Analytical modeling of flow behavior in non-volumetric reservoirs

Abstract

Material balance has long been used in reservoir engineering practice as a simple yet powerful tool to determine the original hydrocarbon in place. Traditional material balance methods incorporate shut-in pressure data. However, adequate shut-in pressure data is not available in some reservoirs. Integration of time variable functions and pressure transient analysis into material balance equation (MBE) provides us the flowing material balance technique. Evaluation of the initial hydrocarbon and average reservoir pressure are typical findings of such methods. Although this method is widely used in oil and gas reservoirs, it has not been implemented in water drive reservoirs so far. The objective of this study is to develop a water drive model of dynamic MBE in oil and gas reservoirs. To do so, the average reservoir pressure and water influx are calculated by a newly proposed approach which is applicable for variable rate case as well. In order to incorporate the effect of water encroachment, a novel relationship is derived for material balance pseudo-time. Even though the concept is used practically in gas reservoirs, it has not been applied in oil reservoirs yet. A numerical model was also constructed to verify the presented approach. The findings revealed that there was a high agreement between analytical and numerical schemes. • The amount of water influx can be calculated through flowing wellbore pressure. • The verification of the proposed methodology for variable rate oil and gas reservoirs was accomplished. • A new definition of pseudo-time is introduced to compensate the “non-volumetric effect”. • The proposed model is applicable to either volumetric systems or non-volumetric systems.