Water removal from porous media by gas injection: experiments and simulation

The flow of a saturated gas through a porous medium, partially occupied by a liquid phase, causes evaporation due to gas expansion. This process, referred to as flow-through drying, is important in a wide variety of natural and industrial applications, such as natural gas production, convective drying of paper, catalysts, fuel cells and membranes. X-ray imaging experiments were performed to study the flow-through drying of water-saturated porous media during gas injection. The results show that the liquid saturation profile and the rate of drying are dependent on the viscous pressure drop, the state of saturation of the gas and the capillary characteristics of the porous medium. During the injection of a completely saturated gas, drying occurs only due to gas expansion. Capillary-driven flow from regions of high saturation to regions of low saturation lead to more uniform saturation profiles. During the injection of a dry gas, a drying front develops at the inlet and propagates through the porous medium. The experimental results are compared with numerical results from a continuum model. A good agreement is found for the case of sandstone. The comparison is less satisfactory for the experiments with limestone.     

Matrix–Fracture Transfer through Countercurrent Imbibition in Presence of Fracture Fluid Flow

Although a lot of research has been done in modeling the oil recovery from fractured reservoirs by countercurrent imbibition, less attention has been paid to the effect of the fracture fluid velocity upon the rate of oil recovery. Experiments are conducted to determine the effect of fracture flow rate upon countercurrent imbibition. A droplet detachment model is proposed to derive the effective water saturation in a thin boundary layer at the matrix–fracture interface. This effective boundary water saturation is a function of fluid properties, fluid velocity in the fracture and fracture width. For a highly water–wet porous medium, this model predicts an increase in the boundary water saturation with increase in fracture fluid velocity. The increase in boundary water saturation, in turn, increases the oil recovery rate from the matrix, which is consistent with the experimental results. The model also predicts that the oil recovery rate does not vary linearly with the boundary water saturation.     

How to predict viscous fingering in three component flow

In a WAG process (Water Alternate Gas), water and a miscible solvent (gas) are injected into a reservoir containing water and oil. The solvent will finger through the oil, leading to early breakthrough and poor recovery. Compared with a miscible flood, when only solvent is injected, fingering is supressed by the simultaneous injection of water, since this reduces the apparent mobility contrast between the injected and displaced fluids. The fingering in a miscible flood, with only hydrocarbon flowing, can be modelled successfully using a Todd and Longstaff fractional flow. In this paper, we demonstrate how to modify the effective Todd and Longstaff mobility ratio self-consistently to account for fingering in three component systems. The resultant empirical equations of flow are solved exactly in one dimension and are in excellent agreement with the averaged saturation and concentration profiles computed using two dimensional high resolution simulation, for a variety of injected water saturations, in both secondary and tertiary displacements.     

EM Heating-Stimulated Water Flooding for Medium–Heavy Oil Recovery

We report a study of heavy oil recovery by combined water flooding and electromagnetic (EM) heating at a frequency of 2.45 GHz used in domestic microwave ovens. A mathematical model describing this process was developed. Model equations were solved, and the solution is presented in an integral form for the one-dimensional case. Experiments consisting of water injection into Bentheimer sandstone cores, either fully water saturated or containing a model heavy oil, were also conducted, with and without EM heating. Model prediction was found to be in rather good agreement with experiments. EM energy was efficiently absorbed by water and, under dynamic conditions, was transported deep into the porous medium. The amount of EM energy absorbed increases with water saturation. Oil recovery by water flooding combined with EM heating was up to \(37.0\%\) larger than for cold water flooding. These observations indicate that EM heating induces an overall improvement in the mobility ratio between the displacing water and the displaced heavy oil.     

Two-phase jet flows in porous media

An analytical model describing the development of the filtration instability of the displacement front of fluids with different viscosities in a porous medium with account for capillary forces is proposed. A set of laboratory experiments on viscous fluid displacement from a porous medium is carried out. To describe the observable flows the model deals with the characteristic profile of the mean water saturation along the flow rather than with the curves of relative phase permeabilities of the fluids. The analytical model developed well describes the results of the laboratory modeling and the data of an actual oil field operation.     

