Notice also, during the anomaly, for all cases, the intercept of the pressure derivative curve is always higher than 0,5 (for dual-linear flow). Escobar (2008) presented a summary of the advances in characterization of long and homogenous reservoirs using transient pressure analysis. Step 9 - Estimate the total skin factor with Equations 21. Their well test analysis was performed by non-linear regression analysis and no interpretation technique was presented. [Links], Massonet, G. J., Norris, R. J., & Chalmette, J-C. (1993). Palabras clave: linear flow, radial flow, permeability, pressure tests, deposits facies. The intercept of the pseudo-linear flow regime pressure derivative reduces as the reservoir width increases, see Figure 6, and increases as permeability increases, Figure 7. All the examples were also worked by Escobar et al. Estimate reservoir width and reservoir area with Equations 3b and 3c, respectively. The reservoir width changes during dual-linear flow are correlated (R2=0,9999) by: b) Anomaly occurs after thw dual-linear flow ends. For reservoir width changes, replace the dimensionless quantities given by Equations 2b, 2c and 2e in Equation 4a and solve for the value of the reservoir width in the other side of the reservoir variation, YE,pL: During radial flow regime, the dimensionless pressure derivative value is 0,5. A., & Hernndez, C. M. (2007a). Calgary, Alberta, Canada, 15-18 March. At the intercept of this line with the pseudo-linear pressure derivative line, tRlPi, given by Equation 4a, after replacing the dimensionless quantities, will result the following expression: The pseudo-linear skin factor is obtained by dividing Equation 4b by 4a and solving for spL.
This means the reservoir was assumed to have a perfect rectangular shape. 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. (2007a) developed the below given expressions to estimate reservoir width, drainage area and dual-linear skin factor. Many buildup and drawdown pressure tests are run in elongated reservoir systems. Eng.., Vol 12, 171-181. Pressure Transient Analysis of Wells in Very Long Narrow reservoirs. Por ende, se desea identificar y caracterizar estos tipos de sistemas, lo que conducir a decisiones competentes y una adecuada gerencia del yacimiento. 
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. Sci. [Links], Escobar, F. H., Muoz, O. F., Seplveda, J. However, they called it "dipolar flow". Symp. In this case, the pressure derivative always shifts upwards. Straight Line Methods for Estimating Permeability or Width for Two-Zone Composite Channelized Reservoirs. 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. SPE 15421. Also read the intersection points of the pseudo-linear flow line with the radial line, tRpLi, and with the late pseudosteady-state line, tpLPPSi. Later, Escobar & Montealegre (2006) studied the impact of the geometric skin factors on elongated systems. Solution. 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. (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. Once dual-linear flow vanishes, it is observed in Figures 1 that as permeability increases pressure derivative also increases and so does its intercept. 48 (467): 365-379. [Links], Wong, D. W., Mothersele, C. D., Harrington, A. G., & Cinco-ley, H. (1986). In the first simulated example, the expected permeability value was 140 md.
Since the pressure derivative during late-time pseudosteady state regime is given by. 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. This last one has been lately presented for homogeneous and constant width reservoirs. A., & Montealegre, M. (2005). 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. Determine the value of permeability at the other side of the anomaly, reservoir area and total skin factor. e-mail: fescobar@usco.edu.co matildelina2005@hotmail.com dcarrillom@pep.pemex.com, (Received, Jan. 29, 2010; Accepted May 26, 2010), * To whom correspondence may be addressed. SPE Latin American and Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, April 15-18. Use this new value in Equations 10 and 12 to determine geometric skin factor and reservoir area. The first solution to water influx in a linear aquifer was presented by Miller (1966). (1985). Then, appropriate versions of the equations to estimate reservoir width and skin factors were provided. The synthetic examples were provided to verify the accuracy of the equations and the overall methodology. As observed in Figures 5 and 6, the shifting upwards or downwards of the pressure derivative curves is a function of the gradual change in either reservoir width or mobility. 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. J. [Links], Raghavan, R. & Chu, W.C., (1966). Contrary to case i, the intercept takes values lesser than 0,5. It is worth to clarify that still linear flow is dealt with since the streamline vector are yet parallel. Pressure Transient Analysis for Long Homogeneous Reservoirs using TDS Technique. Other results are summarized in Table 3. Many reservoirs in the Magdalena River Valley Basin in Colombia, South America, display channelized behavior due to, probably, fluvial deposition. 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). The results of changes in permeability and width agree with those reported by Escobar et al. 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. Recent Advances in Well Test Analysis for Long an Narrow Reservoirs, 431pp. Several simulation experiments were run to understand the behavior of the reservoir under these new conditions. [Links], Nutakki, R. & Mattar, L. (1982). Their governing pressure equation possesses a wrong constant but they provided the first mathematical insights to work on long and narrow reservoir systems and provided a conventional straight-line methodology for well test interpretation. The effect of changes in reservoir width is shown in Figure 2. In this case, the single-linear flow regime characterized by a dimensionless intercept of. 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. Derivative Analysis without Type Curves. We estimated 144,9 md, instead. (2009). 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. The following information was read from Figure 12. Key words: flujo lineal, flujo radial, permeabilidad, pruebas de presin, yacimientos, facies. CT&F - Ciencia, Tecnologa y Futuro. Escobar et al. A pressure buildup test was run in a an oil well inside a small reservoir located in the Magdalena River Middle Valley Basin in Colombia, South America. This new line may not be referred as linear flow regime because it is really not. SPE 25423. Sci. 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). Petrol. 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. An average reservoir width value of 595,5 ft was found for this example. Therefore, it is desirable to identify and characterize these types of systems which lead to competent decisions and adequate reservoir management. SPE Western Regional Meeting, Anchorage, Alaska. The respective pressure derivative equations only differ on the intercept value. Ehlig-Economides & Economides (1985) presented an analytical solution for linear flow to a constant-planar source solution in drawdown tests. An absolute deviation of 3,5 % was obtained. Edited by Korin L. Montclaire. Determination of Areal Anisotropy from a single vertical Pressure Test and Geological Data in Elongated Reservoirs. This behavior is clearly seen in Figures 1 to 4. Se corrieron varios experimentos numricos para entender el comportamiento de un yacimiento bajo estas nuevas condiciones. 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. [Links], El-Banbi, A. H., & Wattenberger, R. A. Table 1 contains the input information for the simulation.
