Improved Prediction of Oil Recovery From Waterflooded Fractured Reservoirs Using Homogenization

2009 ◽  
Vol 13 (01) ◽  
pp. 44-55 ◽  
Author(s):  
Hamidreza Salimi ◽  
Johannes Bruining
Keyword(s):  
Travel Time ◽  
Oil Recovery ◽  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Fractured Media ◽  
Rate Dependent ◽  
Matrix Block ◽  
The Matrix ◽  
Order Of Magnitude ◽  
Time Required

Summary Most simulations of waterflooding in fractured media are based on the Warren and Root (WR) approach, which uses an empirical transfer function between the fracture and matrix block. We use homogenization to obtain an improved flow model in fractured media, leading to an integro-differential equation; also called the boundary-condition (BC) approach. We formulate a well-posed numerical 3D model for the BC approach. This paper derives this numerical model to solve full 3D integro-differential equations in a field reservoir simulation. We compare the results of the upscaled model with ECLIPSETM results. For the interpretation, it is useful to define three dimensionless parameters that characterize the oil production in fractured media. The most important of these parameters is a Peclet number, defined as the ratio between the time required to imbibe water into the matrix block and the travel time of water in the fracture system. The results of the WR approach and the BC approach are in good agreement when the travel time is of the same order of magnitude as the imbibition time. However, if the travel time is shorter or longer than the imbibition time, the approaches give different results. The BC approach allows the use of transfer functions based on fundamental principles (e.g., the use of a rate-dependent capillary pressure function). When implemented, it can be used to improve recovery predictions for waterflooded fractured reservoirs.

A Critical Review for Proper Use of Water/Oil/Gas Transfer Functions in Dual-Porosity Naturally Fractured Reservoirs: Part I

2009 ◽  
Vol 12 (02) ◽  
pp. 200-210 ◽  
Author(s):  
Benjamin Ramirez ◽  
Hossein Kazemi ◽  
Mohammed Al-kobaisi ◽  
Erdal Ozkan ◽  
Safian Atan
Keyword(s):  
Mass Transfer ◽  
Oil Recovery ◽  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Gas Injection ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fine Grid ◽  
Matrix Block ◽  
The Matrix

Summary Accurate calculation of multiphase-fluid transfer between the fracture and matrix in naturally fractured reservoirs is a crucial issue. In this paper, we will present the viability of the use of simple transfer functions to account accurately for fluid exchange resulting from capillary, gravity, and diffusion mass transfer for immiscible flow between fracture and matrix in dual-porosity numerical models. The transfer functions are designed for sugar-cube or match-stick idealizations of matrix blocks. The study relies on numerical experiments involving fine-grid simulation of oil recovery from a typical matrix block by water or gas in an adjacent fracture. The fine-grid results for water/oil and gas/oil systems were compared with results obtained with transfer functions. In both water and gas injection, the simulations emphasize the interaction of capillary and gravity forces to produce oil, depending on the wettability of the matrix. In gas injection, the thermodynamic phase equilibrium, aided by gravity/capillary interaction and, to a lesser extent, by molecular diffusion, is a major contributor to interphase mass transfer. For miscible flow, the fracture/matrix mass transfer is less complicated because there are no capillary forces associated with solvent and oil; nevertheless, gravity contrast between solvent in the fracture and oil in the matrix creates convective mass transfer and drainage of oil. Using the transfer functions presented in this paper, fracture- and matrix-flow calculations can be decoupled and solved sequentially--reducing the complexity of the computation. Furthermore, the transfer-function equations can be used independently to calculate oil recovery from a matrix block.

