Abo Bibliothek: Guest
Digitales Portal Digitale Bibliothek eBooks Zeitschriften Referenzen und Berichte Forschungssammlungen
Journal of Porous Media
Impact-faktor: 1.752 5-jähriger Impact-Faktor: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Druckformat: 1091-028X
ISSN Online: 1934-0508

Volumes:
Volumen 24, 2021 Volumen 23, 2020 Volumen 22, 2019 Volumen 21, 2018 Volumen 20, 2017 Volumen 19, 2016 Volumen 18, 2015 Volumen 17, 2014 Volumen 16, 2013 Volumen 15, 2012 Volumen 14, 2011 Volumen 13, 2010 Volumen 12, 2009 Volumen 11, 2008 Volumen 10, 2007 Volumen 9, 2006 Volumen 8, 2005 Volumen 7, 2004 Volumen 6, 2003 Volumen 5, 2002 Volumen 4, 2001 Volumen 3, 2000 Volumen 2, 1999 Volumen 1, 1998

Journal of Porous Media

DOI: 10.1615/JPorMedia.2020033939
pages 1015-1041

SOLUTIONS AND TYPE CURVES OF A FLUID FLOW MODEL FOR NATURALLY FRACTURED RESERVOIRS WITH INFLUX RECHARGE

Luis Xavier Vivas-Cruz
Centro de Ingeniería y Desarrollo Industrial (CIDESI), Av. Playa Pie de la Cuesta 702, Desarrollo San Pablo, Querétaro, Qro, 76125, México
Jorge Adrián Perera-Burgos
CONACYT – Unidad de Ciencias del Agua, Centro de Investigación Científica de Yucatán A.C., Calle 8, No. 39, Mz. 29, S.M. 64, Cancún, Quintana Roo, 77524, México
M. A. Taneco-Hernández
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas, Cd. Universitaria Sur, Chilpancingo, Guerrero, 39087, México
Alfredo González-Calderón
CONACYT – CIDESI sede Campeche, Ctra. Carmen Puerto Real km 7.5, Mundo Maya, Cd. del Carmen, Campeche 24153, México

ABSTRAKT

Modeling of fluid flow considering radially symmetric reservoirs is common in groundwater science and petroleum engineering. The Hankel transform is suitable for solving boundary value problems, considering this flow geometry. However, there are few applications of this transform for reservoirs with a finite wellbore radius, although there are formulas of the finite Hankel transform for homogeneous boundary conditions. In this work, we refer to them as the Cinelli formulas, which are used to obtain novel solutions for transient fluid flow in bounded naturally fractured reservoirs with time-varying influx at the outer boundary, i.e., a technique to incorporate inhomogeneous boundary conditions based on the Cinelli formulas is developed. An analysis shows that the results of the solutions are highly oscillating and slowly convergent. Nevertheless, we show that this problem is largely overcome when the long-time solution is expressed as a closed relationship. Accordingly, we present the characteristic drawdown pressure curves and its Bourdet derivatives for a double-porosity reservoir with influx recharge. These curves allow us to distinguish between the pressure drops of a single-porosity reservoir with influx recharge from that of a double-porosity closed reservoir, which have been stated in the literature to resemble one another. Similarly, double- and triple-porosity reservoirs are analyzed.

REFERENZEN

  1. Ahmed, T. and McKinney, P., Advanced Reservoir Engineering, Amsterdam: Elsevier, 2011. .

  2. Babak, P. and Azaiez, J., Unified Fractional Differential Approach for Transient Interporosity Flow in Naturally Fractured Media, Adv. Water Resour., vol. 74, pp. 302-317, 2014. .

  3. Boulton, N.S. and Streltsova, T.D., Unsteady Flow to a Pumped Well in a Fissured Water-Bearing Formation, J. Hydrol., vol. 35, nos. 3-4, pp. 257-270,1977. .

  4. Bourdet, D., Well Test Analysis: the Use of Advanced Interpretation Models, vol. 3, Amsterdam: Elsevier, 2002. .

  5. Bourdet, D., Whittle, T.M., Douglas, A.A., and Pirard, Y.M., A New Set of Type Curves Simplifies Well-Test Analysis, World Oil, vol. 196, no. 6, pp. 95-106, 1983. .

  6. Bourdet, D., Ayoub, J.A., and Pirard, Y.M., Use of Pressure Derivative in Well Test Interpretation, Soc. Petrol. Eng. J, vol. 4, no. 2, pp. 293-302, 1989. .

  7. Cai, J., Mirzaei-Paiaman, A., Vafai, K., and Wang, F., Preface: Theoretical and Mathematical Modeling of Flow and Transport in Porous Media, Special Topics Rev. Porous Media: Int. J, vol. 7, no. 2, pp. v-vii, 2016. .

