An Investigation Concerning the Material Balance Equation Part One: The Linear Form of the Equation

Abstract

Abstract The Material Balance Method, as applied to petroleum reservoirs, isinvestigated in this paper. Using less restrictive assumptions than are usuallyemployed, a Material Balance Equation is derived which is linearin theunknown reservoir parameters - initial oil, free gas, interstitial water androck material in place, and water encroachment factor. Both systematic andrandom errors are discussed. The elimination of random errors by the use of the Principle of Least Squares and the detection of systematic errors, althoughonly mentioned at this time, will be shown in detail in the second part of thestudy. Introduction The solution of specific problems in petroleum engineering often dependsupon the successful application of ideas, methods, techniques and tools, originally developed in other branches of engineering or the sciences.Consequently, every year, new ideas are introduced into petroleum engineeringfrom other disciplines. Recently, for instance, the expanding usage ofelectronic computer devices has drawn attention to the mathematical methods of Linear Algebra. Naturally, it is now realized that the application of thismethod need not be restricted to computer usage. In general, the introduction of a new technique will necessitate areappraisal of present methods. This action may result in some modification inthe approach to and the formulation of certain problems. Such alterations mayormay not require modifications of the original principles involved. This investigation presents the case of the ‘Material Balance Principle’ andthe ‘Material Balance Equation’ in view of the above-mentioned Linear Algebra.The original form of the Equation and several of its modifications suffer fromtheir non-linear character, which severely restricts their usefulness, whenconsidering modern requirements. Thus, the application of the Principle of Least Squares - another one of the more recently acquired tools - is found tobe an awkward task. For example, the use of the Principle may lead to atrial-and-error search for the ‘best’ numerical values of certain reservoirparameters.