Effect of viscosity-compressibility product variation on the analysis of fractured well performances in tight unconventional reservoirs

Abstract

This research study for a Master of Science degree has been conducted under the Unconventional Reservoir Engineering Project (UREP) at the Marathon Center of Excellence for Reservoir Studies (MCERS) in the Petroleum Engineering Department of Colorado School of Mines. The main objective of the research is to investigate the effect of pressure-dependent viscosity-compressibility product on the analysis of fractured, tight-gas well performances. Pressure drops required to economically produce fractured, tight-gas wells may be in the thousands of psi. Under these conditions, the gas compressibility-viscosity product may exhibit variations 3 to 10 times greater than the initial values in the vicinity of the fracture and have a significant impact on the observed rate-time behavior. Consequently, solutions and procedures used in conventional gas-well performance evaluation, which assume negligible variation of the viscosity-compressibility product, yield lower than expected permeability values. Further, since most of the property variation occurs very close to the fracture surface, accurately modeling their effects using finite difference methods is difficult due to severe time-step restrictions to ensure numerical stability and/or accuracy. In this research, analytical, semianalytical, and numerical models are used. The spectral solution was developed by Thompson (2014), but has not been reported earlier. It is verified and used to observe the effects of variable viscosity-compressibility product in the analysis of fractured, tight-gas well performances in this thesis. In addition, a new perturbation solution is developed to discuss the validity of the superposition time in the analysis of nonlinear, tight-gas well performances. Data obtained from a commercial simulator (Eclipse) and numerical results from existing fully analytical solutions for constant viscosity-compressibility product are used for the verification of the new solutions. A similarity solution for infinite-acting reservoirs, provided by Thompson (2014), is also used in the verifications. Comments are made on the advantages and disadvantages of the numerical solutions. The new solutions presented in this thesis demonstrate the shortcomings of the existing solutions and procedures in the analysis of fractured, tight-gas well performances. It is shown that the conventional definition of the superposition time is not accurate enough for tight-gas wells. Based on the new solutions, guidelines are provided to improve the analysis of fractured, tight-gas well performances.