Influence of Reservoir Drive Mechanism on Uncertainties of Material Balance Calculations
Authors: Wang B. , Hwan R.R. 
Published: December 2007

Abstract
The uncertainties of material balance calculations, such as the original-hydrocarbon-in-place (OHIP) estimate, are generally affected by the input data accuracy and the drive mechanisms. This paper describes the investigation of the effect of pressure data quality and drive mechanisms on the material balance calculation. Results of this work indicate that for a depletion type reservoir, the impact of pressure data error on the material balance calculation is minimal, but for a water drive or initial gas-cap reservoir, the impact can be significant, depending on the size of aquifer or gas-cap.
The Reservoir Voidage Replacement plot is a good measure to quantify the uncertainty level. The results show that to obtain a reasonable OOIP/OGIP estimate (i.e. 25% error) for the pressure data quality within 25 psi, it requires (1) more than 20% of gas (or oil+formation) voidage replacement ratio (VRR) for a water drive reservoir, (2) more than 65% of oil VRR for an initial gas-cap reservoir. It is very difficult to estimate OOIP/OGIP for an initial gas-cap reservoir with water influx.
Although the OHIP calculations are difficult for strong water drive reservoirs, we found the water influx estimates are normally very good due to its high VRR. A similar result was found in gas-cap reservoirs. The OGIP estimates are more accurate than the OOIP estimates for large gas-cap reservoirs.
Several OHIP calculation methods are evaluated and suggested to minimize the uncertainty level, such as, coupling a statistics-based history matching system in material balance calculations, etc.

Introduction
Material balance techniques have been widely used to estimate original-hydrocarbon-in-place (OHIP) by selecting the best-fit regressed pressure value. Although the techniques are very powerful, many field cases indicated that the calculated OHIP values were not correct. In the literature, there have been voluminous publications on the various techniques of material balance calculation, but there were few discussions on the uncertainties of the calculation results.
The errors of the material balance calculation can be introduced through rearranging a material balance equation for a water-drive oil reservoir from a 3-variable equation to a 2-variable equation as discussed by Tehrani. Most of the material balance techniques were based on the 2-variable equation because the least-squares calculations are simpler to calculate. Tehrani's paper focused on the material balance equation of water-drive oil reservoirs which have a 3-variable equation and did not discuss other types of reservoirs, such as an under-saturated oil reservoir, which has a 2-variable equation; a water-drive gas reservoir, which has a 3-variable equation; or an oil reservoir with a gas cap and an aquifer, which has a 4-variable equation.
A method for assessing the confidence limits of the material balance calculation was described by Galas. The discussion was mainly restricted to oil reservoirs with gas caps. The effect of uncertainty in pressure on the confidence limits was investigated by changing the random component of the pressure values. Carlson used a mathematical approach to error analysis for the Havlena and Odeh material balance. In this paper, a statistical approach was used to investigate and provide the explanation for the uncertainties of the material balance calculation for various types of the reservoir. Generally speaking, the material balance calculation error can be attributed to two major factors: input data quality (PVT, production and pressure) and reservoir drive mechanism. The average reservoir pressure is the most critical data but its quality is difficult to control. The error of the pressure data can be easily over 25 psi (0.5% of a reservoir pressure of 5000 psia) due to the measurement error, the field averaging error, etc. P. 767^