Verification and Proper Use of Water-Oil Transfer Function for Dual-Porosity and Dual-Permeability Reservoirs

2009 ◽  
Vol 12 (02) ◽  
pp. 189-199 ◽  
Author(s):  
Adetayo S. Balogun ◽  
Hossein Kazemi ◽  
Erdal Ozkan ◽  
Mohammed Al-kobaisi ◽  
Benjamin Ramirez
Keyword(s):  
Transfer Function ◽  
Oil Recovery ◽  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Fracture Network ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fluid Exchange ◽  
Matrix Block ◽  
Naturally Fractured

Summary Accurate calculation of multiphase fluid transfer between the fracture and matrix in naturally fractured reservoirs is a very crucial issue. In this paper, we will present the viability of the use of a simple transfer function to accurately account for fluid exchange resulting from capillary and gravity forces between fracture and matrix in dual-porosity and dual-permeability numerical models. With this approach, fracture- and matrix-flow calculations can be decoupled and solved sequentially, improving the speed and ease of computation. In fact, the transfer-function equations can be used easily to calculate the expected oil recovery from a matrix block of any dimension without the use of a simulator or oil-recovery correlations. The study was accomplished by conducting a 3-D fine-grid simulation of a typical matrix block and comparing the results with those obtained through the use of a single-node simple transfer function for a water-oil system. This study was similar to a previous study (Alkandari 2002) we had conducted for a 1D gas-oil system. The transfer functions of this paper are specifically for the sugar-cube idealization of a matrix block, which can be extended to simulation of a match-stick idealization in reservoir modeling. The basic data required are: matrix capillary-pressure curves, densities of the flowing fluids, and matrix block dimensions. Introduction Naturally fractured reservoirs contain a significant amount of the known petroleum hydrocarbons worldwide and, hence, are an important source of energy fuels. However, the oil recovery from these reservoirs has been rather low. For example, the Circle Ridge Field in Wind River Reservation, Wyoming, has been producing for 50 years, but the oil recovery is less than 15% (Golder Associates 2004). This low level of oil recovery points to the need for accurate reservoir characterization, realistic geological modeling, and accurate flow simulation of naturally fractured reservoirs to determine the locations of bypassed oil. Reservoir simulation is the most practical method of studying flow problems in porous media when dealing with heterogeneity and the simultaneous flow of different fluids. In modeling fractured systems, a dual-porosity or dual-permeability concept typically is used to idealize the reservoir on the global scale. In the dual-porosity concept, fluids transfer between the matrix and fractures in the grid-cells while flowing through the fracture network to the wellbore. Furthermore, the bulk of the fluids are stored in the matrix. On the other hand, in the dual-permeability concept, fluids flow through the fracture network and between matrix blocks. In both the dual-porosity and dual-permeability formulations, the fractures and matrices are linked by transfer functions. The transfer functions account for fluid exchanges between both media. To understand the details of this fluid exchange, an elaborate method is used in this study to model flow in a single matrix block with fractures as boundaries. Our goal is to develop a technique to produce accurate results for use in large-scale modeling work.

scholarly journals Simulation of counter-current imbibition in water-wet fractured reservoirs based on discrete-fracture model

Open Physics ◽  
2017 ◽  
Vol 15 (1) ◽  
pp. 536-543
Author(s):  
Yueying Wang ◽  
Jun Yao ◽  
Shuaishi Fu ◽  
Aimin Lv ◽  
Zhixue Sun ◽  
...  
Keyword(s):  
Mixed Finite Element ◽  
Fractured Reservoirs ◽  
Mixed Finite Element Method ◽  
Fractured Media ◽  
Fracture Model ◽  
Discrete Fracture Model ◽  
Matrix Block ◽  
Discrete Fracture ◽  
The Matrix ◽  
Counter Current

AbstractIsolated fractures usually exist in fractured media systems, where the capillary pressure in the fracture is lower than that of the matrix, causing the discrepancy in oil recoveries between fractured and non-fractured porous media. Experiments, analytical solutions and conventional simulation methods based on the continuum model approach are incompetent or insufficient in describing media containing isolated fractures. In this paper, the simulation of the counter-current imbibition in fractured media is based on the discrete-fracture model (DFM). The interlocking or arrangement of matrix and fracture system within the model resembles the traditional discrete fracture network model and the hybrid-mixed-finite-element method is employed to solve the associated equations. The Behbahani experimental data validates our simulation solution for consistency. The simulation results of the fractured media show that the isolated-fractures affect the imbibition in the matrix block. Moreover, the isolated fracture parameters such as fracture length and fracture location influence the trend of the recovery curves. Thus, the counter-current imbibition behavior of media with isolated fractures can be predicted using this method based on the discrete-fracture model.

