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Partial-differential equations (PDEs) that describe fluid flow dynamics in porous media can be linear or nonlinear equations; however, they are always composed of only first-order and second-order derivatives. Therefore, good understanding of basic differential calculus forms the backbone of reservoir modeling of recovery processes.

The definition of a first-order derivative of a continuous function, f, is given by

(3.1)

If function f is a continuous function of the independent variables x and y and expressed as f = f(x, y), then

(3.2a)
(3.2b)

Eqs. 3.2a and 3.2b represent the first-order partial derivatives of function f(x, y) with regard to x and y, respectively.

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