ABSTRACT
The description of groundwater flow and the transport of solutes and heat requires the use of differential equations, with their initial and boundary conditions. Research on reservoir topics requires the solution of these equations for the hydrogeological or geothermal problem in question. Unlike a few special idealized cases with very simple geometry, finding analytical solutions for regions of arbitrary shape is impossible. In real reservoir problems, numerical mathematical methodsmust be used to obtain approximate results. Numerical techniques allow finding solutions in irregularly bounded areas or when boundary conditions vary in time as for instance, in aquifers whose space, solute, source, and sink parameters vary as fluid is extracted or injected, and in cases where energy transport varies in time. Logically, an essential condition is the availability of data describing the system. The characteristic shared by the numerical methods used is, generally speaking, the substitution of partial differential equations by systems of algebraic equations or by ordinary differential equations that can be solved by means of different algorithms. The availability of small and low-cost computers such as PCs or workstations has led to the use of powerful numerical methods to solve complex hydrogeological or geothermal problems.
