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Abstract The storage capacity ratio, w, measures the flow capacitance of the secondary porosity and the interporosity flow parameter, l, is related to the heterogeneity scale of the system. Currently, both parameters l and w are obtained from well test data by using the conventional semilog analysis, type-curve matching or the TDS Technique. Warren and Root showed how the parameter w can be obtained from semilog plots. However, no accurate equation is proposed in the literature for calculating fracture porosity. This paper presents an equation for the estimation of the l parameter using semilog plots. A new equation for calculating the storage capacity ratio and fracture porosity from the pressure derivative is presented. The equations are applicable to both pressure buildup and pressure drawdown tests. The interpretation of these pressure tests follows closely the classification of naturally fractured reservoirs into four types, as suggested by Nelson. The paper also discusses new procedures for interpreting pressure transient tests for three common cases:the pressure test is too short to observe the early-time radial flow straight line and only the first straight line is observed, the pressure test is long enough to observe the late-time radial flow straight line, but the first straight line is not observed due to inner boundary effects, such as wellbore storage and formation damage, and Neither straight line is observed for the same reasons, but the trough on the pressure derivative is well defined. Analytical equations are derived in all three cases for calculating permeability, skin, storage capacity ratio and interporosity flow coefficient, without using type curve matching. In naturally fractured reservoirs, the matrix pore volume, therefore the matrix porosity is reduced as a result of large reservoir pressure drop due to oil production. This large pressure drop causes the fracture pore volume, therefore fracture porosity, to increase. This behavior is observed particularly in reservoir where matrix porosity is much greater than fracture porosity. Fractures in reservoirs are more vertically than horizontally oriented, and the stress axis on the formation is also essentially vertical. Under these conditions, when the reservoir pressure drops, the fractures do not suffer from the stress caused by the drop. Using these principles, a new method is introduced for calculating fracture porosity from the storage capacity ratio, without assuming the total matrix compressibility is equal to the total fracture compressibility. Several numerical examples are presented for illustration purposes. Introduction Nelson identifies four types of naturally fractured reservoirs; based on the extent the fractures have altered the reservoir matrix porosity and permeability: In Type 1 reservoirs, fractures provide the essential reservoir storage capacity and permeability. Typical Type-1 naturally fractured reservoirs are the Amal field in Libya, Edison field California, and pre-Cambrian basement reservoirs in Eastern China. All these fields contain high fracture density. In Type 2 naturally fractured reservoirs, fractures provide the essential permeability, and the matrix provides the essential porosity, such as in the Monterey fields of California, the Spraberry reservoirs of West Texas, and Agha Jari and Haft Kel oil fields of Iran. In Type 3 naturally fractured reservoirs, the matrix has an already good primary permeability. The fractures add to the reservoir permeability and can result in considerable high flow rates, such as in Kirkuk field of Iraq, Gachsaran field of Iran, and Dukhan field of Qatar. Nelson includes Hassi Messaoud (HMD) in this list. While indeed there are several low-permeability zones in HMD that are fissured; in most zones however the evidence of fissures is not clear or unproven.
- North America > United States > Texas (1.00)
- North America > United States > California (1.00)
- Asia > Middle East > Iran (1.00)
- (2 more...)
- North America > United States > Texas > Permian Basin > Yeso Formation (0.99)
- North America > United States > Texas > Permian Basin > Yates Formation (0.99)
- North America > United States > Texas > Permian Basin > Wolfcamp Formation (0.99)
- (75 more...)
Abstract Naturally fractured reservoirs are prolific producers since fractures provide the main path for fluid flow towards the wellbore. Conventional drawdown and buildup tests are not always practical due to various technical difficulties to maintain a constant flow rate during a drawdown test or the loss of production during the shut-in period of a buildup test. In this case multirate tests represent a practical and effective alternative. This paper presents a complete multi-rate test analysis methodology in naturally fractured reservoirs. The convolution theorem was used to accommodate the change in the rate if the test is multirate. The integral method is used if the rate is continuously changing. It was found that the pressure derivative provides a powerful tool for analyzing multirate pressure transient tests. The Tiab's Direct Synthesis (TDS) technique, which uses exact analytical solutions to obtain reservoir parameters, was applied to different possible cases and the results were compared to those obtained from the other conventional techniques. In the case of long series of constant flow rate, the log-log plot of pressure and pressure derivative using equivalent radial time or equivalent linear time give approximately similar results. If the wellbore storage effect is large, the error in the permeability (especially during the early radial flow) is greater mainly if the late radial flow is not observed. When the early radial flow is missing, the dimensionless storage capacity ratio ? and the interporosity flow parameter ? cannot be estimated using conventional methods. In such case, they can be determined only from the pressure derivative plot using the TDS technique. During a multirate test, the changing flow rate must be systematically recorded since it is an integral part of all the analysis equations. Several examples were solved to illustrate the use of the techniques developed. The results show that the multiple rate