Coupled Effect of Imbibition Capillary Pressure and Matrix-Fracture Transfer on Oil Recovery from Dual-Permeability Reservoirs

2021 ◽  
Author(s):  
Aymen AlRamadhan ◽  
Yildiray Cinar ◽  
Arshad Hussain ◽  
Nader BuKhamseen
Keyword(s):  
Capillary Pressure ◽  
Oil Recovery ◽  
Reservoir Simulation ◽  
Shape Factor ◽  
Numerical Study ◽  
Fractured Reservoirs ◽  
Matrix Block ◽  
Matrix Fracture ◽  
The Matrix ◽  
The Impact

Abstract This paper presents a numerical study to examine how the interplay between the matrix imbibition capillary pressure (Pci) and matrix-fracture transfer affects oil recovery from naturally-fractured reservoirs under waterflooding. We use a dual-porosity, dual-permeability (DPDP) finite difference simulator to investigate the impact of uncertainties in Pci on the waterflood recovery behavior and matrix-fracture transfer. A comprehensive assessment of the factors that control the matrix-fracture transfer, namely Pci, gravity forces, shape factor and fracture-matrix permeabilities is presented. We examine how the use of Pci curves in reservoir simulation can affect the recovery assessment. We present two conceptual scenarios to demonstrate the impact of spontaneous and forced imbibition on the flood-front movement, waterflood recovery processes, and ultimate recovery in the DPDP reservoir systems of varying reservoir quality. The results demonstrate that the inclusion of Pci in reservoir simulation delays the breakthrough time due to a higher displacement efficiency. The study reveals that the matrix-fracture transfer is mainly controlled by the fracture surface area, fracture permeability, shape factor, and the uncertainty in Pci. We underline a discrepancy among various shape factors proposed in the literature due to three main factors: (1) the variations in matrix-block geometries considered, (2) how the physics of imbibition forces that control the multiphase fluid transfer is captured, and (3) how the assumption of pseudo steady-state flow is addressed.

Low-IFT Foaming System for Enhanced Oil Recovery in Highly Heterogeneous/Fractured Oil-Wet Carbonate Reservoirs

SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2243-2259 ◽  
Author(s):  
Pengfei Dong ◽  
Maura Puerto ◽  
Guoqing Jian ◽  
Kun Ma ◽  
Khalid Mateen ◽  
...  
Keyword(s):  
Oil Recovery ◽  
Fractured Reservoirs ◽  
Surfactant Solution ◽  
Capillary Forces ◽  
Mobility Control ◽  
Carbonate Reservoirs ◽  
Residual Oil ◽  
High Permeability ◽  
The Matrix ◽  
Foam Flooding

