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In this case, also, the governing pressure equations for the linear flow regimes were modified with some correction factors to account for the variations of either permeability or reservoir width. SPE 25423. (3) 3, 137-146. It is required to determine the variation in reservoir width and total skin factor. Besides, for an increment in reservoir permeability, the intercept of the half-slope pressure derivative curve is always greater than and gets lower than that for reductions of reservoir permeability. Palabras clave: linear flow, radial flow, permeability, pressure tests, deposits facies. The first solution to water influx in a linear aquifer was presented by Miller (1966). 1998 Gas Tech. They also corrected the pressure equation provided by Nutakki & Mattar (1982) and classified the linear flow regime in to two cathegories: (a) dual-linear flow regime when the flow takes along both sides of the well thoughtout the elongated reservoir part, and (b) single-linear flow regime when flow comes from one side of the reservoir. The reservoir width changes during dual-linear flow are correlated (R2=0,9999) by: b) Anomaly occurs after thw dual-linear flow ends. Well Test Interpretation in Geologically Complex Channelized Reservoirs, 68th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers. Since the pressure derivative during late-time pseudosteady state regime is given by. Analysis of Pressure and Pressure Derivatives without Type-Curve Matching-III. [Links], Escobar, F. H., Tiab, D., & Tovar, L. V. (2007b). Step 2 - Estimate wellbore storage coefficient, permeability, skin factor and reservoir area using Equations 13, 18, 19 and 20, respectively, as indicated by Tiab (1993-1995). [Links], Sui, W., Mou, J. Bi, L., Den, J., & Ehlig-Economides, C. (2007). Case i. [Links], Tiab, D. (1993). If the change of the mentioned parameters takes place after the dual- linear flow has ended a new half-slope line is observed on the pressure derivative curve. Determine the value of permeability at the other side of the anomaly, reservoir area and total skin factor. Several simulation experiments were run to understand the behavior of the reservoir under these new conditions. [Links], Mattar, L. (1997). Escobar et al. Figure 8 shows a perfect behavior between these parameters with respect to the shifting of the pressure derivative. [Links], All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License, Ecopetrol S.A, Centro de Innovacin y Tecnologa- ICP, Consejo Editorial CT&F, The TDS technique was extended to characterize elongated oil formations (channels) for vertical oil wells when either variations in mobility or reservoir width are presented. [Links], Escobar, F. H., Muoz, O. F., Seplveda, J. Eng.., Vol 12, 171-181. Use this new value in Equations 10 and 12 to determine geometric skin factor and reservoir area. We separated the study in two parts to consider the variation or anomaly for: i) once dual-linear flow has ended, Figures 1 to 5, and ii) during dual-linear flow regime, Figures 6 and 7. Escobar, Hernndez & Hernndez (2007a) introduced the application of the TDS technique for characterization of long and homogeneous reservoirs presenting new equations for estimation of reservoir area, reservoir width and geometric skin factors. In all the above systems, the reservoir geometry was considered to be constant. Analysis of Linear Flow in Gas Well Production. All the examples were also worked by Escobar et al. The following information was read from Figure 12. When, the anomaly occurs during dual- linear flow the new half-slope line of the pressure derivative curve may be shifted upwards or downwards depending upon the magnitude of either mobility or reservoir width. These deviations lead to confirm that the formulated equation are correct and, then, may be applied to field cases, such as the third worked example. Houston, TX. Also read the intersection points of the pseudo-linear flow line with the radial line, tRpLi, and with the late pseudosteady-state line, tpLPPSi. 48 (467): 365-379. Step 6 - According to the most probable situation, case i or ii, estimate the multiplier factor, FM, using either Equations 6a, 6b, 7a or 7b. However, the numerical modeling does not account yet for the variations in reservoir width, as used in this paper, therefore, the goal was not achieved. An average reservoir width value of 595,5 ft was found for this example. Determine the other value of reservoir width, reservoir area and total skin factor. We tried to solve this problem using the non-linear regression analysis method of a commercial well test interpretation software. Step 7 - For the case of change in permeability find the new permeability value, kpL, with Equation 14. [Links], Escobar, F. H., & Montealegre, M. (2006). The Petroleum Society. A pressure and pressure derivative plot for a channelized reservoir in which reservoir width change from 400 to 600 ft is presented in Figure 12. Then, a plateau in the pressure derivative is observed between 30 and 90 hr which may indicate that the reservoir width increase more, as occurred in Figure 5. Due to geologic and tectonic events many reservoirs have an elongated geometry in which dual-linear and single-linear flow regimes may be developed. Step 5 - Read the pressure and pressure derivative values, PpL and (t*P')pL, at any convenient point on the pseudo-linear flow regime, tpL. (3) 5, 107-124. New Finding on Pressure Response In Long, Narrow Reservoirs. 