Simultaneous Estimation of Relative Permeability and Capillary Pressure Using Ensemble-Based History Matching Techniques

An ensemble-based technique has been developed and successfully applied to simultaneously estimate the relative permeability and capillary pressure by history matching the observed production profile. Relative permeability and capillary pressure curves are represented by using a power-law model. Then, forward simulation is performed with the initial coefficients of the power-law model, all of which are to be tuned automatically and finally determined once the observed data is assimilated completely and history matched. The newly developed technique has been validated by a synthetic coreflooding experiment with two scenarios. The endpoints are fixed for the first scenario, whereas they are completely free in the second scenario. Simultaneous estimation of relative permeability and capillary pressure has been found to improve gradually as more observation data is assimilated. There exists an excellent agreement between both the updated relative permeability and capillary pressure and their corresponding reference values, once the discrepancy between the simulated and observed production history has been minimized. Compared with coefficients of capillary pressure curve, coefficients of relative permeability curves, irreducible water saturation and residual oil saturation are found to be more sensitive to the observed data. In addition, water relative permeability is more sensitive to the observation data than either oil relative permeability or capillary pressure. It is shown from its application to a laboratory coreflooding experiment that relative permeability and capillary pressure curves can be simultaneously evaluated once all of the experimental measurements are assimilated and history matched.     

Three-Phase Flow Modelling Using Pore-Scale Capillary Pressures and Relative Permeabilities for Mixed-Wet Media at the Continuum-Scale

When regions of three-phase flow arise in an oil reservoir, each of the flow parameters, i.e. capillary pressures and relative permeabilities, are generally functions of two phase saturations and depend on the wettability state. The idea of this work is to generate consistent pore-scale based three-phase capillary pressures and relative permeabilities. These are then used as input to a 1-D continuum core- or reservoir-scale simulator. The pore-scale model comprises a bundle of cylindrical capillary tubes, which has a distribution of radii and a prescribed wettability state. Contrary to a full pore-network model, the bundle model allows us to obtain the flow functions for the saturations produced at the continuum-scale iteratively. Hence, the complex dependencies of relative permeability and capillary pressure on saturation are directly taken care of. Simulations of gas injection are performed for different initial water and oil saturations, with and without capillary pressures, to demonstrate how the wettability state, incorporated in the pore-scale based flow functions, affects the continuum-scale displacement patterns and saturation profiles. In general, wettability has a major impact on the displacements, even when capillary pressure is suppressed. Moreover, displacement paths produced at the pore-scale and at the continuum-scale models are similar, but they never completely coincide.     

1D Simulations for Microbial Enhanced Oil Recovery with Metabolite Partitioning

We have developed a mathematical model describing the process of microbial enhanced oil recovery (MEOR). The one-dimensional isothermal model comprises displacement of oil by water containing bacteria and substrate for their feeding. The bacterial products are both bacteria and metabolites. In the context of MEOR modeling, a novel approach is partitioning of metabolites between the oil and the water phases. The partitioning is determined by a distribution coefficient. The transfer part of the metabolite to oil phase is equivalent to its ”disappearance,” so that the total effect from of metabolite in the water phase is reduced. The metabolite produced is surfactant reducing oil–water interfacial tension, which results in oil mobilization. The reduction of interfacial tension is implemented through relative permeability curve modifications primarily by lowering residual oil saturation. The characteristics for the water phase saturation profiles and the oil recovery curves are elucidated. However, the effect from the surfactant is not necessarily restricted to influence only interfacial tension, but it can also be an approach for changing, e.g., wettability. The distribution coefficient determines the time lag, until residual oil mobilization is initialized. It has also been found that the final recovery depends on the distance from the inlet before the surfactant effect takes place. The surfactant effect position is sensitive to changes in maximum growth rate, and injection concentrations of bacteria and substrate, thus determining the final recovery. Different methods for incorporating surfactant-induced reduction of interfacial tension into models are investigated. We have suggested one method, where several parameters can be estimated in order to obtain a better fit with experimental data. For all the methods, the incremental recovery is very similar, only coming from small differences in water phase saturation profiles. Overall, a significant incremental oil recovery can be achieved, when the sensitive parameters in the context of MEOR are carefully dealt with.     

Two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection

This paper examines the two-phase flow for a horizontal well penetrating a naturally fractured reservoir with edge water injection by means of a fixed streamline model. The mathematical model of the vertical two-dimensional flow or oil-water for a horizontal well in a medium with double-porosity is established, and whose accurate solutions are obtained by using the characteristic method. The saturation distributions in the fractured system and the matrix system as well as the formula of the time of water free production are presented. All these results provide a theoretical basis and a computing method for oil displacement by edge water from naturally fractured reservoirs.     