tests and the TDS technique can be successfully used to characterize naturally fractured reservoirs. Introduction Well testing is a powerful tool to detect and evaluate heterogeneities and flow parameters in naturally fractured reservoirs. Pressure transient testing techniques are extensively used to determine reservoir and production behavior of such reservoirs. Many techniques are used to characterize naturally fractured reservoirs including, Warren and Root technique, and Tiab's Direct Synthesis (TDS) technique. The drawdown test requires a constant flow rate; however, it is often impractical or impossible to maintain a strictly constant producing rate, and the well cannot be shut in because of financial reasons. In such conditions, a multi-rate test is preferable. It has the advantage of providing transient test data while production continues. It tends to minimize changes in the wellbore storage and phase segregation effects and, thus, may provide better results than the drawdown and buildup test. In 1999 Mongi and Tiab introduced the pressure derivative to interpret multiple rate tests in homogeneous reservoirs. They applied the TDS technique to multi-rate tests for both oil and gas reservoirs. This technique utilizes the characteristic intersection points and slopes of various straight lines from log-log plot of pressure and pressure derivative. It uses exact analytical solutions to obtain reservoir parameters. The main objectives of this study are:Develop a complete methodology to interpret multi-rate tests in naturally fractured reservoirs for both oil and gas wells; Extend the Tiab's Direct Synthesis (TDS) technique to interpret multi-rate pressure transient tests in naturally fractured reservoirs; Compare the results obtained using TDS technique with those provided by conventional methods; Analyze the tests using the equivalent time (rigorous method) and real time. Oil Reservoirs Mathematical Model The model assumes:The matrix blocks are homogeneous and isotropic and are contained within a systematic array of identical rectangular parallelepipeds; Only the fractures feed the wellbore; These fractures are oriented parallel to the principal permeability axes; The formation and fluid properties are independent of pressure; the fluids are of small compressibility and gravity effects are negligible. Warren and Root model also assumed that the interporosity flow is at pseudo-steady state.
- Research Report > New Finding (0.34)
- Research Report > Experimental Study (0.34)
Summary. Methods are presented for matching observed pressure data during drawdown or buildup tests. The methods, illustrated with step-by-step examples, allow calculation of fracture transmissivity, storage capacity coefficient, skin, size of matrix blocks, fracture porosity, fracture storage. and radius of investigation. The effect of matrix block shapes in the transition period has been investigated by use of a stratum model, a model made of cubes with spaces between the cubes, and a model made of "matchsticks" separated by two orthogonal fracture planes. Consideration has been given to a gradient flow model as well as to unsteady-state and pseudosteady-state interporosity flow. Because many naturally fractured reservoirs are fault-related, the effect of single and intercepting sealing faults hav been investigated. Even after a match of observed pressure data is obtained, there is uncertainty about calculated parameters. Consequently, a synergetic approach integrating geologic models, logs, cores, outcrops, and well testing is the only sound procedure for evaluating naturally fractured reservoirs. Introduction Naturally fractured reservoirs have been studied intensively during the last 10 years in the geologic and engineering fields. Transient pressure analysis has received particular attention. particular attention. Barenblatt and Zheltov assumed pseudosteady-state interporosity flow in a model made of orthogonal, equally spaced fractures. Warren and Root used the same assumption and concluded that a conventional semilog plot of pressure vs. time should result in two parallel straight lines with a transition period in between. The separation of the two lines allowed calculation of the storativity ratio-i.e.. the fraction of the total storage within the fracture system. Kazemi used a numerical model of a finite reservoir with a horizontal fracture under the assumption of unsteady-state interporosity flow, substantiating Warren and Root's conclusion concerning the two parallel straight lines. The transition period, however, was different because of the unsteady-state rather than pseudosteady-state interporosity flow assumption. A breakthrough in the analysis of naturally fractured reservoirs was provided by de Swaan-O., who developed a diffusivity equation and analytic solutions to handle unsteady-state interporosity flow. This method, however, could not analyze the transition period between the two parallel straight lines. Najurieta developed approximate analytic solutions of de Swaan's radial diffusivity equation that could handle the transition period, as well as the first and late straight lines. More recently, Streltsova used a gradient flow model and indicated that the transition period yielded a straight line with a slope equal to one-half the slope of the early and late straight lines. Her examples showing the one-half slope yielded values of storativity ratio equal to 0.37, 0.26, and 0.48. Serra et al. reached the same conclusion using a stratum model for the cases in which the storativity ratio was smaller than 0.0099. Various type curves have been developed to analyze naturally fractured reservoirs with unsteady-state and pseudosteady-state interporosity flow. The curves, pseudosteady-state interporosity flow. The curves, including the pressure derivative, are valuable but must be used carefully to avoid potential errors resulting from multiple matches, especially when working by hand. This paper presents straightforward equations for well test analysis of naturally fractured reservoirs. The equations can be handled analytically and allow matching of measured pressure points. The equations are approximate but have the advantage of encompassing pseudosteady-state, unsteady-state, and