58 (1-2): 68-82. J. La metodologa propuesta se verific satisfactoriamente aplicndola a ejemplos de campo y sintticos en yacimientos elongados que involucran cambios en movilidad o ancho del yacimiento durante el camino de la onda de transiente de presin. The identification and determination of parameters for such reservoirs are conducted by conventional techniques (straight-line method), type-curve matching of pressure versus time and the Tiab's Direct Synthesis (TDS) technique. e-mail: [email protected] [email protected] [email protected], (Received, Jan. 29, 2010; Accepted May 26, 2010), * To whom correspondence may be addressed. We have named it as pseudo-linear flow regime, instead. Edited by Korin L. Montclaire. If any of these intercepts is different, we are not referring to these specific flow regimes but others. The single-linear flow may be altered by changes in facies (mobility) or reservoir width (composite reservoir). Linear flow regimes will develop during a transient pressure tests in this specific geometry. SPE 26464. Permeability changes during dual linear flow are given by the following correlation (R2=0,9998): Notice that the pressure derivative values during the dual-linear and pseudo-linear flow regimes must be read at the same time, txt, of course, at least one of the half-slope line has to be extrapolated. 0,29293 is the dimensionless intercept of the pseudo-linear line. Case ii. La identificacin y determinacin de parmetros para tales sistemas se conduce mediante tcnicas convencionales (mtodo de la lnea recta), curvas tipo de presin versus tiempo y la tcnica de la sntesis directa de Tiab (TDS). Figure 11 shows the pressure and pressure derivative plot for an elongated reservoir in which a variation in permeability from 100 md to 140 md was considered. They called this as parabolic flow. On the Determination of Reservoir Pressure when Radial-Flow Conditions are Nonexistent, Gas Technology Conference, Calgary, Alberta, Canada. According to Figure 9, the developed correlation (R2=0,9999)is: Permeability changes after dual-linear flow can be estimated only for variations of 60 % < k < 140 %. In the first simulated example, the expected permeability value was 140 md. Petroleum Science Research Progress. (2009) to include the application of the pressure and pressure derivative for well test interpretation without the application of type-curve matching, also known as the TDS Technique. SPE 11221. In this case, the single-linear flow regime characterized by a dimensionless intercept of. Sci. [Links], Wong, D. W., Mothersele, C. D., Harrington, A. G., & Cinco-ley, H. (1986). This means the reservoir was assumed to have a perfect rectangular shape. The synthetic examples were provided to verify the accuracy of the equations and the overall methodology. Once dual-linear flow vanishes, it is observed in Figures 1 that as permeability increases pressure derivative also increases and so does its intercept. The following information was obtained from Figure 11. (1998). CT&F - Ciencia, Tecnologa y Futuro. For more than one increasing in reservoir width, a plateau in the pressure derivative may be seen due to the change in path of the streamlines. By integration of the above equation will result: The determination of in the above equations requires to establish the intercept of the straight line in dimensionless form plus an appropriate correction to account for either changes in permeability (or mobility) or reservoir width. Raghavan & Chu (1966) presented a method to estimate average pressure when radial flow conditions are nonexistent for linear and bilinear flow regimes which may be applicable to channel reservoirs. [Links], Escobar, F. H., Hernndez, Y. The results of changes in permeability and width agree with those reported by Escobar et al. Vertically Fractured Wells in Closed Systems. Their well test analysis was performed by non-linear regression analysis and no interpretation technique was presented. As reported in Table 4, along with more results, we found that the reservoir width increases from 112 ft to 155 ft. Analysis of Pressure and Pressure Derivative without Type-Curve Matching: 1- Skin and Wellbore Storage. Estimation of the intercept of this straight line is achieved by: The multiplier factor, FM, is found according to: a) Anomaly occurs during dual-linear flow. Calgary, Alberta, Canada, 15-18 March. Then, find from Equation 5. Then, using any arbitrary point during this straight line, with coordinates tpL and (t*P')pL, the governing equation of this new regime may developed. Normally, the intercept of the dual-linear flow regime is higher than the other half-slope line, with a few exceptions. New Flow Regimes for Well Near-Constant- Pressure Boundary. The proposed methodology was successfully