A non-empirical model for gas transfer through circular nanopores in unconventional gas reservoirs

Jiangtao Li,Zheng Sun,Jianguang Wei,Liang Ji,Anlun Wang,Gen Rong,Jiyao Li,Lin Chen

doi:10.1007/s13202-021-01145-x

Abstract

It is difficult to predict the flow performance in the nanopore networks since traditional assumptions of Navier–Stokes equation break down. At present, lots of attempts have been employed to address the proposition. In this work, the advantages and disadvantages of previous analytical models are seriously analyzed. The first type is modifying a mature equation which is proposed for a specified flow regime and adapted to wider application scope. Thus, the first-type models inevitably require empirical coefficients. The second type is weight superposition based on two different flow mechanisms, which is considered as the reasonable establishment method for universal non-empirical gas-transport model. Subsequently, in terms of slip flow and Knudsen diffusion, the novel gas-transport model is established in this work. Notably, the weight factors of slip flow and Knudsen diffusion are determined through Wu’s model and Knudsen’s model respectively, with the capacity to capture key transport mechanism through nanopores. Capturing gas flow physics at nanoscale allows the proposed model free of any empirical coefficients, which is also the main distinction between our work and previous research. Reliability of proposed model is verified by published molecular simulation results as well. Furthermore, a novel permeability model for coal/shale matrix is developed based on the non-empirical gas-transport model. Results show that (a) nanoconfined gas-transport capacity will be strengthened with the decline of pressure and the decrease in the pressure is supportive for the increasing amplitude; (b) the greater pore size the nanopores is, the stronger the transport capacity the nanotube is; (c) after field application with an actual well in Fuling shale gas field, China, it is demonstrated that numerical simulation coupled with the proposed permeability model can achieve better historical match with the actual production performance. The investigation will contribute to the understanding of nanoconfined gas flow behavior and lay the theoretical foundation for next-generation numerical simulation of unconventional gas reservoirs.

Highlights

In the past 10 years, the rapid development of unconventional gas reservoir has significantly shaped diverse aspects of global energy industry, including supply and demand pattern, recovery methods and technical innovation (Chu and Majumdar 2012; Ma et al 2020; Dejam 2018; Sun et al 2020)
The majority of documented analytical models contain empirical coefficients, which greatly restrict its application (Javadpour 2009; Beskok and Karniadakis 1999; Wu et al 2015, 2016a, b; Wu and Chen 2016; Karniadakis and Bekok 2002; Adzumi 1937b, c; Civan 2010; Civan et al 2012, 2013; Azom and Javadpour 2012; Aguilera et al 2012; Shahri et al 2012; Klinkenberg 1941; Ettehad et al 2012; Ertekin, et al 2013; Karniadakis et al 2005; Rahmanian et al 2012; Shi et al 2013; Singh et al 2014). For those analytical mathematic models without empirical coefficients, they cannot be applied to the entire range of Knudsen number (Liu et al 2002; Knudsen 1909; Yang et al 2013)
Because the existed production prediction models or numerical simulators consider that the flow mechanism in coal/ shale matrix belongs to Knudsen diffusion, which is against the actual gas-transport type in the development process of unconventional gas reservoirs

Summary

Introduction

In the past 10 years, the rapid development of unconventional gas reservoir has significantly shaped diverse aspects of global energy industry, including supply and demand pattern, recovery methods and technical innovation (Chu and Majumdar 2012; Ma et al 2020; Dejam 2018; Sun et al 2020). According to slip flow and Knudsen diffusion, the unified non-empirical gas-transport model is established utilizing the second method. It further indicates the necessity for the production prediction model or numerical simulator to account for the varied gas-transport capacity within the shale matrix. The existed production prediction model or numerical simulator assume the gas-transport type in the shale matrix is Knudsen diffusion.

Results

Conclusion