Synopsis

The course starts with some background to the geology, geophysics and engineering involved in the recovery of oil from deep inside the Earth. The lectures then fall into three areas:

Flow through porous media - balance laws, Darcy's law, analytical and numerical methods, upscaling.

Grid generation and geometric modelling - surface modelling, structured and unstructured grids.

Spatial Statistics - Kriging, stochastic sampling.

All topics involve much application of partial differential equations and the calculus of variations. The mathematical theory applies equally to groundwater modelling, the study of subsurface pollution and remediation, and even to problems outside the geosciences.

Reading List

• Murray R. Spiegel, Vector Analysis and an Introduction to Tensor Analysis, Schaum's Outline Series, 1959

• G.F. Carrier and C.E. Pearson, Partial Differential Equations: Theory and Technique, Academic Press, 1988

• Knupp, P.M and S.Steinberg Fundamentals of Grid Generation, CRC Press, Boca Raton, 1993

• J.J. Binney, N.J. Dowrick, A.J. Fisher and M.E.J. Newman, The Theory of Critical Phenomena, Oxford University Press, Oxford, 1992, (Appendix L in particular.)

• D.W. Peaceman, Fundamentals of Numerical Reservoir Simulation, Elsevier, 1977.

• For background
  R.C. Selley, Elements of Petroleum Geology, Academic Press, San Diego, 1998