verified by interpreting both synthetic and field pressure tests for elongated oil reservoirs which involve changes in either mobility or reservoir width during the path of the transient wave. In the second synthetic example the expected value of reservoir width was 600 ft. We obtained an average reservoir width value of 595,5 ft indicating an absolute deviation of 0,75 %. This new line may not be referred as linear flow regime because it is really not. Solution. The effect of changes in reservoir width is shown in Figure 2. Por tanto, hay que considerar una modificacin del intercepto de la linea de pendiente de de 0,5 para flujo dual lineal a un valor mayor o menor, el cual es diferente de (caso de flujo lineal nico) para proporcionar nuevas ecuaciones para la estimacin de nuevos valores de permeabilidad o ancho del reservorio. We estimated 144,9 md, instead. SPE 39972. Pressure Transient Analysis of Wells in Very Long Narrow reservoirs. To alleviate this assumption, Escobar, Montealegre & Carrillo- Moreno (2009) presented a solution for the dertemination of changes in either permeability or width in channelized systems using the conventional straight-line method. Only in the first problem the value of the pseudolinear skin factor was lower than the dual-linear skin factor. Then, appropriate versions of the equations to estimate reservoir width and skin factors were provided. [Links], Raghavan, R. & Chu, W.C., (1966). For all cases when the intercept of the half-slope line results different to , it cannot be referred as single-linear flow regime. Many buildup and drawdown pressure tests are run in elongated reservoir systems. Wong, Mothersele, Harrington & Cinco-ley (1986) presented new type curves to interpret pressure transient analysis for rectangular reservoirs. (2009). Characterization of pressure tests in elongated systems using the conventional method was presented by Escobar & Montealegre (2007). venous accessanesthesiology Nova Publishers. En este trabajo, se extiende la metodologa TDS para incorporar variaciones ya sea en movilidad o ancho del yacimiento. Petrol. Step 9 - Estimate the total skin factor with Equations 21. This means that the following correlation applies for pressure derivative ratios greater than 1. In this paper, an extension of the TDS technique to incorporate variations in either mobility or reservoir width is presented. El flujo lineal sencillo podra ser alterado por cambios en facies (movilidad) o cambios del ancho del yacimiento (yacimiento compuesto). CT&F - Ciencia, Tecnologa y Futuro. At the point of intersection, referred here as tpLpssi, between this line with the pseudo-linear pressure derivative line will result the following equation once the dimensionless variables have been replaced: Also, the intersection of the radial line with the pseudosteady-state line at a time called tRPSSi, will provide another equation for reservoir drainage area after plugging the dimensionless variables: For changes in permeability, Equations 8, 9, 10 and 12 become: Tiab (1993, 1995) presented the following relationships for the estimation of wellbore storage coefficient, reservoir permeability and skin factor: Finally, the total damage results as the summation of the mechanical plus the geometric skin factors, such as: Step 1 - Build a log-log plot of pressure and pressure derivative, identify and draw the early pseudosteady- state, radial, dual-linear, pseudo-linear and late pseudosteady-state lines. SPE 26138. Se corrieron varios experimentos numricos para entender el comportamiento de un yacimiento bajo estas nuevas condiciones. This may be due to the increase in permeability since no change in the transient path is expected to happen. As seen in the dimensionless pressure derivative plot of Figures 1 through 6, another half-slope straight line is observed after the dual-linear flow regime vanishes which is not considered to be the linear flow regime, instead we have call it here as "pseudo linear" flow and it is labeled with suffix pL. Escobar, Muoz, Seplveda & Montealegre (2005) introduced a new flow regime exhibiting a negative half slope on the pressure derivative curve once duallinear flow has ended. An absolute deviation of 3,5 % was obtained. $seepage reservoirs fractured vuggy$ However, they called it "dipolar flow". Paper 97-51, 48th Annual Technical Meeting of the Petroleum Society, Calgary, Alberta, Canada. According to the pressure derivative plot, Figure 14, the radial flow regime shows up at about 1 hr and lasts a couple of hours. geosciences disciplines turnkey services opc drilling subsurface engineering specialist The respective pressure derivative equations only differ on the intercept value. This new line is shifted upwards the original dual-linear line without regarding the variation of one of the studied parameter. Therefore, a modification of the intercept of the -slope line from 0,5 for dual-linear flow regime to a greater or smaller value, which may be different from (single-linear flow case) has to be considered in order to provide new equations for the estimation of new values of either permeability or reservoir width.