Investigations of Matrix-Fracture Transfer Flows in Dual Porosity Modeling of Naturally Fractured Reservoirs

1995 ◽  
Author(s):  
Jianping Chen ◽  
Mark A. Miller ◽  
Kamy Sepehrnoori
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Matrix Fracture ◽  
Naturally Fractured

New Transfer Functions for Simulation of Naturally Fractured Reservoirs with Dual Porosity Models

SPE Journal ◽  
2006 ◽  
Vol 11 (03) ◽  
pp. 328-340 ◽  
Author(s):  
Pallav Sarma ◽  
Khalid Aziz
Keyword(s):  
Transfer Function ◽  
Multiphase Flow ◽  
Shape Factor ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fine Grid ◽  
Pressure Diffusion ◽  
Matrix Fracture ◽  
Naturally Fractured

Summary This paper discusses new techniques for the modeling and simulation of naturally fractured reservoirs with dual-porosity models. Most of the existing dual-porosity models idealize matrix-fracture interaction by assuming orthogonal fracture systems (parallelepiped matrix blocks) and pseudo-steady state flow. More importantly, a direct generalization of single-phase flow equations is used to model multiphase flow, which can lead to significant inaccuracies in multiphase flow-behavior predictions. In this work, many of these existing limitations are removed in order to arrive at a transfer function more representative of real reservoirs. Firstly, combining the differential form of the single-phase transfer function with analytical solutions of the pressure-diffusion equation, an analytical form for a shape factor for transient pressure diffusion is derived to corroborate its time dependence. Further, a pseudosteady shape factor for rhombic fracture systems is also derived and its effect on matrix-fracture mass transfer demonstrated. Finally, a general numerical technique to calculate the shape factor for any arbitrary shape of the matrix block (i.e., nonorthogonal fractures) is proposed. This technique also accounts for both transient and pseudosteady-state pressure behavior. The results were verified against fine-grid single-porosity models and were found to be in excellent agreement. Secondly, it is shown that the current form of the transfer function used in reservoir simulators does not fully account for the main mechanisms governing multiphase flow. A complete definition of the differential form of the transfer function for two-phase flow is derived and combined with the governing equations for pressure and saturation diffusion to arrive at a modified form of the transfer function for two-phase flow. The new transfer function accurately takes into account pressure diffusion (fluid expansion) and saturation diffusion (imbibition), which are the two main mechanisms driving multiphase matrix-fracture mass transfer. New shape factors for saturation diffusion are defined. It is shown that the prediction of wetting-phase imbibition using the current form of the transfer function can be quite inaccurate, which might have significant consequences from the perspective of reservoir management. Fine-grid single-porosity models are used to verify the validity of the new transfer function. The results from single-block dual-porosity models and the corresponding single-porosity fine-grid models were in good agreement. Introduction A naturally fractured reservoir (NFR) can be defined as a reservoir that contains a connected network of fractures (planar discontinuities) created by natural processes such as diastrophism and volume shrinkage (Ordonez et al. 2001). Fractured petroleum reservoirs represent over 20% of the world's oil and gas reserves (Saidi 1983), but are, however, among the most complicated class of reservoirs. A typical example is the Circle Ridge fractured reservoir located on the Wind River Reservation in Wyoming, U.S.. This reservoir has been in production for more than 50 years but the total oil recovery until now has been less than 15% (www.fracturedreservoirs.com 2000). It is undeniable that reservoir characterization, modeling, and simulation of naturally fractured reservoirs present unique challenges that differentiate them from conventional, single-porosity reservoirs. Not only do the intrinsic characteristics of the fractures, as well as the matrix, have to be characterized, but the interaction between matrix blocks and surrounding fractures must also be modeled accurately. Further, most of the major NFRs have active aquifers associated with them, or would eventually be subjected to some kind of secondary recovery process such as waterflooding (German 2002), implying that it is essential to have a good understanding of the physics of multiphase flow for such reservoirs. This complexity of naturally fractured reservoirs necessitates the need for their accurate representation from a modeling and simulation perspective, such that production and recovery from such reservoirs be predicted and optimized.

