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Abstract
Unconventional gas resources from low-permeability formation, i.e., tight and shale gas, are currently received great attention because of their potential to supply the world with sufficient energy for decades to come. In the past few years, as a result of industry-wide R&D effort, progresses are being made towards commercial development of gas and oil from such unconventional resources. However, studies, understandings, and effective technologies needed for development of unconventional reservoirs are far behind the industry needs, and gas recovery from those unconventional resources remains low (estimated at 10-30% of GIP).

Gas flow in low-permeability unconventional reservoirs is highly nonlinear, coupled by many co-existing processes, e.g., non-Darcy flow and rock-fluid interaction within tiny pores or micro-fractures. Quantitative characterization of unconventional reservoirs has been a significant scientific challenge currently. Because of complicated flow behavior, strong interaction between fluid and rock, the traditional Darcy law may not be applicable for describing flow phenomena in general. In this paper, we will discuss a general mathematical model of gas flow through unconventional porous media and use both numerical and analytical approaches to analyze gas flow in unconventional reservoirs. In particular, we will present analytical and numerical solutions of incorporating Klinkenberg effect, non-Darcy flow with threshold pressure gradient, and flow behavior in pressure sensitive media. We will discuss the numerical implementation of the mathematical model and show applications of the mathematical model and solutions in analyzing transient gas flow in conventional reservoirs.

Introduction
This paper presents our continual effort in developing simulation models and tools for unconventional gas reservoirs (Wu and Fackahroenphol, 2011). As unconventional gas resources from low-permeability reservoirs are receiving great attention in the world, many studies and progresses are being made towards commercial development of gas and oil from these unconventional resources (Denny, 2008; Bybee, 2008; King, 2010). However, our understandings of gas flow and effective tools for effective development of unconventional reservoirs are far behind the industry needs (Wu et al. 2009). Unlike flow in traditional reservoir s, nanoscale observations and field data analysis tell us that gas flow in such extremely low-permeability formations is complicated by flow condition and many co-existing processes, such as severe heterogeneity on any scales, Klinkenberg effect or known as Knudsen diffusion (Klinkenberg, 1941), non-Darcy flow behavior (Wu, 2002), adsorption/desorption (Silin and Kneafsey, 2011), strong interactions between fluid (gas and water) molecules and solid materials within tiny pores (Severino et al. 2010) as well as micro- and macro- fractures of shale and tight formations (Shabro et. al. 2011). As a result, there is a general lack in technologies or approaches available for effective gas production from unconventional reservoirs (MIT, 2010) or effective and applicable reservoir simulation technologies currently available and few modeling efforts (Kelkar and Atiq, 2010).