**Donald W. Peaceman**

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In this essay, Donald Peaceman begins with a discussion of the early history of reservoir modeling and recalls some of the excitemnt of discovery. Prior to 1951, when Peaceman arrived at Humble Oil and Refinery Company (a subsidiary of Standard Oil of New Jersey), physical analog and some early mathmatical models were in use. The latter were based on infinite series solutions of the Laplace and heat equations in ideal geometries. When he arrived, Henry Rachford and John Rice were experimenting with finite difference methods on an IBM 604. Peaceman discusses collaborations with Rachford, Rice and Jim Douglas. He recalls the discovery and elaboration of the Alternating Direction Implicit Method (ADI). He discusses the attempts to compute on the IBM Card-Programmed Calculator , the Bendix G-15 and the IBM 704. and the subsequent evaluation of ADI and its applications to increasingly more difficult problems.

ADI was eventaully superceded by a new method, SIP, developed by Herb Stone at Exxon.

**Key words**: reservoir modeling, Darcy flow, Laplace equation, finite-difference methods, IBM604, von Neumann stability analysis, implicit equations, IBM CPC, Bendix G-15, extrapolated Liebmann method, successive over-relaxation, Alternating Direction Implicit (ADI) method, IBM 704, SIP

**Funding agency**:

**Time frame**: 1950's, 1960's, 1970's

**People**: Henry Rachford, John Rice, L.H. Thomas, John von Neumann, Jim Douglas, Herb Stone

**Locations**: Humble Oil and Refinery Company, Standard Oil of New Jersey, Exxon Production Research,

**Copyright**: History of Scientific Computing, Stephen G. Nash, editor, ACM Press,

Association for Computing Machinery, New York, 1990, pp 106 - 128. with permission