Analysis of Pressure and Rate Transient Data From Wells in Multilayered Reservoirs: Theory and Application

Abstract

Abstract A new solution technique is described for the analysis of multi-layered tests. This technique is based on an analytical conversion of a single-layer transient pressure response into a multi-layer response. Formation cross-flow is taken into account and a wide variety of inner and outer boundary conditions are possible. The method is successfully applied to a field example for which single-layer analysis failed to give consistent results. Regression is used to simultaneously match observed pressures and layer rates. In the absence of measurable layer rate transients, as encountered in the field example, simple flow profile measurements to obtain relative layer production are all that is required to perform a multi-layer analysis. Introduction There is geological evidence (logs, core analysis) that numerous reservoirs have strongly heterogeneous characteristics with respect to the vertical direction: they are multi-layered reservoirs. Conventional pressure transient analysis, based on the assumption of a single, vertically homogeneous layer, does not take layering into account. But it has been observed that pressure transients in multilayered reservoirs often show a significant deviation from the response that would be obtained in a vertically homogeneous reservoir having equivalent thickness-averaged properties. This deviation became particularly obvious at the advent of high resolution, downhole electronic gauges, allowing very accurate pressure measurements; and with the development of analysis techniques based on the pressure derivative. The more recent incorporation of downhole flow rate measurements revealed an irregular distribution of the rates from diverse horizons along the vertical direction, and made even more flagrant the invalidity of single-layer analysis for multilayered reservoirs. These considerations have boosted the development of both models and analysis techniques for multilayered reservoirs. The models already published address two main aspects:the possibility of having a great number of horizons of distinct properties (layers)the incorporation of interlayer formation crossflow, or leakage Those two aspects have been for a long time mutually exclusive. The former led to the commingled system model, which accommodates an unlimited number of layers but does not account for formation crossflow. This model has been described by Lefkovits et al. for a bounded reservoir. Tariq and Ramey extended the model by included wellbore storage and allowing for a different radius in each layer. Their solution is first computed in the Laplace domain, then numerically inverted using the Stehfest algorithms. P. 187^