  8. Camacho Velazquez, R., Gomez, S., Vasquez-Cruz, M.A., Fuenleal, N.A., Castillo, T., Ramos, G., Minutti, C., Mesejo, A., and Fuentes-Cruz, G., Well-Testing Characterization of Heavy-Oil Naturally Fractured Vuggy Reservoirs, SPE Heavy and Extra Heavy Oil Conference: Latin America, Society of Petroleum Engineers, 2014. .

  9. Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford, UK: Oxford University Press, 1959. .

  10. Chen, Z.X., Transient Flow of Slightly Compressible Fluids through Double-Porosity, Double-Permeability Systems - A State-Of-The-Art Review, Transp. Porous Media, vol. 4, no. 2, pp. 147-184, 1989. .

  11. Chen, Z.X., Analytical Solutions for Double-Porosity, Double-Permeability and Layered Systems, J. Petrol. Sci. Eng., vol. 5, no. 1, pp. 1-24, 1990. .

  12. Cinelli, G., An Extension of the Finite Hankel Transform and Applications, Int. J. Eng. Sci, vol. 3, no. 5, pp. 539-559, 1965. .

  13. Clossman, P. J., An Aquifer Model for Fissured Reservoirs, Soc. Pet. Eng. J, vol. 15, no. 5, pp. 385-398,1975. .

  14. Da Prat, G., Well Test Analysis for Fractured Reservoir Evaluation, vol. 27, New York: Elsevier, 1990. .

  15. De Smedt, F., Analytical Solution for Constant-Rate Pumping Test in Fissured Porous Media with Double-Porosity Behaviour, Transp. Porous Media, vol. 88, no. 3, pp. 479-489, 2011. .

  16. Debnath, L. and Bhatta, D., Integral Transforms and Their Applications, London, New York: CRC Press, 2014. .

  17. del Angel, Y., Nunez Lopez, M., and Velasco-Hernandez, J.X., Pressure Transient Analysis with Exponential and Power Law Boundary Flux, J. Petrol. Sci. Eng., vol. 121, pp. 149-158,2014. .

  18. Doublet, L.E. and Blasingame, T.A., Decline Curve Analysis Using Type Curves: Water Influx/Waterflood Cases, Waterflood Cases, paper SPE 30774 presented at the 1995 Annual Technical Conf. and Exhibition, Dallas, Texas, pp. 1-23, 1995. .

  19. Ehlig-Economides, C.A. and Joseph, J., A New Test for Determination of Individual Layer Properties in a Multilayered Reservoir, SPE Form. Eval., vol. 2, no. 3, pp. 261-283, 1987. .

  20. Goltz, M.N. and Oxley, M.E., Analytical Modeling of Aquifer Decontamination by Pumping when Transport Is Affected by Rate-Limited Sorption, Water Resour. Res., vol. 27, no. 4, pp. 547-556, 1991. .

  21. Gomes, E. and Ambastha, A.K., An Analytical Pressure-Transient Model for Multilayered, Composite Reservoirs with Pseudosteady-State Formation Crossflow, SPE Western Regional Meeting, Society of Petroleum Engineers, pp. 221-233,1993. .

  22. Gonzalez-Calderon, A., Vivas-Cruz, L.X., and Salmeron-Rodriguez, U., Exact Analytical Solution of the Telegraphic Warren and Root Model, Transp. Porous Media, vol. 120, no. 2, pp. 433-448, 2017. .

  23. Greenberg, M.D., Advanced Engineering Mathematics, Upper Saddle River, NJ: Prentice-Hall, 1998. .

  24. Gringarten, A.C., From Straight Lines to Deconvolution: The Evolution of the State of the Art in Well Test Analysis, SPE Reservoir Eval. Eng., vol. 11, no. 1, pp. 41-62, 2008. .

  25. Hurst, W., Unsteady Flow of Fluids in Oil Reservoirs, Phys., vol. 5, no. 1, pp. 20-30, 1934. .

  26. Javandel, I. and Witherspoon, P. A., Analytical Solution of a Partially Penetrating Well in a Two-Layer Aquifer, Water Resour Res., vol. 19, no. 2, pp. 567-578, 1983. .

  27. Jiang, Q. and Gao, C., On the General Expressions of Finite Hankel Transform, Sci. China Phys. Mech, vol. 53, no. 11, pp. 2125-2130,2010. .

  28. Ju, B., Mathematical Model and Analytical Solutions for Unsteady Flow in Natural Gas Reservoirs, J. Porous Media, vol. 17, no. 4, pp. 279-285,2014. .

