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

Viscosity of synthetic brines consIstmg of sodium chloride, potassium chloride, and calcium chloride were measured at concentrations ranging from 0.99 to 16.667 wt% and at temperatures up to 275°C. From the use of laboratory-derived data, a method is presented whereby the viscosity of a geothermal brine may be estimated from a knowledge of its composition.

Summary A prediction method based on the use of performance history of a waterflood proposed in 1978 by Ershaghi and Omoregie is scrutinized here. Using a reservoir simulation approach, performance data for some hypothetical waterfloods are generated to test the application of the proposed technique to various floodpatterns, reservoir properties, and field operating conditions. Recently published results on the behavior of relative permeability curves for immiscible processes areused to substantiate the assumptions inherent in the proposed technique. The limitations of the technique are discussed and applications to some actual case studies are presented. Introduction Conventional waterfloods and modified waterfloodsusing various additives still constitute the bulk of the fluid injection projects active in the U.S. and elsewhere. During the history of a water injection project, reservoir engineers are expected to predict performance using the past response data. A literature review shows that over the last 40 years, there have been many techniques proposed for such prediction purposes. These techniques range from empirical correlations to various analytical models. In addition to these techniques, the advent of reservoir simulation has resulted in the availability of a very powerful tool for performance prediction. Many operators are still reluctant to use reservoir simulators because of inadequate reservoir data or insufficiently trained personnel to conduct simulation studies. Simple models often fail because of the inherentassumption as to the nature of the displacement mechanism or the misrepresentation of the real reservoir conditions. Many years of field and laboratory research by the petroleum industry and the academia has resulted in abetter understanding of the multitude of parameters influencing the efficiency of fluid injection projects. It is well established that for immiscible displacements, reservoir heterogeneity, relative permeability characteristics, fluid viscosities, and flood pattern are the most important factors. No prediction method can be used successfully in afield where the real reservoir is represented by laboratory-derived data and inadequately defined reservoir heterogeneity. A successful prediction technique requires input from the real reservoir performance. Alumped-parameter model that would embody all properties of the reservoir and the operating conditions can lead us to a realistic prediction of performance. In 1978, Ershaghi and Omoregie presented a technique for extrapolation of water-cut vs. recovery curvesin waterflood operations. The technique allows one togenerate a field composite relative permeability ratiocurve that includes reservoir properties as well as operational problems. The main assumptions were (1) the plot of log (krw/kro) vs. Sw is a straight line and (2) the leaky-piston displacement concept of Buckley and Leverett is applicable. Since Ref. 1 was published, many operators have contacted the authors with questions and comments about applying the technique to their specific cases-ranging from natural bottomwater drive to modified waterflood. Two additional papers about the technique haveappeared in the literature by others. This paper is aimed at clarifying ambiguities about the technique and providing guidelines for its application. Review of the Technique Assuming that log (krw/kro) vs. Sw is a straight line, the concepts of fractional flow and the frontal advance theory proposed by Buckley and Leverett may be used toderive the following relationship between the recovery and the fractional water cut: ER = (m . X) + n, where ER = recovery, X = ln[(1/fw) - 1] - (1/fw)fw = fractional water cut, m = 1/[b(1 - Swi)], n = -1/(1 - Swi)[Swi + 1/b ln(A)], A = a(mu w/mu o), and a and b from kro/krw = a ebSw. JPT P. 664^

BSTRACT laboratory scale physical model tests. Theoretical approaches include various A series of laboratory flow experiments filtration models where the emphasis is on the ere conducted to examine the relative effects rate and the properties of cake buil~up f various factors causing gradual losses in against a permeable formation. Only in recent njectivities in fieldwide water injection years emphasis is being focused on including perations. Injectivity losses were measured the pressure losses due to fine migration and n a small scale during radial flow injection deep bed filtration.Because of the f carefully prepared particle suspensions complicated nature of the interactions of ith KC1 as a base fluid, various factors influencing fine invasion and Systematic matching of rocks mean pore migration, a universally applicable prediction izes and the mean particle sizes in the model has not yet been proposed. Empirical uspension pointed out their effect and observations and correlations are needed to ontrol on the mechanism of inj~>tivity elucidate the exact nature of the phenomena. mpairment.Step-rate-tests are a very useful tool Additional factors studied included the for determining injectivity indices.

This paper presents the application of a new concept, i.e.; fractal model, to analyze pressure transient test data in complex naturally fractured geothermal reservoir. Application of conventional type curves has been unsuccessful in analyzing and interpreting the interference test results in Kamojang geothermal reservoir which is considered as a complex naturally fractured system. Using the conventional type curve method, the pressure test data, in this case, cannot match to the curve, primarily at early time data. The match, however, can be achieved by using the type curves generated based on "fractal reservoir model" which has been previously developed by Chang and Yortsos in 1990. Using the diffusivity equation of fractal reservoir, the equation for interference test has been derived and the result is then used for generating a new type curve method. In addition, the procedure to use this method has also been developed. Using the generated type curves, application has been performed on analyzing the interference test data from Kamojang geothermal reservoir. The analyzing results demonstrate the viability of the model in describing characteristics of the reservoir such as transmissibility, storativity and fractal dimension of the medium. Introduction Previous work showed that the fractal reservoir model could be used satisfactorily in describing the pressure transient behavior in the reservoir. In their model, the fracture network is assumed to be connected and distributed as a fractal object within a homogeneous medium (matrix) of Euclidean geometry. Fluid flow from reservoir to wells, in such a reservoir, occurs only through the perfectly connected fracture network. Based on these approaches, they used diffusivity equation to model a transient flow in the fractal reservoir for single well problems. In this paper, the application of fractal reservoir model for handling the multiple well problems, especially in analyzing the interference test data, is discussed. Physical and mathematical descriptions of this model are basically adopted from the model that had been developed by Chang and Yortsos (1990). By involving several mathematical manipulations into the model, the formulation can be extended and used for multiwell test problems. Then, using this equation, type curve model for interference test analysis can be generated by plotting two variable groups which have been defined in this study. The interference test data in Kamojang geothermal reservoir which is considered as a complex naturally fractured reservoir has been analyzed to determine transmissibility, storativity and fractal dimension of the reservoir. DEVELOPMENT OF THE PROPOSED MODEL The fractal model is able to appropriately described the complex naturally fractured reservoir which has a large number of different scale, poor fracture connectivity and disorder spatial distribution. In the pressure transient case, the application of fractal model has been examined by Acuna et al. for analyzing single well test data in naturally fractured reservoir of geothermal field. Using their model, the method that could be used in the Interference Test Analysis was developed. By considering at least two interference wells in a fractal reservoir, one of them is an active well and the others are observation wells (see Figure 1), a pressure transient equation has been formulated in this study. Using this equation, a procedure of type curve matching is then proposed for analyzing some reservoir parameters, such as reservoir transmissibility, storativity and fractal dimension. P. 511^