Summary This study develops an improved model for analysis of pressure transient tests of naturally fractured reservoirs. The development was prompted by observations of actual well tests that showed anomalous slope prompted by observations of actual well tests that showed anomalous slope changes during the transition period and where the behavior could not be explained by dual-porosity models. Geometrical configurations studied include both the strata model, where horizontal matrix layers are separated by fractures, and the uniformly distributed blocks, which are separated by an orthogonal set of fractures. These systems were assumed to be under gradient flow conditions. In both cases, two separate sets of matrix proper- ties were assumed. The formulation of response was solved semianalytically. The solutions included the early time effects of both the afterflow and skin. Observations made from the theoretical predictions are that the fracture-controlled early times and portions of the transition period will resemble the behavior of a dual-porosity system. The latter part of the transition zone, however, exhibits slope changes; the duration is a function of 1/ 2 (ratio of interporosity flow coefficients for the two matrix types) and 1 / 2 (ratio of fluid capacitance coefficients). A correlation developed on the basis of numerous sensitivity runs allows the estimation of w1 /w2 and 1/ 2 with the times that correspond to the onset of anomalous slope changes. Because an infinite-acting slope may develop before the matrix blocks of the lowest show their existence during the anomalous slope changes, recognition of the various matrix properties emphasized in this study will also safeguard against properties emphasized in this study will also safeguard against extrapolation of incorrect late-time curves. Introduction During the last 20 years, pressure transient behavior in naturally fractured reservoirs has been the subject of many investigations. Dual-porosity models have been widely used to explain the flow behavior in the matrix/fracture network of such reservoirs. A major flaw with dual-porosity models is the assumption of uniform matrix properties throughout the system. properties throughout the system. Double-porosity models have long been used for representation of naturally fractured reservoirs. Pressure transient behaviors in such reservoirs have been analyzed under the assumption that homogeneous matrix properties prevail throughout the system. Fractures provide the properties prevail throughout the system. Fractures provide the highest permeabilities (very high order of magnitude compared with matrix permeability) and are the main conduits of fluid flow into the producing wells. Matrix blocks do not produce the fluid directly into the wellbore but act as a source that feeds the fluid into the high-permeability fractures. Two parameters have been used commonly to describe the properties of the matrix and the interconnecting fracture network. The interporosity flow parameter, indicates the degree of interporosity flow between the matrix blocks and fracture system. The fluid capacitance coefficient, w, represents the ratio of fracture storage capacity to the total storage capacity. The standard semilog plot of the buildup-pressure response vs. shut-in time or the drawdown-pressure response vs. flowing time, neglecting wellbore storage effects, is characterized by parallel straight lines of the early and late times with a transition period in between. The displacement of these straight lines is a function of and . Under a pseudosteady-state condition, I pressure throughout the matrix blocks instantaneously drops as soon as pressure depletion occurs in the fractures. This assumption has a characteristic "S" -shaped intermediate segment with a point of inflection. For relatively large matrix blocks, however, the unsteady-state assumption may no be valid; here, unsteady-state or gradient flow is a more realistic representation. A notable feature of this assumption is that the transition curve of pressure response exhibits more linearity compared with the case of the pseudosteady-state model. Fig. 1 illustrates the expected pseudosteady-state model. Fig. 1 illustrates the expected behavior of both models. Development of the Proposed Model We propose an improved model for the analysis of pressure transient tests in naturally fractured reservoirs. pressure transient tests in naturally fractured reservoirs. SPEFE p. 113

Pressure-transient tests in naturally fractured reservoirs often exhibit nonuniform responses, Various models explain such nonuniformity; however, their relevance is often not justified on a geologic basis. Fractal geometry provides a method to account for a great variety of such transients under the assumption that the network of fractures is fractal. This paper presents an application to real well tests in various fractured reservoirs. The physical meaning of the fractal parameters is presented in the context of well testing. Examples showing a behavior similar to the finite-conductivity fracture model or to spherical flow are presented and explained by the alternative of fractal networks. A behavior that can be mistakenly interpreted as a double-porosity case is also analyzed.

Introduction The electrical resistivity of dilute aqueous salt solutions has been studied for a number of years, but very few data exist on concentrations above 0.1 molar. Normal groundwaters commonly are near 0.1 molar, while most geothermal and oilfield fluids are at least several molar (Table 1). Thus, the interpretation of electrical measurements in geothermal areas at present is based mainly on extrapolation of lower temperature and lower concentration data. Such extrapolation may introduce serious errors into the interpretation of geothermal reservoir characteristics determined from electrical measurements. This paper presents new experimental data and an improved descriptive model of the electrical properties of brines as a function of temperature properties of brines as a function of temperature from 22 to 375 deg. C and concentration from roughly 3 to 26 wt% while under 31 MPa hydrostatic pressure. Data and models are given for brines composed of the chlorides of sodium, calcium, and potassium, and their mixtures. Comparison of the older log interpretation formulas to the new models illustrates an order of magnitude improvement in accuracy with an overall fit to within 2%. Resistivity Dependence Upon Temperature Some researchers have postulated that the electrical resistivity of fluid saturated rocks follows the temperature dependence of the saturating fluid in the absence of conducting minerals or significant surface conduction along altered pore walls. This assumption resulted from the success of a simple empirical formula relating the resistivity of a rock to the resistivity of the fluid filling the pores of the rock: Pr=FPw, where Pr= resistivity of clay-free, nonshale material that is 100% saturated, Pw= resistivity of saturating solution, and F= formation resistivity factor. A number of investigators have derived formulas that add the temperature of the saturating fluids. Experimental observations have shown that some rocks obey these formulas while others do not. 17–19 Part of the problem is the inadequate knowledge of Part of the problem is the inadequate knowledge of the resistivity dependence on temperature for the solution that fills the rock pores. We have found empirically that the best fit of the resistivity data to temperature is pw=bo+b1T-1 +b2T+b3T2+b4T3, where T is temperature and coefficients b are found empirically.

