Composite Elastic Modulus Aids Well Performance and Permeability Predictions
|International Journal of Engineering Trends and Technology (IJETT)||
|© 2015 by IJETT Journal|
|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. www.ijettjournal.org. 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.
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stress-sensitivity, well performance, permeability predictions.