Probing the roots of Arps hyperbolic relation and assessing variable-drive mechanisms for improved DCA

Abstract

This paper explores the relationship between the natural form of pressure buildup/falloff response to Arps hyperbolic formula in conventional reservoir systems. The primary motivation stems from the fact that semianalytical proof exists for obtaining average-reservoir pressure from either pressure buildup or falloff response with the rectangular hyperbola method (RHM), whereas the Arps hyperbolic relation is anchored in empiricism. Despite its origin, the hyperbolic relationship has served the industry very well in performance predictions under diverse reservoir-drive mechanisms since its inception in 1945. Most reserves estimation in conventional reservoirs is anchored in Arps decline-curve analysis (DCA) to meet regulatory guidelines.We show that the Arps hyperbolic parameters b and D can be estimated from the RHM, thereby giving credence to its basis. Note that the RH method is a semianalytical proof of pressure-buildup/falloff relation. We also show that Arps hyperbolic parameter b is tied to the energy support available for production and can be estimated using a type curve instead of the parameter-regression approach. Besides, we point out that well shut-in periods need to be collapsed to obtain valid b and D parameters; otherwise, optimistic b values are estimated, leading to performance overprediction. Synthetic examples verified the approach presented here, and several field examples with diverse b-factors validated the overall methodology as espoused here.