An investigation of hydraulic fracturing. Part II: two-phase flow model

In the previous work presented in Part I (Theoret. Appl. Fracture Mech. 18, 89–102 (1993)), hydraulic fracture in an infinitely large saturated porous medium is analyzed under an assumption of one-phase flow in the medium. The investigation is extended in this paper to the case of a two phase saturated immiscible flow of oil and water in the porous medium. The medium is initially saturated with oil. Flow in the medium is induced by diffusion of water injected into the fracture. The quasi-static growth of the fracture for a prescribed injection rate is analyzed based on the assumptions that the pressure in the fracture is uniform and that the permeating flow in the medium is unidirectional. The constant fracture toughness criterion for plane strain deformation is employed and the effect of capillary pressure is neglected. Empirical formulas are used for the permeabilities of the oil and water phases. It is seen that the distributions of water saturation and pore pressure in the medium are governed by two nonlinear partial differential equations. Numerical solutions are obtained by a finite difference scheme with iterations. It is found that the injected water is restricted within a layer near the surface of the fracture whose thickness is small compared with the length of the fracture. Thus the flow in the medium is governed essentially by the oil phase. To compare our problem with the corresponding problem of one-phase flow, we find that the difference in crack growth in these two problems is small for the ration of kinematic viscosities of the oil and water phases within the practical range. Hence our study confirms the validity of the one phase flow assumption used in the previous work for prediction of hydraulic fracture growth.     

Characterizing the Role of Shale Geometry and Connate Water Saturation on Performance of Polymer Flooding in Heavy Oil Reservoirs: Experimental Observations and Numerical Simulations

Many heavy oil reservoirs contain discontinuous shales which act as barriers or baffles to flow. However, there is a lack of fundamental understanding about how the shale geometrical characteristics affect the reservoir performance, especially during polymer flooding of heavy oils. In this study, a series of polymer injection processes have been performed on five-spot glass micromodels with different shale geometrical characteristics that are initially saturated with the heavy oil. The available geological characteristics from one of the Iranian oilfields were considered for the construction of the flow patterns by using a controlled-laser technology. Oil recoveries as a function of pore volumes of injected fluid were determined from analysis of continuously recorded images during the experiments. We observed a clear bypassing of displacing fluid which results in premature breakthrough of injected fluid due to the shale streaks. Moreover, the results showed a decrease of oil recovery when shales’ orientation, length, spacing, distance of the shale from production well, and density of shales increased. In contrast, an increase of shale discontinuity or distance of the shale streak from the injection well increased oil recovery. The obtained experimental data have also been used for developing and validating a numerical model where good matching performance has been observed between our experimental observations and simulation results. Finally, the role of connate water saturation during polymer flooding in systems containing flow barriers has been illustrated using pore level visualizations. The microscopic observations confirmed that besides the effect of shale streaks as heterogeneity in porous medium, when connate water is present, the trapped water demonstrates another source of disturbance and causes additional perturbations to the displacement interface leading to more irregular fingering patterns especially behind the shale streaks and also causes a reduction of ultimate oil recovery. This study reveals the application of glass micromodel experiments for studying the effects of barriers on oil recovery and flow patterns during EOR processes and also may provide a set of benchmark data for recovery of oil by immiscible polymer flood around discontinuous shales.     

TWO－PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

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Dynamic Relative Permeability and Simulation of WAG Injection Processes

In this work, we investigate the impact of mobility changes due to flow reversals from co-current to counter-current flow on the displacement performance of water alternating gas (WAG) injection processes. In WAG processes, the injected gas will migrate toward the top of the formation while the injected water will migrate toward the bottom of the formation. The segregation of gas, oil and water phases will result in counter-current flow occurring in the vertical direction in some portions of the reservoir during the displacement process. Previous experimental and theoretical studies of counter-current flow have shown that the relative mobility of each of the phases in a porous medium is considerably less when counter-current flow prevails as compared to co-current flow settings. A reduction of the relative permeability in the vertical direction results in a dynamic anisotropy in phase mobilities. This effect has, to the best of our knowledge, not previously been considered in the modeling and simulation of WAG processes. A new flow model that accounts for flow reversals in the vertical direction has been implemented and tested in a three-phase compositional reservoir simulator. In order to investigate the impact of flow reversals, results from the new flow model are compared to cases where counter-current flow effects on the phase mobilities are ignored. A range of displacement settings, covering relevant slug sizes, have been investigated to gauge the impact of mobility reductions due to flow reversals. Significant differences, in terms of saturation distribution, producing GOR and oil recovery, are observed between the conventional flow model (ignoring mobility reductions due to counter-current flow) and the proposed new model that accounts for reductions in phase mobility during counter-current flow. Accordingly, we recommend that an explicit representation of flow transitions between co-current and counter-current flow (and the related impact on phase mobilities) should be considered to ensure accurate and optimal design of WAG injection processes.     

