Solution of temperature field problems in oil strata using integral transforms

Abstract

Heat equations related to some temperature fields in oil strata (such as exact formulation, lumped and the incomplete lumped, and the Lauwerier formulations) are discussed. We survey some oil strata problems and their solutions. The integral transform (Laplace, Hankel, generalized Hankel transforms, etc.) method is used to obtain an analytical solution of such problems. It is shown that Efros' theorem (a generalized form of the Laplace convolution) is suitable to deal with inverse transforms. Such problems are extended to include fractional derivatives and some cases of internal heat production. Numerical treatments of some fractional extensions of the temperature field problems are discussed.

Keywords:

• Hankel transform
• Laplace transform
• oil strata
• temperature fields
• convolution
• differential equations
• Efros' theorem

2010 Mathematics Subject Classifications:

• 44A10
• 44A35
• 35A22
• 44A20
• 80A20

Acknowledgements

The authors are thankful to the reviewers for their useful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.