gradient flow models, as well pseudosteady-state, unsteady-state, and gradient flow models, as well as matrix blocks of any shape. Comparison with results from a numerical simulator indicates that the equations presented here are valid for most cases. presented here are valid for most cases. Theory The models in this study are shown in Figs. 1 through 3. Fig. 1 shows a uniformly fractured, stratified reservoir with the distance between fractures equal to hm. Fig. 2 shows a uniformly fractured reservoir made of cubes with spaces in between. The size of each matrix block is hm. The spaces represent the fractures. Fig. 3 shows a uniformly fractured reservoir made of rectangular parallelepipeds separated by two orthogonal fractured parallelepipeds separated by two orthogonal fractured planes, or a matchstick model. In a microscopic sense. planes, or a matchstick model. In a microscopic sense. both matrix and fractures are homogeneous and isotropic. The matrix blocks have a uniform distribution throughout the reservoir. Geologically, Fig. 1 would represent a shallow reservoir (less than about 2,500 ft 176- m]) or a deep reservoir dominated by thrust faulting. Fig. 2 would be an idealization of a reservoir with regional or tectonic shear fractures cut by horizontal fractures, and Fig. 3 would represent a reservoir with regional or tectonic shear fractures that is not cut by horizontal fractures. Fluid movement toward the wellbore occurs only in the fractures. SPEFE P. 239
- Geology > Structural Geology > Fault (0.69)
- Geology > Geological Subdiscipline > Geomechanics (0.54)
Abstract This work is a rigorous evaluation of vertically fractured well responses producing fractured reservoirs. Detailed evaluation of plausible responses to be expected from short-term teats are provided. New diagnostic rules, analytical provided. New diagnostic rules, analytical procedure., and working curves are presented. The procedure., and working curves are presented. The effect of fracture length on flow patterns in the reservoir is documented. Practical issues that the analyst must be cognizant of are documented. Introduction This work, considers production via a vertically fractured well located at the center of a closed circular reservoir, accomplishes the following objectives:provides a critical evaluation of flow patterns that result as a consequence of the production of a naturally fractured reservoir via a production of a naturally fractured reservoir via a hydraulic fracture, provides for a convenient methodology to analyze well responses, and provides a simple procedure to compute long-time provides a simple procedure to compute long-time (pseudoradial and pseudosteady state) responses of a well in a closed system; the basis for our method is clearly documented and ad hoc procedures are avoided. In passing, we note that, for the systems considered here, the characteristic pressure traces of heterogeneous reservoirs or the characteristic responses of the wells produced via vertical fractures are usually not evident. Our solutions highlight the need to obtain information on the heterogeneous character of the formation prior to stimulation programs. We further note one other characteristic of fractured wells which is usually ignored. Although fractured well solutions in the literature cover a wide range of values of dimensionless fracture conductivity, the solutions are not unique once the dimensionless conductivity falls below 3 (see Ref. 1). More importantly, buildup responses for all practical purposes become insensitive to fracture half-length once the dimensionless fracture conductivity becomes less than 5. MATHEMATICAL MODEL We consider a well produced by a vertical fracture that is located at the center of a closed circular reservoir. The reservoir is assumed to be a naturally fractured system and, for purposes of discussion, we assume that the slab idealization of Kazemi and de Swaan-O is applicable (Fig. 1). The parameters that govern reservoir characteristics will parameters that govern reservoir characteristics will be denoted by ' and lamba' where ' =, (1) and ' = 12. (2) Here, h mt is the thickness of the matrix system and h ft is the thickness of the fracture system, i.e., the total thickness, h = h mt +h ft = n (h m + h f) where n is the total number of fractures. Thus, h m is the characteristic block dimension. The subscripts m and f refer to the matrix and fracture systems respectively. As is well known, if boundary effects are ignored, then three flow regimes may manifest themselves due to the heterogeneous nature of the rock: Flow Regime 1 where the well response is unaffected by the matrix system, Flow Regime 2 wherein we have unsteady flow in the fracture and the matrix systems, and Flow Regime 3 wherein the flow in the matrix system becomes pseudosteady (center line of the matrix system affects the well response). P. 565
INTRODUCTION During the last few years, there has been an explosion of information in the field of well test analysis. Because of increased physical understanding of transient fluid flow, the entire pressure history of a well test can be analyzed, not just long-time data as in conventional analysis.! It is now often possible to specify the time of beginning of the correct semilog straight line and determine whether the correct straight line has been properly identified. It is also possible to identify wellbore storage effects and the nature of wellbore stimulation as to permeability improvement, or fracturing, and perform quantitative analyses of these effects. These benefits were brought about in the main by attempts to understand the short-time pressure data from well testing, data which were often classified as too complex for analysis. One recent study of short-time pressure behavior2 showed that it was important to specify the physical nature of the stimulation in consideration of stimulated well behavior. That is, statement of the van Everdingen-Hurst infinitesimal skin effect as negative was not sufficient to define short-time well behavior. For instance, acidized {but not acid fraced) and hydraulically fractured wells did not necessarily have the same behavior at early times, even though they might possess the same value of negative skin effect.