Pressure derivative analysis for naturally-fractured reservoirs with partial constant-pressure boundary
Abstract
The complexity of conventional resources is increasing, and, therefore an optimum characterization is required. Existing models to study pressure behavior in heterogeneous formations consider only either constant-pressure or closed boundaries. In this paper the pressure derivative for a vertical oil well in a naturally fractured reservoir with a variable open external boundary is analyzed. The parameters governing the pressure response are: final flow rate at the external boundary (qWI) and time at which begins the invasion of fluid at the external boundary (τ), depending on its variability of these parameters, there are three conditions in which the external border acts: closed, partially open and constant-pressure. Lines and characteristic points were identified for each indi- vidual case to obtain the fundamental basis to generate the equations for the determination of the parameters that describe this type of reservoirs, such as: qWI and τ. Finally, the TDS technique was extended to interpret pressure tests in these systems. The methodology was satisfactorily verified by solving synthetic examples.
References
Barenblatt, G., Zheltov, Y., y Kochina, I. (1960). Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks (strata). Journal of applied mathematics and mechanics, 24(5), 1286-1303.
Del Angel, Y., Núñez-López, M., y Velasco-Hernández, J. (2014). Pressure transient analysis with exponential and power law boundary flux. Journal of Petroleum Science and Engineering, 121, 149-158.
Engler, T., y Tiab, D. (1996a). Analysis of pressure and pressure derivative without type curve matching, 4. Naturally fractured reservoirs. Journal of Petroleum Science and Engineering, 15(2-4), 127–138.
Engler, T., y Tiab, D. (1996b). Analysis of pressure and pressure derivative without type-curve matching, 5. Horizontal well tests in naturally fractured reservoirs. Journal of Petroleum Science and Engineering, 15(2-4), 139–151.
Escobar, F., Sanchez, J., y Cantillo, J. (2008). Rate transient analysis for homogeneous and heterogeneous gas reservoirs using the TDS technique. Ciencia, Tecnología y Futuro, 4(4), 45-59.
Escobar, F., Hernandez, D., y Saavedra, J. (2010). Pressure and pressure derivative analysis for long naturally fractured reservoirs using the TDS technique. Dyna, 77(163), 102-114.
Escobar, F., Zambrano, A., Giraldo, D., y Cantillo, J. (2011). Pressure and pressure derivative analysis for non-newtonian pseudoplastic fluids in double-porosity formations. Ciencia, Tecnología y Futuro, 5(3), 47-59.
Escobar, F., Zhao, Y., y Zhang L. (2014). Interpretation of pressure tests in horizontal wells in homogeneous and heterogeneous reservoirs with threshold pressure gradient. Journal of Engineering and Applied Sciences, 9(11), 2220-2228.
Escobar, F., Camacho, R., y Rojas, J. (2014). Pressure and pressure derivative analysis for tripleporosity and dual-permeability systems in naturally fractured vuggy reservoirs. Journal of Engineering and Applied Sciences, 9(12), 2500-2512.
Hsieh, B., Chilingar, G., y Lin, Z. (2007). Propagation of radius of investigation from producing well. Energy Sources, Part A, 29(5), 403-417.
Hsieh, B., Chilingar, G., y Lin, Z. (2008). Determination of the constant coefficient in pressure propagation equation. Energy Sources, Part A, 30(13), 1223-1232.
Mathews, C., y Russell, D. (1967). Pressure buildup and flow tests in wells (SPE Monograph Series, vol. 1). Dallas, EE. UU.: Society of Petroleum Engineers of AIME
Pascal, H., y Pascal, F. (1985). Flow of non-Newtonian fluid through porous media. International Journal of Engineering Science, 23(5), 571-585.
Tiab, D. (1993, 1 enero). Analysis of Pressure and Pressure Derivatives Without Type-Curve Matching: I-Skin and Wellbore Storage. En Society of Petroleum Engineers, SPE Production Operations Symposium. Conferencia llevada a cabo en Oklahoma, EE. UU. doi: 10.2118/25426-MS.
Tiab, D. (1995). Analysis of pressure and pressure derivative without type-curve matching: I-skin and wellbore storage. Journal of Petroleum Science and Engineering, 12(3), 171-181.
Van Everdingen, A., y Hurst, W. (1949). The application of the laplace transformation to flow pro- blems in reservoirs. Journal of Petroleum Technology, 1(12), 305-324b. doi:10.2118/949305-G.
Wang, D., Yao, J., Cai, M., y Liu, P. (2015). Transient pressure and productivity analysis in dual medium reservoir with changing outer boundary flux (artículo inédito remitido para su publicación a Journal of Natural Gas Science Engineering).
Warren, J., y Root, P. (1963). The Behavior of Naturally Fractured Reservoirs. Society of Petroleum Engineers Journal, 3(3), 245-255. doi: 10.2118/426-PA.