  29. Katz, M.L. and Tek, M.R., A Theoretical Study of Pressure Distribution and Fluid Flux in Bounded Stratified Porous Systems with Crossflow, Soc. Petrol. Eng. J, vol. 2, no. 1, pp. 68-82, 1962. .

  30. Kruseman, G.P., De Ridder, N.A., and Verweij, J.M., Analysis and Evaluation of Pumping Test Data, 2nd Ed., The Netherlands: International Institute for Land Reclamation and Improvement, 1994. .

  31. Kuhlman, K.L., Malama, B., and Heath, J.E., Multiporosity Flow in Fractured Low-Permeability Rocks, Water Resour Res., vol. 51, no. 2, pp. 848-860, 2015. .

  32. Liu, M.X. and Chen, Z.X., Exact Solution for Flow of Slightly Compressible Fluids through Multiple-Porosity, Multiple-Permeability Media, Water Resour Res., vol. 26, no. 7, pp. 1393-1400, 1990. .

  33. Lu, J., Shi, S., and Rahman, M.M., New Mathematical Models for Production Performance of a Well Producing at Constant Bottomhole Pressure, Special Topics Rev. Porous Media: Int. J., vol. 9, no. 3, pp. 261-278, 2018. .

  34. Lu, J., Owayed, J.F., Xu, J., and Rahman, M.M., An Analytical Model on Production Performance of Multiple Wells Producing at Constant Bottomhole Pressures, Special Topics Rev. Porous Media: Int. J, vol. 10, no. 1,pp. 31-48,2019a. .

  35. Lu, J., Qu, J., and Rahman, M.M., A New Dual-Permeability Model for Naturally Fractured Reservoirs, Special Topics Rev. Porous Media: Int. J, vol. 10, no. 5, pp. 485-502, 2019b. .

  36. Matthews, C.S. and Russell, D.G., Pressure Buildup and Flow Tests in Wells, vol. 1, Richardson, Texas: Society of Petroleum Engineers, 1967. .

  37. Mavor, M.J. and Cinco-Ley, H., Transient Pressure Behavior of Naturally Fractured Reservoirs, SPE California Regional Meeting, Society of Petroleum Engineers, 1979. .

  38. Moench, A.F., Convergent Radial Dispersion in a Double-Porosity Aquifer with Fracture Skin: Analytical Solution and Application to a Field Experiment in Fractured Chalk, Water Resour. Res., vol. 31, no. 8, pp. 1823-1835,1995. .

  39. Muskat, M., The Flow of Compressible Fluids through Porous Media and Some Problems in Heat Conduction, Phys, vol. 5, no. 3, pp. 71-94,1934. .

  40. Nie, R.S., Meng, Y.F., Jia, Y.L., Zhang, F.X., Yang, X.T., and Niu, X.N., Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir, Transp. Porous Media, vol. 92, no. 1, pp. 213-235,2012. .

  41. Ozkan, E. and Raghavan, R., Some New Solutions to Solve Problems in Well Test Analysis: Part 1-Analytical Considerations, SPE J., pp. 1-63,1988. .

  42. Poularikas, A.D., Transforms and Applications Handbook, London, New York: CRC Press, 2010. .

  43. Prats, M., Interpretation of Pulse Tests in Reservoirs with Crossflow between Contiguous Layers, SPE Form. Eval., vol. 1, no. 5, pp. 511-520, 1986. .

  44. Russell, D.G. and Prats, M., Performance of Layered Reservoirs with Crossflow-Single-Compressible-Fluid Case, Soc. Petrol. Eng. J, vol. 2, no. 1, pp. 53-67, 1962. .

  45. Shah, P.C. and Thambynayagam, R.K.M., Transient Pressure Response of a Well with Partial Completion in a Two-Layer Crossflowing Reservoir, SPE Annual Technical Conf. and Exhibition, Society of Petroleum Engineers, pp. 213-225, 1992. .

  46. Shanks, D., Non-Linear Transformations of Divergent and Slowly Convergent Sequences, Stud. Appl. Math, vol. 34, nos. 1-4, pp. 1-42, 1955. .

  47. Singhal, B.B.S. and Gupta, R.P., Applied Hydrogeology of Fractured Rocks, New York: Springer Science & Business Media, 2010. .

  48. Sneddon, I.N., On Finite Hankel Transforms, London, Edinburgh Dublin Philos. Mag. J. Sci., vol. 37, no. 264, pp. 17-25,1946. .

  49. Stehfest, H., Algorithm 368: Numerical Inversion of Laplace Transforms [D5], Commun. ACM, vol. 13, no. 1, pp. 47-49, 1970. .

