Pressure Transient Analysis of Naturally Fractured Reservoirs with Uniform Fracture Distribution

1969 ◽  
Vol 9 (04) ◽  
pp. 451-462 ◽  
Author(s):  
H. Kazemi
Keyword(s):  
Fractured Reservoirs ◽  
Low Flow ◽  
Fractured Reservoir ◽  
Naturally Fractured Reservoir ◽  
Pressure Transient ◽  
Flow Capacity ◽  
Naturally Fractured ◽  
The Matrix ◽  
Fracture Distribution

Abstract An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. Introduction The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.).

Pressure Transient Analysis Methods for Bounded Naturally Fractured Reservoirs

1985 ◽  
Vol 25 (03) ◽  
pp. 451-464 ◽  
Author(s):  
Chih-Cheng Chen ◽  
Kelsen Serra ◽  
Albert C. Reynolds ◽  
Rajagopal Raghavan
Keyword(s):  
Flow Regime ◽  
Fractured Reservoirs ◽  
Flow Regimes ◽  
Fractured Reservoir ◽  
Pressure Data ◽  
Naturally Fractured Reservoir ◽  
State Flow ◽  
Wellbore Pressure ◽  
Naturally Fractured ◽  
The Matrix

Abstract New methods for analyzing drawdown and buildup pressure data obtained at a well located in an infinite, pressure data obtained at a well located in an infinite, naturally fractured reservoir were presented recently. In this work, the analysis of both drawdown and buildup data in a bounded, naturally fractured reservoir is considered. For the bounded case, we show that five possible flow regimes may be exhibited by drawdown data. We delineate the conditions under which each of these five flow regimes exists and the information that can be obtained from each possible combination of flow regimes. Conditions under which semilog methods can be used to analyze buildup data are discussed for the bounded fractured reservoir case. New Matthews-Brons-Hazebroek (MBH) functions for computing the average reservoir pressure from buildup data are presented. pressure from buildup data are presented. Introduction This work considers the analysis of pressure data obtained at a well located at the center of a cylindrical, bounded, naturally fractured reservoir of uniform thickness. As is typical, a naturally fractured reservoir indicates a reservoir system in which the conductive properties of the rock are mainly due to the fracture system, and the rock matrix provides most of the storage capacity of the system. Several models of naturally fractured reservoirs have been presented m the literature. Warren and Root and Odeh presented m the literature. Warren and Root and Odeh assume "pseudosteady-state flow" in the matrix, whereas Kazemi, deSwaan, Najurieta, and Kucuk and Sawyers assume unsteady-state flow. The model used in this study is identical to the one considered in Refs. 4, 5, 7, and 8; however, these works considered only infinite-acting reservoirs. To our knowledge, the behavior of wells in bounded, naturally fractured reservoirs with unsteady-state flow in the matrix system has not been examined until now. This work considers the analysis of constant-rate production and buildup pressure data in a bounded, naturally production and buildup pressure data in a bounded, naturally fractured reservoir. For a bounded reservoir, we show that there are five distinct, useful flow regimes that may be exhibited by drawdown data. Flow Regimes 1, 2, and 11 are identical to the flow regimes identified in Refs. 7 and 8. During each of these three flow regimes, a semilog plot of the dimensionless wellbore pressure drop vs. plot of the dimensionless wellbore pressure drop vs. dimensionless time exhibits a straight line. The information that can be obtained from the various possible combinations of Flow Regimes 1 through 3 is discussed in Refs. 7 and 8. Flow Regime 5 corresponds to pseudo-steady-state flow. Flow Regime 4 denotes a flow pseudo-steady-state flow. Flow Regime 4 denotes a flow period during which a Cartesian graph of the dimensionless period during which a Cartesian graph of the dimensionless wellbore pressure drop vs. the square root of dimensionless time will be a straight line. In this work, we first establish the conditions under which each of the flow regimes exists. In particular, we show that Flow Regime 3 does not exist unless either the drainage radius or the dimensionless fracture transfer coefficient is large. Second, we show that useful information can be obtained from drawdown pressure data that reflect Flow Regime 4. Third, we delineate conditions that ensure that the methods of Refs. 7, and 8 can be used to analyze buildup data. Finally, we present new MBH functions for computing the average reservoir pressure in a naturally fractured reservoir. Mathematical Model We consider laminar flow of a slightly compressible, single-phase fluid of constant viscosity in an isotropic, cylindrical, naturally fractured reservoir of uniform thickness. Gravitational forces are negligible. The top, bottom, and outer reservoir boundaries are closed. A well located at the center of the cylinder is produced at a constant rate and then shut in to obtain buildup data. Initially, the pressure is uniform throughout the reservoir. We assume that all production is by way of the fracture system and that we have one-dimensional (ID), unsteady-state flow in the matrix. The matrix structure consists of "rectangular slabs"; that is, the matrix is divided by a set of parallel horizontal fractures. A schematic of the reservoir geometry is shown in Fig. 1. We consider an infinitesimally thin skin and neglect wellbore storage effects. The properties of both the matrix and fracture systems are assumed to be constant. Thus, our current model is identical to the one considered in Ref. 7 except that here the reservoir is assumed to be bounded. Because of symmetry, the mathematical problem can be formulated by considering only the repetitive element of Fig. 1. SPEJ p. 451

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.

