Dynamic Material Balance Equation and Solution Technique Using Production and PVT Data
Authors: Ojo K.P. , Tiab D. , Osisanya S.O. 
Published: March 2010

Abstract
This paper presents a method that allows the simultaneous determination of the initial oil-in-place (N), ratio of initial gas to oil (m), reservoir permeability (K) or skin factor (S), and average pressure decline history of a reservoir from the combination of a solution to the material balance equation and pressure transient analysis theory. Cumulative production history and pressurevolume- temperature (PVT) data of the reservoir are used without any pressure data.
The measured cumulative production from a reservoir, because it captures the processes that occur throughout the life cycle of the reservoir, is expected, especially for a fully developed reservoir, to give global reservoir-wide heterogeneity effects and also the extent and size of the reservoir. By accurately measuring and analyzing the production performance and how it changes with time, we are able to determine how the average pressure in the reservoir is declining and how large the reservoir is.
By introducing a time variable into the classical material balance equation (MBE) and combining the solutions of the resulting equations with the theory of pressure transient analysis, the cumulative production history of the reservoir and readily available PVT data of the reservoir fluids provide an estimate not only of the original reserves in place, but also determine the average reservoir pressure decline history as indicated by the net fluid withdrawal from the reservoir. The reservoir permeability and skin factor as seen within the drainage area of each producing well can then be estimated from the already determined average pressure decline history. This is obtained from equations derived from solutions to analytical pressure-transient analysis equations.
The solution method considers the material balance equation and its derivative with time to obtain the reservoir average pressure history as predicted by the measured net fluid withdrawals from the reservoir. This method assumes a fully-developed bounded reservoir in which no flow exist across its boundary. The obtained average reservoir pressure, N and m values, can then be used to estimate for each producing well, the reservoir permeability (as seen at the well) and/or the skin factor for the well from its production rate history. This method is very useful because the analysis procedure can easily be programmed and solved with a computer without much input from the user.

Introduction
The material balance equation (MBE) is one of the several methods used for estimating reserves for oil and gas reservoirs and thus allows for the making of critical decisions concerning depletion plans and development strategies regarding the reservoir. The MBE makes these estimates by considering different time intervals in the production history of the reservoir and maintaining that there exist a volumetric balance in the reservoir at these different time intervals. Several methods have been developed and published applying the MBE to various types of reservoirs and solving the equation to obtain the initial oil-in-place (N) and the ratio of the initial free gas to oil (m) in the reservoir.