Composite Elastic Modulus Aids Well Performance and Permeability Predictions

  IJETT-book-cover  International Journal of Engineering Trends and Technology (IJETT)          
© 2015 by IJETT Journal
Volume-29 Number-1
Year of Publication : 2015
Authors : Tom Aage Jelmert
DOI :  10.14445/22315381/IJETT-V29P203


Tom Aage Jelmert "Composite Elastic Modulus Aids Well Performance and Permeability Predictions", International Journal of Engineering Trends and Technology (IJETT), V29(1),12-17 November 2015. ISSN:2231-5381. published by seventh sense research group

A traditional analytical model for well performance predictions is based on Darcy’s law and the slightly compressible fluid assumption. The latter assumption is not consistent with the principle of conservation of mass. Quadratic gradient terms are neglected. The elastic moduli of fluid and rock may give rise to quadratic terms. Many studies investigate the effect of one or two quadratic gradient terms. The objective of the present study is to generalize the traditional model to accommodate an arbitrary number of quadratic gradient terms and to facilitate well performance and permeability predictions. The methodology depends on the assumption that each pressure dependent variable may be approximated by an exponential function of pressure or equivalently of a constant value of the corresponding elastic modulus. This assumption may be reasonable for some deep reservoirs. Then, the non-linear Darcy equation may be linearized by use of a composite elastic modulus. We find that the effect of quadratic terms cannot be overlooked for large values of the composite elastic modulus and/or large pressure differences between the outer boundary and the wellbore. Hence, we expect the generalized model to work better for deep reservoirs than for shallow ones. The technique may be extended to time dependent flow, but with reduced accuracy. The diffusivity still depends on pressure. Then, perturbation techniques may be necessary.


[1] Matthews, C. S., and Russell, D. G. Pressure Buildup and Flow Tests in wells. Monograph 1, Dallas, TX: Society of petroleum engineers of AIME, ser Henry. Doherty, 1977.
[2] Kikani, J. and Pedrosa, O.A. “Perturbation Analysis of Stress-Sensitive Reservoirs” (includes associated papers 25281 and 25292). SPE Formation Evaluation, vol. 6 , pp. 379-386, Sept. 1991.
[3] Chakrabarty, C., Ali, S. M., & Tortike, W. S. “Analytical Solutions for Radial Pressure Distribution Including the Effects of the Quadratic?Gradient Term.” Water resource research, vol. 29, pp. 1171-1177, no 4, 1993.
[4] Jelmert, T. A., and Vik, S. A. “Analytic Solution to the Non- Linear Diffusion Equation for Fluids of Constant Compressibility”. Journal of Petroleum Science and Engineering, vol. 14 , pp.231-233, no. 3, 1996.
[5] Jelmert, T. A. and Selseng, H. “Pressure transient behavior of stress-sensitive reservoirs.” SPE Latin American and Caribbean Petroleum Engineering Conference. Paper SPE 38970, 1997.
[6] S. Ai, and Y. Yao, Flow Model for Well Test Analysis of Low- Permeability and Stress-Sensitive Reservoirs, Special topics of & Reviews in Porous Media – An international journal, vol. 3, 125-128, no.2,2012
[7] Jelmert, T. A. and Selseng, H. “Permeability Function Describes Core Permeability in Stress-sensitive Rocks.” Oil and Gas Journal, vol. 96, pp. 60-62, Dec. 7, 1998.
[8] Jelmert, T.A., Torsaeter, O. and Selseng, H. and [2000] Technique Characterizes Permeability of Stress-Sensitive Reservoirs”, Oil and Gas Journal vol. 98, pp.52-60, Jun. 12, 2000.
[9] Chen, S., Li, H., Zhang, Q and Zhang, Q. “A New Technique for Production Prediction in Stress –Sensitive Reservoirs.” Journal of Canadian Petroleum Technology, vol. 47, pp. 49-54, 2008.
[10] Fang, Y., and Yang, B. “Application of New Pseudo-Pressure for Deliverability Test Analysis in Stress-Sensitive Gas Reservoir.” Asia Pacific Oil and Gas Conference & Exhibition. Society of Petroleum Engineers, Paper SPE 120141, 2009.

stress-sensitivity, well performance, permeability predictions.