A review of analytical and semi-analytical fluid flow models for ultra-tight hydrocarbon reservoirs

Abstract

In the last decade, numerous approaches, e.g., analytical and semi-analytical pressure solutions, production decline curve, reservoir-scale numerical models, have been used to increase our understanding of fluid transport in hydraulically fractured ultra-tight reservoirs and to improve predictions of well production. Among these approaches, analytical and semi-analytical methods have proved useful to petroleum engineers, because of the balance between the reliability of theoretical model outputs and the computational cost. Analytical or semi-analytical solutions can be used to analyze pressure-transient responses, to estimate hydraulic and induced fracture properties, to forecast production, and to optimize well spacing and multi-stage hydraulic fracking.This work reviews the development of analytical/semi-analytical multi-linear and radial flow models for hydraulically-fractured horizontal wells over the past decade. In particular, the review summarizes and compares the fundamental physics and mathematics of the gas transport mechanisms that are important in unconventional reservoirs. We highlight the analytical approaches that have successfully coupled 1) reservoir spatial heterogeneity, e.g., subdivision of the stimulated reservoir volume (SRV) and fractal SRV, 2) non-continuum flow mechanisms, e.g., Knudsen diffusion, surface diffusion, and gas slip, into diffusivity equations, and 3) the impact of pressure depletion on gas desorption, and pore size change in propped and unpropped fractures. We also discuss the gas permeability models that have been proposed in the past decade and the challenges that remain to the development of oil flow models. Our knowledge of fluid transport, especially for confined fluid at multiple reservoir scales, remains incomplete, and our understanding of flow contributions from different flow regions, and mass transfer between them remains limited.