  50. Tong, D. and Hu, H., Flow Analysis of Non-Newtonian Viscoelastic Fluids in Porous Media, J. Porous Media, vol. 13, no. 5, pp. 477-486,2010. .

  51. Uldrich, D.O. and Ershaghi, I., A Method for Estimating the Interporosity Flow Parameter in Naturally Fractured Reservoirs, Soc. Petrol. Eng. J, vol. 19, no. 5, pp. 324-332, 1979. .

  52. van Everdingen, A.F. and Hurst, W., The Application of the Laplace Transformation to Flow Problems in Reservoirs, J. Petrol. Technol., vol. 1, no. 12, pp. 305-324, 1949. .

  53. Wang, D., Yao, J., Cai, M., and Liu, P., Transient Pressure and Productivity Analysis in Carbonate Geothermal Reservoirs with Changing External Boundary Flux, Therm. Sci., vol. 21, no. 1, pp. S177-S184, 2017. .

  54. Wang, X. and Gong, Y., An Elastodynamic Solution for Multilayered Cylinders, Int. J. Eng. Sci., vol. 30, no. 1, pp. 25-33,1992. .

  55. Warren, J.E. and Root, P. J., The Behavior of Naturally Fractured Reservoirs, Soc. Petrol. Eng. J, vol. 3, no. 3, pp. 245-255,1963. .

  56. Wu, Y.S., An Approximate Analytical Solution for Non-Darcy Flow Toward a Well in Fractured Media, Water Resour. Res., vol. 38, no. 3, pp. 1-7, 2002. .

  57. Wu, Y.S., Ehlig-Economides, C., Qin, G., Kang, Z., Zhang, W., Ajayi, B., and Tao, Q., A Triple-Continuum Pressure-Transient Model for a Naturally Fractured Vuggy Reservoir, SPE J., 2007. .

  58. Xi, W. and Yuning, G., A Theoretical Solution for Axially Symmetric Problems in Elastodynamics, Acta Mech. Sin.-PRC, vol. 7, no. 3, pp. 275-282, 1991. .

  59. Yao, Y., Wu, Y.S., and Zhang, R., The Transient Flow Analysis of Fluid in a Fractal, Double-Porosity Reservoir, Transp. Porous Media, vol. 94, no. 1, pp. 175-187,2012 .

  60. Young, R., Pressure Transients in a Double-Porosity Medium, Water Resour. Res., vol. 28, no. 5, pp. 1261-1270, 1992. .

  61. Zhang, X. and Tong, D., A Generalized Weber Transform and Its Inverse Formula, Appl. Math. Comput., vol. 193, no. 1, pp. 116-126, 2007. .

  62. Zhou, Q., Oldenburg, C.M., and Rutqvist, J., Revisiting the Analytical Solutions of Heat Transport in Fractured Reservoirs Using a Generalized Multirate Memory Function, Water Resour. Res., vol. 55, no. 2, pp. 1405-1428, 2019. .


Articles with similar content:

NONLINEAR SEEPAGE MODEL FOR MULTIPLE FRACTURED HORIZONTAL WELLS WITH THE EFFECT OF THE QUADRATIC GRADIENT TERM
Journal of Porous Media, Vol.21, 2018, issue 3
Ping Guo, Junjie Ren
PRODUCTIVITY INDEX FOR DARCY AND PRE-/POST-DARCY FLOW (ANALYTICAL APPROACH)
Journal of Porous Media, Vol.20, 2017, issue 9
Lidia Bloshanskaya, Akif Ibragimov, Mohamed Y Soliman, Fahd Siddiqui
POWER-LAW FLUID PRESSURE BEHAVIOR IN HOMOGENOUS RESERVOIR WITH SPHERICAL FLOW
Special Topics & Reviews in Porous Media: An International Journal, Vol.5, 2014, issue 3
Iwayemi Olanorin, Alpheus O. Igbokoyi
WATER TABLE FLUCTUATIONS IN A SLOPING AQUIFER: ANALYTICAL EXPRESSIONS FOR WATER EXCHANGE BETWEEN STREAM AND GROUND-WATER WITH SURFACE INFILTRATION
Journal of Porous Media, Vol.13, 2010, issue 4
Rajeev K. Bansal, Samir K. Das
PRESSURE TRANSIENT RESPONSE OF PARTIALLY FRACTURED RESERVOIRS
Special Topics & Reviews in Porous Media: An International Journal, Vol.4, 2013, issue 1
Sakineh Shakerinezhad, Feridun Esmaeilzadeh, Fereshteh Samadi