Pseudo-pressure Type-curve approach for Permeability and Porosity estimation from Pressure-pulse Decay Data

Open Access
Abdelmalek, Botros
Graduate Program:
Energy and Mineral Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 29, 2016
Committee Members:
  • Zuleima T Karpyn, Thesis Advisor
  • Shimin Liu, Thesis Advisor
  • Permeability of Shale Gas
  • Pulse Decay
  • Pseudo Pressure
  • Type Curves
This work presents an improved pseudo-pressure type curve approach to interpret laboratory pulse decay data to estimate rock core permeability and porosity. The proposed method enables the analysis of pulse decay experimental data at low initial pressure and high pulse magnitude. The pseudo-pressure is a mathematical transform that is a function of pressure viscosity and gas deviation factor (Z) that can convert the compressible flow equation from its highly non-linear form to a quasi-linear partial differential equation that can be solved in a simple way without assuming small changes in the viscosity and compressibility. The pseudo-pressure approach resolves calculation problems incurred due to changes in gas viscosity and compressibility during the course of the pulse decay experiment. The type curve analysis proposed in this work allows for comparison of experimental data with theoretical curves generated from analytical models. Five pulse decay experiments were performed at pore pressures ranging from 130 psi to 700 psi in a tri-axial cell to estimate permeability and porosity of ultra-tight shale cores. The experiments were made in an increasing order of equilibration pressure starting from 130 psi until 700 psi, the pressure-pulse was of a relatively large magnitude that is equal to 200 psi and vertical and radial stresses were kept constant at 1500 psi. Permeability estimates from the proposed pseudo-pressure approach, which is based on the compressible flow equation, was compared with the Jones method that is based on the slightly compressible flow model. This comparison demonstrates that the proposed method is able to detect the changes of permeability as a function of stress conditions in more accurate way. There are two main reasons for the inability of the Jones method to detect those changes in permeability. First, the changes in the product of viscosity and compressibility were significant during the pulse decay experiments done in this work and the slightly compressible flow equations assume it to be constant. Second, the Jones method equations had some approximations that can work for a certain range of experimental designs in terms of upstream and downstream volumes sizes relative to each other and to the pore volume. However, the proposed method can accommodate the changes in viscosity and compressibility because the pseudo pressure approach is based on the compressible flow equation. In addition, the proposed method does not have any approximations as it deals with the generalized solution; therefore, the range of experimental designs that it can analyze in terms of upstream, downstream and sample volumes is much wider. Pulse decay experiments at low pressures as demonstrated in this work are useful to describe shale gas reservoirs during its depletion period, and this work demonstrates the pseudo-pressure approach to be suitable for analyzing the pulse decay experiments at low pressures with high pulse magnitude. Consequently, providing a more accurate estimate of sample porosity and permeability for a wide range of system setups.