Summary Oil recovery in heterogeneous carbonate reservoirs is typically inefficient because of the presence of high-permeability fracture networks and unfavorable capillary forces within the oil-wet matrix. Foam, as a mobility-control agent, has been proposed to mitigate the effect of reservoir heterogeneity by diverting injected fluids from the high-permeability fractured zones into the low-permeability unswept rock matrix, hence improving the sweep efficiency. This paper describes the use of a low-interfacial-tension (low-IFT) foaming formulation to improve oil recovery in highly heterogeneous/fractured oil-wet carbonate reservoirs. This formulation provides both mobility control and oil/water IFT reduction to overcome the unfavorable capillary forces preventing invading fluids from entering an oil-filled matrix. Thus, as expected, the combination of mobility control and low-IFT significantly improves oil recovery compared with either foam or surfactant flooding. A three-component surfactant formulation was tailored using phase-behavior tests with seawater and crude oil from a targeted reservoir. The optimized formulation simultaneously can generate IFT of 10−2 mN/m and strong foam in porous media when oil is present. Foam flooding was investigated in a representative fractured core system, in which a well-defined fracture was created by splitting the core lengthwise and precisely controlling the fracture aperture by applying a specific confining pressure. The foam-flooding experiments reveal that, in an oil-wet fractured Edward Brown dolomite, our low-IFT foaming formulation recovers approximately 72% original oil in place (OOIP), whereas waterflooding recovers only less than 2% OOIP; moreover, the residual oil saturation in the matrix was lowered by more than 20% compared with a foaming formulation lacking a low-IFT property. Coreflood results also indicate that the low-IFT foam diverts primarily the aqueous surfactant solution into the matrix because of (1) mobility reduction caused by foam in the fracture, (2) significantly lower capillary entry pressure for surfactant solution compared with gas, and (3) increasing the water relative permeability in the matrix by decreasing the residual oil. The selective diversion effect of this low-IFT foaming system effectively recovers the trapped oil, which cannot be recovered with single surfactant or high-IFT foaming formulations applied to highly heterogeneous or fractured reservoirs.

Visualization and Analysis of Surfactant Imbibition Into Oil-Wet Fractured Cores

SPE Journal ◽  
2016 ◽  
Vol 21 (01) ◽  
pp. 101-111 ◽  
Author(s):  
Mohammad Mirzaei ◽  
David A. DiCarlo ◽  
Gary A. Pope
Keyword(s):  
Oil Recovery ◽  
Fractured Reservoirs ◽  
Surfactant Solution ◽  
Ct Scanning ◽  
Recovery Curves ◽  
The Core ◽  
The Matrix ◽  
Insight Into ◽  
Scaling Group ◽  
Better Than

Summary Imbibition of surfactant solution into the oil-wet matrix in fractured reservoirs is a complicated process that involves gravity, capillary, viscous, and diffusive forces. The standard experiment for testing imbibition of surfactant solution involves an imbibition cell, in which the core is placed in the surfactant solution and the recovery is measured vs. time. Although these experiments prove the effectiveness of surfactants, little insight into the physics of the problem is achieved. In this study, we performed water and surfactant flooding into oil-wet fractured cores and monitored the imbibition of the surfactant solution by use of computed-tomography (CT) scanning. From the CT images, the surfactant-imbibition dynamics as a function of height along the core was obtained. Although the waterflood only displaced oil from the fracture, the surfactant solution imbibed into the matrix; the imbibition is frontal, with the greatest imbibition rate at the bottom of the core, and the imbibition decreases roughly linearly with height. Experiments with cores of different sizes showed that increase in either the height or the diameter of the core causes decrease in imbibition and fractional oil-recovery rate. We also perform numerical simulations to model the observed imbibition. On the basis of the experimental measurements and numerical-simulation results, we propose a new scaling group that includes both the diameter and the height of the core. We show that the new scaling groups scale the recovery curves better than the traditional scaling group.

Matrix Refinement in Mass Transport Across Fracture-Matrix Interface: Application to Improved Oil Recovery in Fractured Reservoirs

2021 ◽  
Author(s):  
Sarah Abdullatif Alruwayi ◽  
Ozan Uzun ◽  
Hossein Kazemi
Keyword(s):  
Fractured Reservoirs ◽  
Block Size ◽  
Grid Cell ◽  
Matrix Interface ◽  
Unsteady State ◽  
Matrix Block ◽  
Matrix Blocks ◽  
The Matrix ◽  
Saturation Distribution ◽  
State Pressure