A Fully Implicit, Compositional, Parallel Simulator for IOR Processes in Fractured Reservoirs

SPE Journal ◽  
2007 ◽  
Vol 12 (03) ◽  
pp. 367-381 ◽  
Author(s):  
Reza Naimi-Tajdar ◽  
Choongyong Han ◽  
Kamy Sepehrnoori ◽  
Todd James Arbogast ◽  
Mark A. Miller
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fractured Reservoir ◽  
Matrix Fracture ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
Dual Porosity Model ◽  
The Matrix ◽  
Porosity Model

Summary Naturally fractured reservoirs contain a significant amount of the world oil reserves. A number of these reservoirs contain several billion barrels of oil. Accurate and efficient reservoir simulation of naturally fractured reservoirs is one of the most important, challenging, and computationally intensive problems in reservoir engineering. Parallel reservoir simulators developed for naturally fractured reservoirs can effectively address the computational problem. A new accurate parallel simulator for large-scale naturally fractured reservoirs, capable of modeling fluid flow in both rock matrix and fractures, has been developed. The simulator is a parallel, 3D, fully implicit, equation-of-state compositional model that solves very large, sparse linear systems arising from discretization of the governing partial differential equations. A generalized dual-porosity model, the multiple-interacting-continua (MINC), has been implemented in this simulator. The matrix blocks are discretized into subgrids in both horizontal and vertical directions to offer a more accurate transient flow description in matrix blocks. We believe this implementation has led to a unique and powerful reservoir simulator that can be used by small and large oil producers to help them in the design and prediction of complex gas and waterflooding processes on their desktops or a cluster of computers. Some features of this simulator, such as modeling both gas and water processes and the ability of 2D matrix subgridding are not available in any commercial simulator to the best of our knowledge. The code was developed on a cluster of processors, which has proven to be a very efficient and convenient resource for developing parallel programs. The results were successfully verified against analytical solutions and commercial simulators (ECLIPSE and GEM). Excellent results were achieved for a variety of reservoir case studies. Applications of this model for several IOR processes (including gas and water injection) are demonstrated. Results from using the simulator on a cluster of processors are also presented. Excellent speedup ratios were obtained. Introduction The dual-porosity model is one of the most widely used conceptual models for simulating naturally fractured reservoirs. In the dual-porosity model, two types of porosity are present in a rock volume: fracture and matrix. Matrix blocks are surrounded by fractures and the system is visualized as a set of stacked volumes, representing matrix blocks separated by fractures (Fig. 1). There is no communication between matrix blocks in this model, and the fracture network is continuous. Matrix blocks do communicate with the fractures that surround them. A mass balance for each of the media yields two continuity equations that are connected by matrix-fracture transfer functions which characterize fluid flow between matrix blocks and fractures. The performance of dual-porosity simulators is largely determined by the accuracy of this transfer function. The dual-porosity continuum approach was first proposed by Barenblatt et al. (1960) for a single-phase system. Later, Warren and Root (1963) used this approach to develop a pressure-transient analysis method for naturally fractured reservoirs. Kazemi et al. (1976) extended the Warren and Root method to multiphase flow using a 2D, two-phase, black-oil formulation. The two equations were then linked by means of a matrix-fracture transfer function. Since the publication of Kazemi et al. (1976), the dual-porosity approach has been widely used in the industry to develop field-scale reservoir simulation models for naturally fractured reservoir performance (Thomas et al. 1983; Gilman and Kazemi 1983; Dean and Lo 1988; Beckner et al. 1988; Rossen and Shen 1989). In simulating a fractured reservoir, we are faced with the fact that matrix blocks may contain well over 90% of the total oil reserve. The primary problem of oil recovery from a fractured reservoir is essentially that of extracting oil from these matrix blocks. Therefore it is crucial to understand the mechanisms that take place in matrix blocks and to simulate these processes within their container as accurately as possible. Discretizing the matrix blocks into subgrids or subdomains is a very good solution to accurately take into account transient and spatially nonlinear flow behavior in the matrix blocks. The resulting finite-difference equations are solved along with the fracture equations to calculate matrix-fracture transfer flow. The way that matrix blocks are discretized varies in the proposed models, but the objective is to accurately model pressure and saturation gradients in the matrix blocks (Saidi 1975; Gilman and Kazemi 1983; Gilman 1986; Pruess and Narasimhan 1985; Wu and Pruess 1988; Chen et al. 1987; Douglas et al. 1989; Beckner et al. 1991; Aldejain 1999).

