Quantifying Uncertainty in Original-Gas-in-Place Estimates With Bayesian Integration of Volumetric and Material Balance Analyses

Abstract

ABSTRACT Accuracy in hydrocarbon reserves estimates affects virtually every phase of the oil and gas business. Unfortunately, reserves estimates are uncertain, since perfect information is seldom available from the reservoir, and uncertainty can complicate the decision-making process. Managers have to make many important decisions early (e.g., facilities expansions, development drilling, etc.) without reliable knowledge of reserves. Thus, it is probably more important to quantify reserves uncertainty early than any other time in the life of a reservoir. Reserves are closely related to original hydrocarbons in place (OHIP). Two methods for estimating OHIP are volumetric and material balance methods. The volumetric method is convenient to calculate OHIP during the early development period, while the material balance method can be used later, after some performance data, particularly pressure and production information, are available. Both methods may have substantial uncertainty. In this paper, we present a methodology that uses a Bayesian approach to quantify the uncertainty of original gas in place (G), aquifer productivity index (J), and the volume of the aquifer (Wi) by combining volumetric and material balance analyses in a water-driven gas reservoir. The results show that we potentially have large uncertainty in OGIP estimates when we consider only volumetric analyses or only material balance analyses. However, by combining the results from both analyses, the uncertainty can be reduced. This reduction in uncertainty should lead to better management decisions in many cases. INTRODUCTION The volumetric method is useful in calculating hydrocarbon reserves prior to availability of representative pressure and production data.[1] This method uses static reservoir properties such as area of accumulation, pay thickness, porosity, and initial saturation distribution. Given the often large uncertainty due to paucity of well data early in the reservoir life, it is common to quantify the uncertainty of volumetric estimates of OHIP using statistical methods such as Monte Carlo analysis. The material balance method can be used later when sufficient amounts of pressure and production data are available. The material balance method is simply an inventory of all materials entering, leaving, and accumulating in the reservoir. Since it relies on different data from the volumetric method, the method can be used as an independent check of volumetric estimates of initial hydrocarbon volumes in place in a reservoir. If the material balance method is properly applied, it can be used to estimate initial hydrocarbon volumes in place, predict future reservoir performance, and predict ultimate hydrocarbon recovery under various types of primary-drive mechanisms. Although uncertainties in material balance methods have been long recognized, they are often considered more accurate than volumetric methods, since they are based on observed performance data. It is not common practice to formally quantify the uncertainty in material balance estimates of OHIP. Bayes' theorem[2–4] provides a mathematical basis for revising preliminary estimates of reservoir characteristics and their uncertainties when additional information becomes available. Floris et al.[5] applied Bayes' theorem to quantify uncertainty in production forecasts from reservoir models conditioned to both static and dynamic reservoir data. Glimm et al.[6] showed that the Bayesian approach can reduce the uncertainty in the prediction of unknown geological parameters in the simulation of an oil field. Galli et al.[7] used the Bayesian approach to evaluate new information for choosing between different exploitation scenarios for a gas field. Ogele et al.[8] used the Bayesian approach to combine volumetric and material balance methods and quantify uncertainty of OHIP estimates in gas-cap driven oil reservoir. They quantified the uncertainty of two parameters, original oil in place and relative gas-cap size, estimated using the Havlena and Odeh form of the material balance equation.