Introduction

Fluid does not leave a void space behind, as it is produced from a hydrocarbon reservoir. As the pressure in the reservoir drops during the production of fluids, the remaining fluids and/or reservoir rock expand or nearby water encroaches to fill the space created by any produced fluids. The volume of oil produced on the surface aids the reservoir engineer in determining the amount of the expansion or encroachment that occurs in the reservoir. Material balance is a method that can be used to account for the movement of reservoir fluids within the reservoir or to the surface where they are produced. The material balance accounts for the fluid produced from the reservoir through expansion of existing fluid, expansion of the rock, or the migration of water into the reservoir. A general material balance equation that can be applied to all reservoir types is developed. The material balance equation includes factors that compare the various compressibilities of fluids, consider the gas saturated in the liquid phase, and include the water that may enter into the hydrocarbon reservoir from a connected aquifer. From this general equation, each of the individual equations for the reservoir types and discussed in subsequent can easily be derived by considering the impact of the various terms of the material balance equation.

The general material balance equation was first developed by Schilthuis in 1936.¹ Since that time, the use of computers and sophisticated multidimensional mathematical models have replaced the zero-dimensional Schilthuis equation in many applications.² However, the Schilthuis equation, if fully understood, can provide great insight for the practicing reservoir engineer. Following the derivation of the general material balance equation, a method of using the equation discussed in the literature by Havlena and Odeh is presented.^3,4