Pressure-Transient Tests and Flow Regimes in Fractured Reservoirs

2015 ◽  
Vol 18 (02) ◽  
pp. 187-204 ◽  
Author(s):  
Fikri Kuchuk ◽  
Denis Biryukov
Keyword(s):  
History Matching ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Hydraulic Fractures ◽  
Fractured Reservoir ◽  
Pressure Transient ◽  
Matrix Block ◽  
Naturally Fractured

Summary Fractures are common features in many well-known reservoirs. Naturally fractured reservoirs include fractured igneous, metamorphic, and sedimentary rocks (matrix). Faults in many naturally fractured carbonate reservoirs often have high-permeability zones, and are connected to numerous fractures that have varying conductivities. Furthermore, in many naturally fractured reservoirs, faults and fractures can be discrete (rather than connected-network dual-porosity systems). In this paper, we investigate the pressure-transient behavior of continuously and discretely naturally fractured reservoirs with semianalytical solutions. These fractured reservoirs can contain periodically or arbitrarily distributed finite- and/or infinite-conductivity fractures with different lengths and orientations. Unlike the single-derivative shape of the Warren and Root (1963) model, fractured reservoirs exhibit diverse pressure behaviors as well as more than 10 flow regimes. There are seven important factors that dominate the pressure-transient test as well as flow-regime behaviors of fractured reservoirs: (1) fractures intersect the wellbore parallel to its axis, with a dipping angle of 90° (vertical fractures), including hydraulic fractures; (2) fractures intersect the wellbore with dipping angles from 0° to less than 90°; (3) fractures are in the vicinity of the wellbore; (4) fractures have extremely high or low fracture and fault conductivities; (5) fractures have various sizes and distributions; (6) fractures have high and low matrix block permeabilities; and (7) fractures are damaged (skin zone) as a result of drilling and completion operations and fluids. All flow regimes associated with these factors are shown for a number of continuously and discretely fractured reservoirs with different well and fracture configurations. For a few cases, these flow regimes were compared with those from the field data. We performed history matching of the pressure-transient data generated from our discretely and continuously fractured reservoir models with the Warren and Root (1963) dual-porosity-type models, and it is shown that they yield incorrect reservoir parameters.

A Critical Review For Proper Use Of Water-Oil-Gas Transfer Functions In Dual-Porosity Naturally Fractured Reservoirs-Part II

2007 ◽  
Author(s):  
Mohammed Al-Kobaisi ◽  
Hossein Kazemi ◽  
Benjamin Alejandro Ramirez ◽  
Erdal Ozkan ◽  
Safian Atan
Keyword(s):  
Critical Review ◽  
Transfer Functions ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Gas Transfer ◽  
Naturally Fractured ◽  
Oil Gas

Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability

2015 ◽  
Vol 18 (04) ◽  
pp. 523-533 ◽  
Author(s):  
Shuhua Wang ◽  
Mingxu Ma ◽  
Wei Ding ◽  
Menglu Lin ◽  
Shengnan Chen
Keyword(s):  
Production Rate ◽  
Flow Rate ◽  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Dual Porosity ◽  
Fracture Permeability ◽  
Permeability Model ◽  
Pressure Behavior ◽  
Naturally Fractured ◽  
Permeability Modulus

Summary Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account. In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs. Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.

Sign in / Sign up

Export Citation Format

Share Document