An Analytical Model Coupled with Orthogonal Experimental Design Is Used to Analyze the Main Controlling Factors of Multi-Layer Commingled Gas Reservoirs

Abstract

The majority of China’s multi-layer low permeability tight gas reservoirs are currently being extracted through the method of multi-layer co-production. However, due to the significant disparity in physical properties and varying degrees of pressure depletion among the production layers, elucidating the primary factors influencing the productivity contribution of each gas layer remains challenging. A multi-factor analytical model is proposed for commingled gas wells with multiple layers. An unstable model is established for the production of commingled layers, and the problem of flow distribution is addressed using the Duhamel convolution principle. The Laplace transform is subsequently employed to derive the solution in the Laplace domain, which can be inverted utilizing the Stehfest inversion algorithm to obtain a real-time domain solution. The influence of reservoir factors on the stratification contribution rate has been comprehensively analyzed, encompassing permeability, porosity, initial pressure, drainage radius, and layer thickness. The orthogonal test design was employed to conduct range analysis and variance analysis separately, yielding the primary and secondary order as well as influence weight of the five factors. The findings demonstrate that, within this gas reservoir, the discharge radius, thickness, and porosity are identified as the primary factors influencing gas well productivity. Furthermore, seven horizontal flow charts illustrating the double-layer gas reservoir and five horizontal flow charts depicting single-factor variations in the double-layer gas reservoir were constructed. These charts provide a clear visualization of the impact of each reservoir factor on stratification’s contribution rate. In contrast to previous studies, this novel approach presents a comprehensive optimization framework that ranks the influence weights of individual factors and identifies the most significant factors impacting multi-layer gas reservoirs. The presented method also serves as a foundation for the subsequent selection of multi-layer gas reservoirs, formulation of gas well stimulation measures, and efficient development.