A theoretical model for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe

A theoretical model has been developed for core-annular flow of a very viscous oil core and a water annulus through a horizontal pipe. Special attention was paid to understanding how the buoyancy force on the core, resulting from any density difference between the oil and water, is counterbalanced. This problem was simplified by assuming the oil viscosity to be so high that any flow inside the core may be neglected and hence that there is no variation of the profile of the oil-water interface with time. In the model the core is assumed to be solid and the interface to be a solid/liquid interface.By means of the hydrodynamic lubrication theory it has been shown that the ripples on the interface moving with respect to the pipe wall can generate pressure variations in the annular layer. These result in a force acting perpendicularly on the core, which can counterbalance the buoyancy effect.To check the validity of the model, oil-water core-annular flow experiments have been carried out in a 5.08 cm and an 20.32-cm pipeline. Pressure drops measured have been compared with those calculated with the aid of the model. The agreement is satisfactory.     

A Dynamic Network Model for Two-Phase Flow in Porous Media

We present a dynamic model of immiscible two-phase flow in a network representation of a porous medium. The model is based on the governing equations describing two-phase flow in porous media, and can handle both drainage, imbibition, and steady-state displacement. Dynamic wetting layers in corners of the pore space are incorporated, with focus on modeling resistivity measurements on saturated rocks at different capillary numbers. The flow simulations are performed on a realistic network of a sandpack which is perfectly water-wet. Our numerical results show saturation profiles for imbibition in agreement with experiments. For free spontaneous imbibition we find that the imbibition rate follows the Washburn relation, i.e., the water saturation increases proportionally to the square root of time. We also reproduce rate effects in the resistivity index for drainage and imbibition.     

TWO－PHASE FLOW FOR A HORIZONTAL WELL PENETRATING A NATURALLY FRACTURED RESERVOIR WITH EDGE WATER INJECTION

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Multiphase flow with a simplified model for oil entrapment

A computationally simple procedure is described to model effects of oil entrapment on three-phase permeability-saturation-capillary pressure relations. The model requires knowledge of airwater saturation-capillary pressure relations, which are assumed to be nonhysteretic and are characterized by Van Genuchten's parametric model; scaling factors equal to the ratio of water surface tension to oil surface tension and to oil-water interfacial tension; and the maximum oil (also referred to as nonwetting liquid in a three-phase medium) saturation which would occur following water flooding of oil saturated soil. Trapped nonwetting liquid saturation is predicted as a function of present oil-water and air-oil capillary pressures and minimum historical water saturation since the occurrence of oil at a given location using an empirically-based algorithm. Oil relative permeability is predicted as a simple function of apparent water saturation (sum of actual water saturation and trapped oil saturation) and free oil saturation (difference between total oil and trapped oil saturation), and water relative permeability is treated as a unique function of actual water saturation. The proposed method was implemented in a two-dimensional finite-element simulator for three-phase flow and component transport, MOFAT. The fluid entrapment model requires minimal additional computational effort and computer storage and is numerically robust. The applicability of the model is illustrated by a number of hypothetical one- and two-dimensional simulations involving infiltration and redistribution with changes in water-table elevations. Results of the simulations indicate that the fraction of a hydrocarbon spill that becomes trapped under given boundary conditions increases as a nonlinear function of the maximum trapped nonwetting liquid saturation. Dense organic liquid plumes may exhibit more pronounced effects of entrapment due to the more dynamic nature of flow, even under static water table conditions. Disregarding nonwetting fluid entrapment may lead to significant errors in predictions of immiscible plume migration.     

Relative Permeability Analysis of Tube Bundle Models,Including Capillary Pressure

The analytical equations for calculating two-phase flow, including local capillary pressures, are developed for the bundle of parallel capillary tubes model. The flow equations that are derived were used to calculate dynamic immiscible displacements of oil by water under the constraint of a constant overall pressure drop across the tube bundle. Expressions for averaged fluid pressure gradients and total flow rates are developed, and relative permeabilities are calculated directly from the two-phase form of Darcy's law. The effects of pressure drop and viscosity ratio on the relative permeabilities are discussed. Capillary pressure as a function of water saturation was delineated for several cases and compared to a steady-state mercury-injection drainage type of capillary pressure profile. The bundle of serial tubes model (a model containing tubes whose diameters change randomly at periodic intervals along the direction of flow), including local Young-Laplace capillary pressures, was analyzed with respect to obtaining relative permeabilities and macroscopic capillary pressures. Relative permeabilities for the bundle of parallel tubes model were seen to be significantly affected by altering the overall pressure drop and the viscosity ratio; relative permeabilities for the bundle of serial tubes were seen to be relatively insensitive to viscosity ratio and pressure, and were consistently X-like in profile. This work also considers the standard Leverett (1941) type of capillary pressure versus saturation profile, where drainage of a wetting phase is completed in a step-wise steady fashion; it was delineated for both tube bundle models. Although the expected increase in capillary pressure at low wetting-phase saturation was produced, comparison of the primary-drainage capillary pressure curves with the pseudo-capillary pressure profiles, that are computed directly using the averaged pressures during the displacements, revealed inconsistencies between the two definitions of capillary pressure.