A well-test interpretation method based on the analysis of the time rate of pressure change an? the. actual pressur~ response is discussed. A differentiation algorithm is proposed, and several field examples illustrate how the method slmpitfies the analysIs process, making interpretation of well tests easier and more accurate.

A new type-curve is presented for analyzing wells with wellbore storage and skin in double porosity systems. This type-curve applies to damaged, acidized, and fractured wells in fissured reservoirs. In addition to the usual well and reservoir parameters (permeability, skin, wellbore storage constant and length of the fracture intersecting the well), analysis yields characteristic parameters that can provide quantitative information on the volume of fissures and the size of porous blocks in the reservoir. These, in classical methods, could only be obtained if semi-log radial flow were present at both early and late times, (thus yielding two characteristic parallel semi-log straight lines on a Horner plot), a condition that is seldom satisfied in practice. The analysis method presented in the paper is illustrated with actual field examples from several different fissured reservoirs. INTRODUCTION The large number of papers1–16 published in the last twenty years on the behavior of naturally fractured reservoirs reflects the importance to the oil industry of this type of producing formation. Although several, apparently different, theoretical models have been proposed, most practical methods for interpretation of transient tests are based on the existence of two parallel, semi-log straight lines, that is considered a characteristic feature of fissured reservoirs. Unfortunately, in most actual tests, the first semi-log straight line is usually obscured, and these methods cannot be used. As a result, only parameters characterizing the homogeneous behavior of the total system can be obtained (when conventional analysis methods are applicable), and those specific to the fracturation are usually not accessible. In this paper, we present new type-curves that can provide all the system parameters, by means of log-log analysis. These curves also permit to detect under which conditions the two parallel, semi-log straight lines are present, and can be used for interpretation. Utilization of the type-curves is illustrated on several actual field data, for which no satisfactory analysis was previously available. PREVIOUS WORK Available solutions for the behavior of fissured reservoirs are discussed in detail in Ref.16. A distinction is made there between models based on a detailed physical description of the fissured system, only suitable in relatively small scale, geotechnical type projects; and models where porous blocks and fissures are assumed uniformly distributed throughout the formation which is then treated as an â??equivalentâ?¿ system, either homogeneous or heterogeneous, as dictated by the general behavior of the actual test data. By â??equivalentâ?¿, it is meant a system whose calculated behavior is similar to the observed behavior of the real system. In this paper, we have only considered the case of reservoirs whose behavior cannot be matched with homogeneous models, and thus indicates the need to take heterogeneities into account. Among the various heterogeneous models suggested in the literature, the double porosity model is certainly the one that has attracted the most attention in the past. Until recently, however, published solutions were restricted to a â??basicâ?¿ model, (a line source or finite radius well, in a horizontal, constant thickness, reservoir of infinite lateral extent, with impermeable upper and lower boundaries), without any of the inner boundary conditions found in practice (wellbore storage, skin, fractures, etc . . .), although outer boundary conditions have been considered by some authors. As a result, these solutions were only applicable to the analysis of interference tests, or to that of data after the start of the infinite acting period in production tests.