Unsteady-State Behavior of Naturally Fractured Reservoirs

1965 ◽  
Vol 5 (01) ◽  
pp. 60-66 ◽  
Author(s):  
A.S. Odeh
Keyword(s):  
Fractured Reservoirs ◽  
Naturally Fractured Reservoirs ◽  
Unsteady State ◽  
Fractured Reservoir ◽  
State Behavior ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix ◽  
Porosity And Permeability ◽  
Bulk Volume

Abstract A simplified model was employed to develop mathematically equations that describe the unsteady-state behavior of naturally fractured reservoirs. The analysis resulted in an equation of flow of radial symmetry whose solution, for the infinite case, is identical in form and function to that describing the unsteady-state behavior of homogeneous reservoirs. Accepting the assumed model, for all practical purposes one cannot distinguish between fractured and homogeneous reservoirs from pressure build-up and/or drawdown plots. Introduction The bulk of reservoir engineering research and techniques has been directed toward homogeneous reservoirs, whose physical characteristics, such as porosity and permeability, are considered, on the average, to be constant. However, many prolific reservoirs, especially in the Middle East, are naturally fractured. These reservoirs consist of two distinct elements, namely fractures and matrix, each of which contains its characteristic porosity and permeability. Because of this, the extension of conventional methods of reservoir engineering analysis to fractured reservoirs without mathematical justification could lead to results of uncertain value. The early reported work on artificially and naturally fractured reservoirs consists mainly of papers by Pollard, Freeman and Natanson, and Samara. The most familiar method is that of Pollard. A more recent paper by Warren and Root showed how the Pollard method could lead to erroneous results. Warren and Root analyzed a plausible two-dimensional model of fractured reservoirs. They concluded that a Horner-type pressure build-up plot of a well producing from a factured reservoir may be characterized by two parallel linear segments. These segments form the early and the late portions of the build-up plot and are connected by a transitional curve. In our analysis of pressure build-up and drawdown data obtained on several wells from various fractured reservoirs, two parallel straight lines were not observed. In fact, the build-up and drawdown plots were similar in shape to those obtained on homogeneous reservoirs. Fractured reservoirs, due to their complexity, could be represented by various mathematical models, none of which may be completely descriptive and satisfactory for all systems. This is so because the fractures and matrix blocks can be diverse in pattern, size, and geometry not only between one reservoir and another but also within a single reservoir. Therefore, one mathematical model may lead to a satisfactory solution in one case and fail in another. To understand the behavior of the pressure build-up and drawdown data that were studied, and to explain the shape of the resulting plots, a fractured reservoir model was employed and analyzed mathematically. The model is based on the following assumptions:1. The matrix blocks act like sources which feed the fractures with fluid;2. The net fluid movement toward the wellbore obtains only in the fractures; and3. The fractures' flow capacity and the degree of fracturing of the reservoir are uniform. By the degree of fracturing is meant the fractures' bulk volume per unit reservoir bulk volume. Assumption 3 does not stipulate that either the fractures or the matrix blocks should possess certain size, uniformity, geometric pattern, spacing, or direction. Moreover, this assumption of uniform flow capacity and degree of fracturing should be taken in the same general sense as one accepts uniform permeability and porosity assumptions in a homogeneous reservoir when deriving the unsteady-state fluid flow equation. Thus, the assumption may not be unreasonable, especially if one considers the evidence obtained from examining samples of fractured outcrops and reservoirs. Such samples show that the matrix usually consists of numerous blocks, all of which are small compared to the reservoir dimensions and well spacings. Therefore, the model could be described to represent a "homogeneously" fractured reservoir. SPEJ P. 60ˆ

Fractured Reservoir Simulation

1983 ◽  
Vol 23 (01) ◽  
pp. 42-54 ◽  
Author(s):  
L. Kent Thomas ◽  
Thomas N. Dixon ◽  
Ray G. Pierson
Keyword(s):  
Fractured Reservoirs ◽  
Fracture Flow ◽  
Fracture System ◽  
Fractured Reservoir ◽  
Three Phase ◽  
Matrix Fracture ◽  
Naturally Fractured ◽  
Matrix Blocks ◽  
The Matrix ◽  
Saturation History

