioned parameters on the GWR are different; porosity and gas relative permeability are the most important factors that affect hydrate production. Thus, detailed geological examination should be performed to ensure the exploitation economy. This study provides a profound theoretical basis for the stepwise depressurization strategy design of NGH exploitation in the field.

Hydraulic fracturing is an effective means for the economic development of shale oil reservoirs. A large volume of water is introduced into the shale matrix during hydraulic fracturing, which leads to the subsequent oil-water two-phase flow in the shale reservoir. The fluid flow behaviors in shale are still ambiguous due to the nonnegligible nanoconfinement effect caused by the omnipresent nanoscale pores and the heterogeneities of mineral types, pore size and wettability of shale. In this study, both the single-phase and oil-water two-phase flow behaviors at pore-scale considering nanoconfinement effects, dual-wettability and pore space characteristic of shale reservoir were investigated using the pore network modeling (PNM) method. We constructed the three-dimension shale digital rock based on scanning electron microscope (SEM) images and extracted the pore network model. The modified single nanotube flow equations considering the adsorption and slip effects were incorporated with the shale pore network model to investigate the single-phase flow at different volumetric total organic content (TOC). Oil-water two-phase flow and relative permeability at different TOC in volume were computed by quasi-static method with consideration of nanoconfinement effect. Results indicated that the TOC and wettability are the primary factors affecting the single-phase flow in shale. Slip effect enhanced the flow capacities of both single-phase water and oil. The wettability effect on two-phase relative permeability curve was not as notable as that on single-phase flow. Oil-water two-phase relative permeability curves were significantly affected by TOC. The two-phase flow region narrows down with the increase of volume TOC, indicating more oil is trapped and thus cannot be displaced. This work provided important insights on pore-scale fluid transport behaviors in shale.

The productivity model with unilateral threshold pressure gradient, real gas effect or non-Darcy effect has been documented in the research of tight gas reservoir. However, the multiple seepage mechanisms are poorly addressed in a productivity model, especially the application of gas-water relative permeability curve changing with the displacement pressure. A novel productivity model of multi-stage fractured horizontal wells with mechanisms of multiple seepage was proposed the present study. Results show that the stress effect has a negative effect on the effective permeability, while the Knudsen diffusion effect of gas has a positive effect. The water flow can inhibit the gas flow in the tight gas reservoir, whose effect is more significant with larger displacement pressure differences. The higher initial water saturation and reservoir temperature, whereas the lower gas well productivity, contribute to a high gas well productivity in the reservoir of high pressure.

In the water-based EOR methods, surfactants and smart water injection methods usually are employed to reduce the water-oil interfacial tension and altered the rock wettability, respectively. The main objective of this study is to employ the combination effects of non-ionic Surfactants (including KEPS 80 and Behamid D) and Smart water Flooding to alter the wettability and interfacial tension (IFT) towards the most favorable conditions. Contact angle, spontaneous imbibition, capillary pressure (Pc), and relative permeability (kr) experiments were performed at various concentrations of the surfactants and ions using carbonate rock to identify the various mechanisms occurring in the Surfactant and Smart water (SSW) flooding process and also to determine the additional oil recovery. The optimum concentrations of surfactant and positive ions (Mg2+, Ca2+) were also obtained. In this regard, concentrations of the employed ions were optimized for altering the carbonate rock surface wettability toward the water-wet. The optimum surfactant concentrations obtained by Mohammadshahi et al. (2019) were also used, in this study. After obtaining the optimum concentrations, some promising aqueous solutions were designed for Amott cell, relative permeability, and capillary pressure experiments using the combination of surfactant and ions. Amott cell tests were implemented for comparing the ability of different aqueous solutions such as base water (Brine with 30,000 ppm NaCl), surfactant solution, smart water, and SSW solution in the oil recovery from the cores. Subsequently, relative permeability and capillary pressure experiments were performed. The results of contact angle experiments depicted that brine containing 24,000 ppm NaCl +6000 ppm Mg2+ yielded the lowest contact angle among the studied samples. In the spontaneous imbibition tests, the oil recovery was obtained to be 7.6% for the base water, 9.5% for the smart water (24,000 ppm NaCl + 6000 ppm Mg), 15.09% for the surfactant solution (1500 ppm KEPE in 30,000 NaCl), and 20.8% for the SSF water. The relative permeability and capillary pressure tests have demonstrated the change of residual oil saturation and wettability of rock while using the SSW method compared to other techniques (i.e. base water, surfactant injection, smart water flooding). Finally, the results indicated that the combination of smart water and surfactant injection could lead to a much higher recovery factor than each method alone.