Abstract In this paper, we will show that it is highly beneficial to model dual-porosity reservoirs using matrix refinement (similar to the multiple interacting continua, MINC, of Preuss, 1985) for water displacing oil. Two practical situations are considered. The first is the effect of matrix refinement on the unsteady-state pressure solution, and the second situation is modeling water-oil, Buckley-Leverett (BL) displacement in waterflooding a fracture-dominated flow domain. The usefulness of matrix refinement will be illustrated using a three-node refinement of individual matrix blocks. Furthermore, this model was modified to account for matrix block size variability within each grid cell (in other words, statistical distribution of matrix size within each grid cell) using a discrete matrix-block-size distribution function. The paper will include two mathematical models, one unsteady-state pressure solution of the pressure diffusivity equation for use in rate transient analysis, and a second model, the Buckley-Leverett model to track saturation changes both in the reservoir fractures and within individual matrix blocks. To illustrate the effect of matrix heterogeneity on modeling results, we used three matrix bock sizes within each computation grid and one level of grid refinement for the individual matrix blocks. A critical issue in dual-porosity modeling is that much of the fluid interactions occur at the fracture-matrix interface. Therefore, refining the matrix block helps capture a more accurate transport of the fluid in-and-out of the matrix blocks. Our numerical results indicate that the none-refined matrix models provide only a poor approximation to saturation distribution within individual matrices. In other words, the saturation distribution is numerically dispersed; that is, no matrix refinement causes unwarranted large numerical dispersion in saturation distribution. Furthermore, matrix block size-distribution is more representative of fractured reservoirs.

Multirate-Transfer Dual-Porosity Modeling of Gravity Drainage and Imbibition

SPE Journal ◽  
2007 ◽  
Vol 12 (01) ◽  
pp. 77-88 ◽  
Author(s):  
Ginevra Di Donato ◽  
Huiyun Lu ◽  
Zohreh Tavassoli ◽  
Martin Julian Blunt
Keyword(s):  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Transport Equations ◽  
Oil Field ◽  
Dual Porosity ◽  
Gravity Drainage ◽  
Stagnant Region ◽  
Dual Porosity Model ◽  
The Matrix ◽  
Porosity Model

Summary We develop a physically motivated approach to modeling displacement processes in fractured reservoirs. To find matrix/fracture transfer functions in a dual-porosity model, we use analytical expressions for the average recovery as a function of time for gas gravity drainage and countercurrent imbibition. For capillary-controlled displacement, the recovery tends to its ultimate value with an approximately exponential decay (Barenblatt et al. 1990). When gravity dominates, the approach to ultimate recovery is slower and varies as a power law with time (Hagoort 1980). We apply transfer functions based on these expressions for core-scale recovery in field-scale simulation. To account for heterogeneity in wettability, matrix permeability, and fracture geometry within a single gridblock, we propose a multirate model (Ponting 2004). We allow the matrix to be composed of a series of separate domains in communication with different fracture sets with different rate constants in the transfer function. We use this methodology to simulate recovery in a Chinese oil field to assess the efficiency of different injection processes. We use a streamline-based formulation that elegantly allows the transfer between fracture and matrix to be accommodated as source terms in the 1D transport equations along streamlines that capture the flow in the fractures (Di Donato et al. 2003; Di Donato and Blunt 2004; Huang et al. 2004). This approach contrasts with the current Darcy-like formulation for fracture/matrix transfer based on a shape factor (Gilman and Kazemi 1983) that may not give the correct average behavior (Di Donato et al. 2003; Di Donato and Blunt 2004; Huang et al. 2004). Furthermore, we show that recovery is exceptionally sensitive to parameters that describe the physics of the displacement process, highlighting the need to make careful core-scale measurements of recovery. Introduction Di Donato et al.(2003) and Di Donato and Blunt (2004) proposed a dual-porosity streamline-based model for simulating flow in fractured reservoirs. Conceptually, the reservoir is composed of two domains: a flowing region with high permeability that represents the fracture network and a stagnant region with low permeability that represents the matrix (Barenblatt et al. 1960; Warren and Root 1963). The streamlines capture flow in the flowing regions, while transfer from fracture to matrix is accommodated as source/sink terms in the transport equations along streamlines. Di Donato et al. (2003) applied this methodology to study capillary-controlled transfer between fracture and matrix and demonstrated that using streamlines allowed multimillion-cell models to be run using standard computing resources. They showed that the run time could be orders of magnitude smaller than equivalent conventional grid-based simulation (Huang et al. 2004). This streamline approach has been applied by other authors (Al-Huthali and Datta-Gupta 2004) who have extended the method to include gravitational effects, gas displacement, and dual-permeability simulation, where there is also flow in the matrix. Thiele et al. (2004) have described a commercial implementation of a streamline dual-porosity model based on the work of Di Donato et al. that efficiently solves the 1D transport equations along streamlines.