Dual fracture models are examined as a more realistic alternative to dual porosity models for the representation of naturally fractured reservoirs. A major component of the fracture system is the network of microfracture which by virtue of their lower permeability respond somewhat later than the macrofractures. A delineation of microfracture response versus matrix response is made using the proposed conceptual models. It is demonstrated that the microfractures response may at times be mistakenly attributed to matrix. Introduction Studies published on diagnostic plots of pressure transient test data indicate strong similarities among certain cases of conceptual reservoir models. In particular, diagnostic plots expected for naturally fractured reservoirs are often times not developed because of either inadequate test duration or wellbore controlled conditions. A major question in the testing of naturally fractured reservoirs is explanation for causes of non-development of transition period1. This transition was predicted by Warren and Root2 in their dual porosity conceptualization of naturally fractured reservoirs. Other researchers have also predicted the transition periods for layered type response3 as well as systems of triple porosity.4 In the dual porosity conceptualization, an assumption is made as to the nature of flow units with interporosity properties. Specifically, two types of flow units are considered. First is a system of tight matrix with substantial storativity for fluid. The second unit is the network of fractures with high fluid conductivity. In this study, the above model is extended to a more realistic one where the effects of microfractures are also included. The objective is to predict response duration for these subsets and develop guidelines for interpretations of pressure transient test data misinterpreted because of the selection of an inappropriate model. Models for Naturally Fractured Reservoirs Over the past several years, numerous models for characterization of naturally fractured reservoirs (NFR) from pressure transient tests have been suggested. One commonly used model is the double porosity model proposed by Barenblat and Zeltov5 and introduced into the petroleum literature by Warren and Root. The idealized model introduced by Warren and Root (Fig. 1) consists of a set of orthogonal fracture planes dividing the matrix into equal blocks. Production at the wellbore is essentially controlled by the fractures. The fracture system contains a small fraction of indigenous oil, yet with hydraulic conductivities superior to that of the matrix, act as primary conduits for flow in the reservoir. Matrix rock, however, contains the bulk of fluid in place and provides pressure support to the fracture system. While this model has been the backbone of various analysis techniques and simulation applications, certain modifications are necessary to bring it closer to realistic representation of NFR. Among the modifications suggested is the work of Abdassah and Ershaghi4 who introduced the Triple Porosity Model. In this model, two distinct matrix systems of different flow and storage capacities are recognized in addition to the fracture system. Another modification was introduced by Bourdet and Johnston 3 where matrix blocks also contribute to production at the wellbore. In this paper new conceptual models are proposed to differentiate between the microfractures and the macrofractures. Dual fracture systems consisting of macrofractures and microfractures (Fig. 2) are introduced as the basis of the reservoir architecture. The theoretical basis of the proposed models are developed and the anticipated pressure transient response on the pressure derivative plot are then compared to those of the existing models. Both the double porosity and the triple porosity models predict transition periods reflecting matrix support to the fracture system. In actual field tests, indications are, at times, and for certain tests, these transition periods may be observed. However, there are cases where the response of naturally fractured reservoirs have lacked a clear definition indicating matrix support. One purpose of this paper is to ascertain the similarities and differences between the support from tight matrix and that of the more permeable microfractures. Models for Naturally Fractured Reservoirs Over the past several years, numerous models for characterization of naturally fractured reservoirs (NFR) from pressure transient tests have been suggested. One commonly used model is the double porosity model proposed by Barenblat and Zeltov5 and introduced into the petroleum literature by Warren and Root. The idealized model introduced by Warren and Root (Fig. 1) consists of a set of orthogonal fracture planes dividing the matrix into equal blocks. Production at the wellbore is essentially controlled by the fractures. The fracture system contains a small fraction of indigenous oil, yet with hydraulic conductivities superior to that of the matrix, act as primary conduits for flow in the reservoir. Matrix rock, however, contains the bulk of fluid in place and provides pressure support to the fracture system. While this model has been the backbone of various analysis techniques and simulation applications, certain modifications are necessary to bring it closer to realistic representation of NFR. Among the modifications suggested is the work of Abdassah and Ershaghi4 who introduced the Triple Porosity Model. In this model, two distinct matrix systems of different flow and storage capacities are recognized in addition to the fracture system. Another modification was introduced by Bourdet and Johnston 3 where matrix blocks also contribute to production at the wellbore. In this paper new conceptual models are proposed to differentiate between the microfractures and the macrofractures. Dual fracture systems consisting of macrofractures and microfractures (Fig. 2) are introduced as the basis of the reservoir architecture. The theoretical basis of the proposed models are developed and the anticipated pressure transient response on the pressure derivative plot are then compared to those of the existing models. Both the double porosity and the triple porosity models predict transition periods reflecting matrix support to the fracture system. In actual field tests, indications are, at times, and for certain tests, these transition periods may be observed. However, there are cases where the response of naturally fractured reservoirs have lacked a clear definition indicating matrix support. One purpose of this paper is to ascertain the similarities and differences between the support from tight matrix and that of the more permeable microfractures.