As reported in Table 4, along with more results, we found that the reservoir width increases from 112 ft to 155 ft. Nova Publishers. SPE 106922. and Applied Sciences, 2 (11): 1627-1639. As shown in Figure 13, the reservoir looks to have an elongated shape with variations in reservoir width. SPE 26464. 
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). The intercept of the pressure derivative curve during dual-linear flow regime has a value of 0,5, Equation 1c, and the intercept of the single-linear flow pressure derivative curve is , Equation 1d. The following information was read from Figure 14. Ehlig-Economides, C., & Economides, M. J. CT&F - Ciencia, Tecnologa y Futuro. For higher changes than the ones shown in here, the half-slope line may not be seen; therefore, the proposed methodology will not apply. Due to geologic and tectonic events many reservoirs have an elongated geometry in which dual-linear and single-linear flow regimes may be developed. Also, Escobar, Tiab & Tovar (2007b) provided a way to estimate reservoir anisotropy when reservoir width is known in the mentioned systems from the combination of information obtained from the linear and radial flow regimes. Si el cambio de los parmetros mencionados toma lugar cuando termina el flujo dual lineal se observar una nueva pendiente de en la curva de la derivada de presin. New Flow Regimes for Well Near-Constant- Pressure Boundary. New Finding on Pressure Response In Long, Narrow Reservoirs. In all the above systems, the reservoir geometry was considered to be constant. Debido a eventos geolgicos y tctnicos muchos yacimeintos presentan geometra alargada en la cual se pueden desarrollar los flujos dual lineal y lineal nico. Eng. It is required to determine the variation in reservoir width and total skin factor. It is necessary to account for an appropriate identification and determination of reservoir parameters, including dimensions, when that is possible. CT&F - Ciencia, Tecnologa y Futuro. Characterization of pressure tests in elongated systems using the conventional method was presented by Escobar & Montealegre (2007). We tried to solve this problem using the non-linear regression analysis method of a commercial well test interpretation software. SPE 11221. If any of these intercepts is different, we are not referring to these specific flow regimes but others. In this paper, an extension of the TDS technique to incorporate variations in either mobility or reservoir width is presented. [Links], Escobar, F. H., Tiab, D., & Tovar, L. V. (2007b). 
Case i. 57th Annual Fall Technical Conference and Exhibition of the Society of Petroleum Engineers, Dallas, TX. 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. Solution. The following information was obtained from Figure 11. Only in the first problem the value of the pseudolinear skin factor was lower than the dual-linear skin factor. 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. In that study, the single-linear flow regime equation is modified with some correction factors to account for the mentioned variations. Paper 97-51, 48th Annual Technical Meeting of the Petroleum Society, Calgary, Alberta, Canada. Determine the other value of reservoir width, reservoir area and total skin factor. (3) 3, 137-146. 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. Theory of Unsteady-State Influx of Water in Linear Reservoirs, J. Inst. 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. (3) 5, 107-124. 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. The pressure and pressure derivative plot is provided in Figure 14.
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 %. En este trabajo, se extiende la metodologa TDS para incorporar variaciones ya sea en movilidad o ancho del yacimiento. Pressure Transient Analysis in Finite Linear Reservoirs Using Derivative and Conventional Techniques: Field Examples, 61st Annual technical Conference and Exhibition of the Society of Petroleum Engineers, New Orleans, LA. 58 (1-2): 68-82. [Links], Escobar, F. H., Hernndez, Y. 
Then, find from Equation 5. (1998). On the Determination of Reservoir Pressure when Radial-Flow Conditions are Nonexistent, Gas Technology Conference, Calgary, Alberta, Canada. (2) 6, 106-111. 1998 Gas Tech. Analysis of Pressure and Pressure Derivatives without Type-Curve Matching-III. 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. This new line is shifted upwards the original dual-linear line without regarding the variation of one of the studied parameter.
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. Analysis of Pressure and Pressure Derivative without Type-Curve Matching: 1- Skin and Wellbore Storage. For all cases when the intercept of the half-slope line results different to , it cannot be referred as single-linear flow regime. They used type-curve matching and conventional techniques to solve some field data examples. A Complementary Conventional Analysis For Channelized Reservoirs. We have named it as pseudo-linear flow regime, instead. 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 %. [Links], Escobar, F. H., Montealegre-M., M., & Carrillo-Moreno, D. (2009). 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. Case ii. For reductions in reservoir width, there will be an increase in the pressure derivative curve over the single-linear flow straight-line pressure derivative. Finally, the present work complements the research recently presented by Escobar et al. Using this new value in Equations 15, 16 and 17 to compute reservoir width, geometric skin factor and reservoir area, respectively. (2009). [Links], Tiab, D. (1993). SPE 39972. Out of this range, the 0,5-slope line may not be seen. Linear flow regimes will develop during a transient pressure tests in this specific geometry. This behavior is observed in Figure 5. Effect of Well Stimulation on the Skin Factor in Elongated Reservoirs.
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