Bivariate Log-Normal Distribution of Stimulated Matrix Permeability and Block Size in Fractured Reservoirs: Proposing New Multilinear-Flow Regime for Transient-State Production

SPE Journal ◽  
2018 ◽  
Vol 23 (04) ◽  
pp. 1316-1342 ◽  
Author(s):  
Salam Al-Rbeawi
Keyword(s):  
Normal Distribution ◽  
Flow Regime ◽  
Fractured Reservoirs ◽  
Block Size ◽  
Analytical Models ◽  
Matrix Permeability ◽  
Matrix Block ◽  
The Matrix ◽  
Log Normal ◽  
Log Normal Distribution

Summary This paper investigates the impacts of varied stimulated matrix permeability and matrix-block size on pressure behaviors and flow regimes of hydraulically fractured reservoirs using bivariate log-normal distribution. The main objective is assembling the variance in these two parameters to the analytical models of pressure and pressure derivative considering different porous-media petrophysical properties, reservoir configurations, and hydraulic-fracture (HF) characteristics. The motivation is eliminating the long-run discretization treatment in the porous media required by applying analytical models to describe the variance in the previously discussed parameters with the distance between HFs. Several analytical models for pressure response were generated in this study for hydraulically fractured reservoirs with rectangular-shaped drainage areas. These models take into account the change in stimulated matrix permeability from the maximum value close to the HF face to the minimum value at the so-called no-flow boundary between fractures. They also consider the change in the matrix-block size, corresponding to the change in the induced-fracture density (number of fractures per foot of length), from the minimum value close to the fracture face to the maximum value at the no-flow boundary. Bivariate log-normal distribution was used to describe the change in the stimulated matrix permeability and matrix-block size. The formations of interest are composed of stimulated reservoir volume (SRV), where the matrix is stimulated by the fracturing process, and unstimulated reservoir volume (USRV), where the stimulation process does not affect the matrix. The outcomes of this study can be summarized as Generating new analytical models for pressure and pressure derivative in hydraulically fractured reservoirs that consider the change in stimulated matrix-block size and permeability using bivariate log-normal distribution Understanding the effect of using the probability-density function (PDF) of matrix-block size and permeability in the pressure distribution of different reservoirs Observing the new multilinear-flow regime that develops at intermediate production time and represents several simultaneous linear-flow regimes inside HFs, SRV, and USRV Developing analytical models for the new multilinear-flow regime Studying the effects of petrophysical properties of HFs, induced fractures, and matrix as well as reservoir size and configuration on pressure behavior The most interesting points in this study are The applicability of bivariate log-normal distribution for describing the variance and nonuniform distribution of matrix-block size and permeability. The large variance in the matrix-block size and permeability causes significant decrease in wellbore-pressure drop. Small value of standard deviation of matrix-block size and permeability indicates the possibilities for significant decrease in wellbore pressure drop. The means of matrix-block size and permeability may not have significant effects on reservoir-pressure distribution. The new multilinear-flow regime is characterized by a one-eighth slope on the pressure-derivative curve and is seen always after HF linear flow and before boundary-dominated flow regime. Multilinear-flow regime develops to bilinear-flow regime with a one-quarter slope for uniform distribution of equal matrix-block size and permeability.

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