Designed as a bridge between engineering and mathematical courses, this book introduces mathematical methods that are essential to successfully obtain a solution for engineering problems. It covers the whole gamut of starting with the physical problem, setting up the appropriate control volume, deriving the differential equations, solving the problem and finally interpreting the results.
The book starts with a review of Relations of Diffusive Flow, e.g. Darcy, Fourier and Fick’s law. Solutions to one-dimensional (1-D) steady state problems that do not require setting up a control volume are offered. In Chapter 2, time dependent processes, which do not require accounting for spatial variation, are modeled. These problems often lead to first order ODE’s. In Chapter 3, the changes with respect to space are included while those with respect to time are ignored. Different engineering problems where steady state solutions are of interest are discussed. Examples include extended surfaces in heat transfer and leak-off from hydraulically fractured wells. The last chapter deals with unsteady state processes where spatial variations are of importance. The methodologies learnt in the previous chapters will be used. Two examples include transient diffusion accompanied by reaction as it occurs in sweetening of sour gases and transient pressure propagation in petroleum reservoirs, i.e. the well-testing problem.
Numerous examples are solved in a step-by-step fashion throughout the book, including a large number of petroleum engineering problems. The reader is encouraged to predict the behavior of the solution, before solving the problem. Experience has shown that this leads to better understanding of the problem and solution; it increases the engineering sense of the students.