The relative permeability of immiscible multi-phase flow in Layered 2D porous media is investigated employing the diffuse interface Lattice Boltzmann model. The interfacial tension is set to small value to mimic the near miscible condition of the fluids. The model is validated with static and dynamic analytical solutions. Three classes of porous media are examined: A high permeable porous media, a low permeable porous media, and layered dual permeable porous media. For the later case, parallel and serie conditions were considered. For each condition, three proportion of layers were studied; 1–25% of the high permeable layer, 2–50% of the high permeable layer, and 3–75% of high permeable layer. For each condition, the viscous coupling effects due to viscosity ratio, the capillary number and the effect of the fluid patterns on the relative permeability curves were investigated. The simulation results showed very small errors compare with the analytical permeability solutions of layered porous media. The findings showed that despite the dual permeable serie system, the relative permeability curve of dual permeable parallel geometry is closely matched with the analytical solution.

Determination of representative saturation functions for permeable reservoir sandstones requires consideration of mm-cm scale laminations and crossbedding common in these heterogeneous porous media. Modelling selected laminated sandstones from CO2CRC's Otway International Test Centre in Victoria, Australia as bimodal composites of different rock types, we analyse drainage relative permeability parallel and perpendicular to the laminae for a range of driving gradients. The results from these numeric drainage experiments are curve fit across a continuous range of flow rates between the capillary and viscous limits. Our analysis shows that laminae-related small, but spatially correlated grainsize and permeability variations give rise to flow-rate dependent drainage behaviour at the bed scale. The flow direction- and rate-dependent behaviour is captured by a new set of anisotropic extended saturation functions that are implemented and presented in a form that is suitable for compositional simulation in the system CO2–H2O–NaCl. For the first time, these new constitutive relationships permit an investigation of feedbacks between the reservoir-scale flow regime and bed-scale phase mobility. To illustrate the application of these functions in reservoir simulation, meter-scale plume spreading simulations are presented for a suite of ten homogenised fluvial-to-estuarine sandstones from the Otway facility.

The accuracy of relative permeability and mobility data can strongly impact the uncertainty in predictions of production in reservoir models. It is of particular importance to identify the most practical conditions to perform relative permeability tests in order to mimic the difference between test and subsurface conditions. It is known that the details of a displacement test, such as capillary number, can immensely impact the characteristics of a displacement. Therefore, it is paramount to perform displacement tests representative of the reservoir conditions. To improve the general understanding and design of displacement tests this work presents an exploration of displacement parameters and their impact on results. A multiphase Lattice Boltzmann Method is used to digitally perform displacement tests for a range of relevant conditions. Direct simulations are performed on 3D models of pore spaces built from microCT images of rock. A parameter space consisting of capillary number, wetting condition, viscosity ratio and driving mechanism is explored on multiple sandstone rock images. Results showing the impact multiple displacement properties have on relative permeability and mobility are presented. Particular attention was paid to the role of capillary number on total mobility. A wide range of capillary numbers (1 × 10−7 to 1 × 10−4) was investigated. It was observed that a quantification of mobility, the minimum total mobility of both fluids, is largely constant for the lower most range of capillary numbers for a specific rock image. This plateau behavior holds when capillary number is below a critical threshold where capillary forces fully dominate the 2-phase flow topology. Above this threshold mobility increases monotonically with capillary number. The study also presents relationships for various wetting conditions, viscosity ratios and driving mechanisms. When using an alternate definition of capillary number which relates velocity and fluid properties at the point of minimum total mobility, broad similarity in mobility data was observed for the various viscosity ratios and driving mechanisms investigated. In contrast, the minimum total mobility was consistently higher for oil-wet displacements when compared to equivalent water-wet displacements.