The Cybernetic Approach To Reservoir Engineering

Publication Rights Reserved This paper is to be presented at the 38th Annual Fall Meeting of the Society of Petroleum Engineers of AIME in New Orleans, La., on Oct. 6–9, 1963, and is considered the property of the Society of Petroleum Engineers. Permission to publish is hereby restricted to an abstract of not more than 300 words, with no illustrations, unless the paper is specifically released to the press by the Editor of JOURNAL OF PETROLEUM TECHNOLOGY or the Executive Secretary. Such abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in JOURNAL OF PETROLEUM TECHNOLOGY or SOCIETY OF PETROLEUM ENGINEERS JOURNAL is granted on request, providing proper credit is given that publication and the original presentation of the paper. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and considered for publication in one of the two SPE magazines with the paper. The basic problem facing the reservoir engineer is the prediction of the behaviour of a reservoir. This paper discusses the problem from the point of view of general systems analysis, considering the reservoir as a system from which information can only be obtained at a finite number of points (wells). This is the cybernetic approach which has been used successfully in many other complex situations. The mathematics of this approach has been developed in the study of multi-variable control systems and it is shown that many methods currently used in reservoir engineering are particular cases of this general theory. Introduction It should be neither surprising nor disturbing to find that, on asking a group of reservoir engineers what each one means by a reservoir study, the answers are varied. Each engineer probably has his own interpretation of the meaning of the words which reflects his personal approach to the problem. While differences exist there is, without doubt, a measure of agreement about the broad objectives of such studies. This may be the result of convention or a conformity to a standard pattern which has developed over recent years and which provides a "Lingua Franca" for those who specialize in the study of reservoirs. Basically there are two ways of approaching the study of reservoirs, whether oil or gas. These are by way of asking the questions either - "what is this reservoir?" or, "what does it do - what is its pattern of behaviour?". The former question leads to what might be called the deterministic or mechanistic approach which seeks to describe, in terms of detailed structure and physical properties, the mechanisms which operate to produce the observed characteristics. The latter might best be called the "cybernetic" approach. This paper is devoted entirely to the cybernetic approach as a means of thinking about and discussing problems of otherwise overwhelming complexity. Before embarking upon specific applications to reservoir engineering it would be advisable to pause and explain what is meant by cybernetics lest the reader be repelled by the terminology or the connotation of automata or machines in general.