A Novel Well Testing Method for Characterization of Non-Darcy Flow Behavior in Low Permeability Reservoirs
Authors: Luo Le , Cheng Shiqing , Yu Haiyang , He Youwei , Wang Yang , Qin Jiazheng , Qin Guan 
Published: October 2017

Abstract
Modeling of non-Darcy flow behavior in low permeability reservoirs is significant in reservoir performance analysis. The objective of this paper is to develop a novel well testing inversion method for efficient characterization of non-Darcy flow behavior inflow velocity and pressure gradient relation at reservoir condition, which can be applied for accurateproductivity calculation and numerical reservoir simulation.
Based on extensive experimental studies, the velocity-pressure gradient relation exhibit strong non-linear flow behavior in low pressure gradient range and is then gradually converged to pseudo-linearflow behavior as pressure gradient increasing. This study introduces dynamic permeability effect (DPE) for illustrating non-Darcy flow. The numerical well testing models with DPE are furtherdeveloped for both fractured wells and non-fractured wells. Irregular grids are conducted in models for accurate calculation and enhancing computation. Then, vertical well model and fractured vertical well model are all validated by comparison with the solution proposed from Gringarten et al. (1974) and Sheng-Tai Lee (1986) respectively. Typical flow behaviors in pressure transient curve are further investigated detailedly. For vertical well model, Ι) wellbore storage, Ⅱ)transient flow and Ⅲ) non-Darcy radial flow is included. The flow regime in fractured well model can be divided into Ι) wellbore storage, Ⅱ) transient flow and Ⅲ) non-Darcy bilinear flow. The build-up test type curves show the pressure response ascended in the late time region (non-Darcy radial flow and non-Darcy bilinear flow), which indicates the effect of non-Darcy flow in the reservoir. And the larger magnitude of pressure response ascended, the more obviously the non-Darcy behavior was. Therefore, history matching of pressure transient in the late time region has an important impact on inversion result of velocity-pressure gradient curves.
Inversion method is proposed with a five-step workflow. First, linear functions, piecewise functions or continuous functions are employed to capture the non-linear behavior in low pressure gradient range. Second, the interpreted parameters are determined from well testing model and approximation function. Third, thepredicted pressure is calculatedby proposed models and calculation convergence must be fulfilled. Fourth, the coefficients of the proposed function are treated as optimization parameters that are determined by matching the pressure data using Levenberg-Marquardt optimization procedure. Consequently and finally, an accurate velocity-pressure gradient relation is established to characterize non-Darcy flow behavior in low permeability reservoirs. The productivity calculation and numerical reservoir simulation can also be done in further works.
The practicality and efficiency of the proposed methodare illustrated in synthetic case studies. First, we demonstrate the function selection process. Linear, piecewise, and continous functions are all used to make pressure history matching for function optimization. And then the fluid flow behaviorson the reservoir scaleare characterized by normalizing the velocity and pressure gradient curvesfromsingle-well analysis. With comparison to the traditional approach, we comfirmedthat the curve of flow behavior, which is obtained from well testing method, performs better in production history matching.