Modeling of non-Darcy flow in porous media and its application

Forchheimer non-Darcy flow has seen significant increase in interest in gas reservoir development and even in light oil reservoir development. Misunderstanding the non-Darcy flow phenomenon could result in considerable revenue loss and errors in estimating oil or gas recovery. Non-Darcy flow in real fields is much more significant than in the laboratory due to reservoir heterogeneity. Therefore, effective estimation of the non-Darcy coefficient through well testing or production rate analysis is critical in the optimization of gas reservoir development. Non-Darcy flow is described by the inertial factor beta, which is a function of permeability. Considering the fact that well damage causes different inertial factor value around the wellbore area, this work derives a Forchheimer number to describe globally distributed non-Darcy flow in porous media and a non-Darcy skin factor to model inertial factor variation around the wellbore area, rather than the traditional approach of using non-Darcy skin factor to describe globally distributed non-Darcy flow.;The Partial Differential Equation (PDE) governing non-Darcy flow in porous media is highly non-linear; therefore, analytical methods and the superposition principle are not applicable to obtaining the results of drawdown, build-up or variable rate tests. This work presents an effective, accurate, and robust semi-analytical model to investigate the effect of Forchheimer non-Darcy flow on the transient pressure and production rate behaviour under constant or variable-rate conditions. Different types of reservoirs, such as single-porosity, dual-porosity, and reservoirs with discrete fracture systems, and different types of wells, such as vertical and hydraulically fractured wells, are considered. Standard type curves for transient pressure analysis are documented. Unique transient pressure behaviours on type curves caused by Forchheimer number and non-Darcy flow skin factor are revealed, which makes it possible to effectively estimate both factors and other reservoir parameters through one single rate test, while traditionally the test would be done under at least two different flow rates. This leads to more than 50% reduction in testing costs. Practical guidelines for well testing analysis are summarized.;The application of this model in hydraulically fracturing design discloses that non-Darcy flow in hydraulically fractured wells might cause a shorter and wider hydraulic fracture, while with Darcy flow, a longer and narrower fracture is better. A simple correlation to calculate the optimal fracture length in well stimulation is obtained and can be directly applied in gas reservoir development optimization.;The real-gas PVT properties and non-Darcy flow are two important factors controlling production rate behaviour. When both effects are ignored, the production decline exhibits an exponential decline; while real gas PVT behaviour causes less severe declining production rate, in contrast, non-Darcy flow causes more severe production declining rate. Due to the fact that real-gas PVT properties are known with good certainty, the non-Darcy flow effect can be effectively identified from production data and, also, fluid driving mechanism in a particular gas reservoir.;The methodology presented is as accurate as analytical methods and is as flexible and widely applicable as numerical methods. Continuous efforts will result in a milestone development of multi-phase well testing and a high-accuracy reservoir simulator. This methodology can also be extended to solve similar non-linear PDE in engineering.