Shale Gas Permeability Measurement Using Stepwise Pressure Protocol
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Solution Overview
Problem
Current methods for determining pressure-dependent shale gas permeability are inefficient, requiring multiple tests and suffering from non-uniqueness in parameter estimation and lack of practical techniques to account for slip flow and Knudsen diffusion effects in nano-scale shale formations.
Innovation Solution
A method using analytical solutions for one-dimensional gas flow to directly measure the relationship between shale gas permeability and pore gas pressure in a single test run, considering mechanical deformation and Knudsen diffusion impacts, with formulas to estimate permeability and porosity from gas transport parameters and pressure measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple pulse-decay permeability tests under different gas pressures are performed to measure pressure dependence, then gas permeability values for different pressures can be obtained, but it takes a relatively long time to equilibrate the test system from one test pressure to the next one
Solution Approach 1:
The patent combines multiple pressure-dependent permeability measurements into a single continuous test by applying a stepwise pressure increase protocol. Instead of performing separate equilibrium tests at each pressure, the method continuously increases pressure in steps and records permeability at each step within the same test run, eliminating the time-consuming equilibration between separate tests.
Solution Approach 2:
The patent applies preliminary confining stress to the rock sample before initiating the gas flow tests. This preliminary action stabilizes the rock matrix and establishes the initial effective stress state, ensuring that subsequent permeability measurements reflect the true pressure-dependent behavior without requiring additional equilibration time for mechanical stabilization at each pressure step.
2Adaptability or versatility
If numerical modeling with parameter estimation is used to determine gas permeability as a function of pressure, then flexibility to incorporate pulse disturbance is achieved, but non-uniqueness of parameter estimation is always a problem
Solution Approach 1:
The patent uses a feedback-based iterative fitting procedure where the numerical model predictions are continuously compared with actual test data, and model parameters are adjusted to minimize the difference. This feedback loop resolves the non-uniqueness problem by converging to the parameter set that best reproduces the observed pressure-dependent permeability behavior, providing both flexibility and precision.
Solution Approach 2:
The patent transforms the permeability parameter from a constant value to a pressure-dependent function k(p) = k0 * (p/p0)^n. By changing the parameter representation from a single constant to a functional form with two parameters (k0 and n), the model gains flexibility to capture pressure dependence while reducing non-uniqueness through the physically motivated functional form that constrains the solution space.
3Ease of manufacture
If conventional permeability measurement methods are used, then standard procedures can be followed, but slip flow and Knudsen diffusion effects in nano-scale shale pores are not adequately accounted for
Solution Approach 1:
The patent modifies the permeability parameter to be pressure-dependent, recognizing that in nano-scale pores, gas flow transitions from conventional Darcy flow to slip flow and Knudsen diffusion regimes. By expressing permeability as k(p) = k0 * (p/p0)^n, the method captures the pressure-dependent nature of gas flow in shale nanopores while maintaining a relatively simple testing procedure that can be implemented with standard equipment.
Solution Approach 2:
The patent replaces the assumption of conventional mechanical Darcy flow with a modified flow model that accounts for molecular-level effects in nanopores. Instead of treating gas flow purely as a continuum mechanical process, the method incorporates slip flow and Knudsen diffusion effects through the pressure-dependent permeability formulation, substituting the simplified mechanical model with one that reflects the actual nanoscale transport mechanisms.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach allows for efficient estimation of shale permeability and porosity with reduced test time, accurately accounting for pressure-dependent effects and separating the impacts of mechanical deformation and Knudsen diffusion on permeability.
Implementation Method 1
In these nano pores, a non-negligible portion of gas molecules collides more often with the pore wall than with other molecules, and thus so-called 'slip flow' and Knudsen diffusion occur.
Implementation Method 2
In these nano pores, a non-negligible portion of gas molecules collides more often with the pore wall than with other molecules, and thus so-called 'slip flow' and Knudsen diffusion occur.
Implementation Method 3
determining the gas transport parameter of the subsurface formation, D(p), using a first formula... determining the permeability function, k(p), of the subsurface formation from gas transport parameter D(p)
Data Source
AI summary
Methods and systems disclosed here include conducting two pressure-dependent permeability tests having the same range of effective stress but two different values of pore pressure. For the test with the higher pore pressure, the permeability is only impacted by the mechanical deformation of the rock, while for the one with lower pore pressure the permeability is impacted by both mechanical deformation of the rock and the Knudsen diffusion. By using the same range of effective stress, the contribution from the mechanical deformation of the rock should be the same. Therefore, by subtracting the permeability with higher pore pressure from the one with lower pore pressure, the impact of Knudsen diffusion and the mechanical deformation of the rock can be determined.