Abstract This paper describes the development of a three-dimensional (3D), three-phase model for simulating the flow of water, oil, and gas in a naturally fractured reservoir. A dual porosity system is used to describe the fluids present in the fractures and matrix blocks. Primary flow present in the fractures and matrix blocks. Primary flow in the reservoir occurs within the fractures with local exchange of fluids between the fracture system and matrix blocks. The matrix/fracture transfer function is based on an extension of the equation developed by Warren and Root and accounts for capillary pressure, gravity, and viscous forces. Both the fracture flow equations and matrix/fracture flow are solved implicitly for pressure, water saturation, gas saturation, and saturation pressure. We present example problems to demonstrate the utility of the model. These include a comparison of our results with previous results: comparisons of individual block matrix/fracture transfers obtained using a detailed 3D grid with results using the fracture model's matrix/fracture transfer function; and 3D field-scale simulations of two- and three-phase flow. The three-phase example illustrates the effect of free gas saturation on oil recovery by waterflooding. Introduction Simulation of naturally fractured reservoirs is a challenging task from both a reservoir description and a numerical standpoint. Flow of fluids through the reservoir primarily is through the high-permeability, low-effective-porosity fractures surrounding individual matrix blocks. The matrix blocks contain the majority of the reservoir PV and act as source or sink terms to the fractures. The rate of recovery of oil and gas from a fractured reservoir is a function of several variables, included size and properties of matrix blocks and pressure and saturation history of the fracture system. Ultimate recovery is influenced by block size, wettability, and pressure and saturation history. Specific mechanisms pressure and saturation history. Specific mechanisms controlling matrix/fracture flow include water/oil imbibition, oil imbibition, gas/oil drainage, and fluid expansion. The study of naturally fractured reservoirs has been the subject of numerous papers over the last four decades. These include laboratory investigations of oil recovery from individual matrix blocks and simulation of single- and multiphase flow in fractured reservoirs. Warren and Root presented an analytical solution for single-phase, unsteady-state flow in a naturally fractured reservoir and introduced the concept of dual porosity. Their work assumed a continuous uniform porosity. Their work assumed a continuous uniform fracture system parallel to each of the principal axes of permeability. Superimposed on this system was a set of permeability. Superimposed on this system was a set of identical rectangular parallelopipeds representing the matrix blocks. Mattax and Kyte presented experimental results on water/oil imbibition in laboratory core samples and defined a dimensionless group that relates recovery to time. This work showed that recovery time is proportional to the square root of matrix permeability divided by porosity and is inversely proportional to the square of porosity and is inversely proportional to the square of the characteristic matrix length. Yamamoto et al. developed a compositional model of a single matrix block. Recovery mechanisms for various-size blocks surrounded by oil or gas were studied. SPEJ P. 42

Experimental and Numerical Analysis of In-Situ Combustion in a Fractured Core

SPE Journal ◽  
2011 ◽  
Vol 16 (02) ◽  
pp. 358-373 ◽  
Author(s):  
H.. Fadaei ◽  
L.. Castanier ◽  
A.M.. M. Kamp ◽  
G.. Debenest ◽  
M.. Quintard ◽  
...  
Keyword(s):  
Combustion Front ◽  
Fractured Reservoirs ◽  
Experimental Studies ◽  
Steam Injection ◽  
Combustion Tube ◽  
Fractured Reservoir ◽  
In Situ Combustion ◽  
Matrix Permeability ◽  
The Matrix

Summary Approximately one-third of global heavy-oil resources can be found in fractured reservoirs. In spite of its strategic importance, recovery of heavy crudes from fractured reservoirs has found few applications because of the complexity of such reservoirs. In-situ combustion (ISC) is a candidate process for such reservoirs, especially for those where steam injection is not feasible. Experimental studies reported in the literature on this topic mentioned a cone-shaped combustion front, indicating that the process was governed by diffusion of oxygen into the matrix. The main oil-production mechanisms were found to be thermal expansion of oil and evaporation of light components (Schulte and de Vries 1985; Greaves et al. 1991). In order to confirm these results, we carried out reservoir-simulation studies presented in Fadaei et al. (2010). We have shown that the front has the shape of a cone, and we have performed a combustion/extinction analysis representing the results in a diagram of cumulative production vs. diffusion coefficient and matrix permeability. Before obtaining quantitative and qualitative comparisons, we need to characterize the systems we want to study. Therefore, we also carried out laboratory experiments using kinetic cells and combustion tubes. The kinetic-cell studies showed that the presence of carbonates has a significant effect on combustion kinetics. Our combustion-tube studies confirmed the previously observed coneshaped front. Previous studies reported in literature used heating elements along the combustion tube to regulate the temperature, which may have caused some undue heating of the core. To avoid that, we chose to use efficient insulation to minimize heat losses. Combustion advanced faster in nonconsolidated matrix, in which the permeability was higher than in consolidated matrix. The results showed that the presence of severe heterogeneities may prevent the combustion front from propagating. Several runs were performed for different air-injection rates and pressures and for different permeability contrasts between the matrix and the fracture. The next step of our work is the upscaling of ISC in the fractured reservoir at interwell scale on the basis of knowledge provided by simulation and experimental studies.

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