No abstract

INTRODUCTION Well tests have been used for many years for evaluating reservoir characteristics, and numerous methods of interpretation have been proposed in the past. A number of these methods have become very popular, and are usually referred to as 'conventional'. In the last ten years, many others have been developed, that are often called 'modern', but the relationship between 'conventional' and 'modern' well test interpretation methods is not always clear to the practicing reservoir engineer. To add to the confusion, some methods have become the subject of much controversy, and conflicting reports have been published on what they can achieve. This is especially true of the 'type-curve matching' technique, which was first introduced in the oil literature in 19701, for analyzing data from wells with wellbore storage and skin effects. This method, also called 'log-log analysis', was supposed to supplement 'conventional' techniques with useful qualitative and quantitative information. In recent years, however, it was suggested that this technique be only used in emergency or as a checking device, after more conventional methods have failed.2,3 The relationship between 'conventional' and 'modern' interpretation methods is examined in detail in this paper. It is shown that type-curve matching is a general approach to well test interpretation, but its practical efficiency depends very much on the specific type-curves that are used. This point is illustrated with a new type-curve for wells with wellbore storage and skin, which appears to be more efficient than the ones already available in the literature. METHODOLOGY OF WELL TEST INTERPRETATION The Concept of Model The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem. In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test. The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc. This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known. Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct. On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced. The Concept of Model The principles governing the analysis of well tests are more easily understood when one considers well test interpretation as a special pattern recognition problem. In a well test, a known signal (for instance, the constant withdrawal of reservoir fluid) is applied to an unknown system (the reservoir) and the response of that system (the change in reservoir pressure) is measured during the test. The purpose of well test interpretation is to identify the system, knowing only the input and output signals, and possibly some other reservoir characteristics, such as boundary or initial conditions, shape of drainage area, etc. This type of problem is known in mathematics as the inverse problem. Its solution involves the search of a well-defined theoretical reservoir, whose response to the same input signal is as close as possible to that of the actual reservoir. The response of the theoretical reservoir is computed for specific initial and boundary conditions (direct problem), that must correspond to the actual ones, when they are known. Interpretation thus relies on models, whose characteristics are assumed to represent the characteristics of the actual reservoir. If the wrong model is selected, then the parameters calculated for the actual reservoir will not be correct. On the other hand, the solution of the inverse problem is usually not unique : i.e., it is possible to find several reservoir configurations that would yield similar responses to a given input signal. However, when the number and the range of output signal measurements increase, the number of alternative solutions is greatly reduced.

A systematic approach for interference tests in reservoirs with double porosity behavior is presented; it applies to both naturally fractured presented; it applies to both naturally fractured reservoirs and multilayered reservoirs with sufficiently high permeability contrast between layers. Type curves are presented for the pressure response at an observation well, the active well being produced at either constant flow rate or constant pressure. They are derived from two models with the assumptions of pseudo-steady state or transient interporosity flow regime. The distinctive specific features they exhibit are clearly identified and quantitatively related to the model parameters. An interpretation method, based on type curve matching, is proposed: after selection of the most appropriate model, and identification of the successive flow regimes, the double porosity behavior of the reservoir is characterized and pertinent parameters are evaluated: flow conductivity kh, interporosity flow parameter lambda, and storativity (phi Vc t)h segregation parameter lambda, and storativity (phi Vc t)h segregation throughout the reservoir. Actual field examples are discussed to illustrate the method. Introduction The paper is concerned with formations composed of two porous media or systems of different porosities and permeabilities, that distinctly contribute to the production process. One medium presents a high production process. One medium presents a high conductivity and thus drains the reservoir fluid to the producing well, whereas the other medium presents a producing well, whereas the other medium presents a much lower conductivity and feeds fluid only to the more conductive system. Because the storativities of both media usually differ by several orders of magnitude, these formations are referred to as double porosity formations, while they are actually characterized porosity formations, while they are actually characterized by a high permeability contrast between media. The success of field development projects as well as stimulation operations for such reservoirs requires an accurate evaluation of reservoir performance, i.e. knowledge of the storativities and flow characteristics of both media. For this reason, and because reservoirs with double porosity behavior are recognized as major contributors to the world hydrocarbon and geothermal production, they have been the subject of many studies over the last years. The concept of a double porosity model was first introduced by Barenblatt, et al. They considered a fissured reservoir and defined for each point in space two pressures: the average fluid pressure in the fissure system -the most conductive- pf, and the average fluid pressure in the matrix system -the less conductive- pm, in the neighborhood of the given point. Furthermore they assumed that the flow of fluid from the matrix to the fissures occured under a pseudo-steady state regime: pseudo-steady state regime: (1) where q* is the interporosity flow, namely the flow from matrix to fissures, and alpha a shape factor representative of the interporosity contact area. A solution was given for the pressure distribution in the matrix system, assuming a negligible fissure storativity. Warren and Root presented the solution for the pressure distribution within the fissure system. They pressure distribution within the fissure system. They showed that two parameters were sufficient to characterize the double porosity model: (2) (3) lambda is the interporosity flow parameter, related to the ability of the fluid to flow from the matrix into the fissures; w is the ratio of the storativity of the fissure system to the storativity of the total-fissure and matrix -system. Later on, Mavor and Cinco-Ley extended Warren and Root's solution to take into account the effects of wellbore storage and skin.