Abstract
Permeability estimation from pressure-pulse decay method is complicated by two facts: (1) the decay curve often deviates from the single-exponential behavior in the early time period and (2) possible existence of gas adsorption. Both the two factors cause significant permeability error in most of pressure-pulse decay methods. In this paper, we first present a thorough analysis of pressure-pulse propagation process to reveal the mechanism behind the early time and later time behaviors of pressure decay curve. Inspired by the findings from these analyses, a new scaled pressure is proposed which can: (1) be easily used to distinguish the early time and later time data and (2) make the decay curves of all cases into a single 1:1 straight line for later time. A new data-proceeding method, which calculates the apparent porosity and permeability using the same set of measured data, is then developed. The new method could not only remove the effects of the adsorption on the permeability estimation, but also identify the apparent porosity as well as proper adsorption model and parameters. The proposed method is verified by comparing with true values and calculated values through numerical simulations that cover variations in typical rock properties (porosity, permeability, slippage, and adsorption) and the experiment configurations. It is found that the new method is accurate and reliable for all test cases, whereas the Brace’s and Cui’s approaches may cause permeability error in some cases. Finally, the new method has been successfully applied to real data measured in pressure-pulse decay experiments involving different types of rocks and gases.
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Abbreviations
- a :
-
The ratio of apparent pore volume to upstream volume
- A :
-
Sample cross-sectional area
- b :
-
The ratio of apparent pore volume to downstream volume
- c :
-
Gas compressibility
- k :
-
True permeability
- k a :
-
Apparent permeability
- L :
-
Sample length
- m L :
-
The maximum gas adsorption capacity
- M :
-
The total gas mass in the control volume
- p :
-
Gas pressure in the sample
- p c :
-
Confining pressure
- p f :
-
Final equilibrium pressure
- p L :
-
Langmuir pressure
- p m :
-
Mean gas pressure
- p 1 :
-
The pressure of upstream chamber
- p 2 :
-
The pressure of downstream chamber
- Δp :
-
Initial pressure difference
- Δp D :
-
Dimensionless pressure difference
- p*:
-
New scaled pressure decay
- Sm :
-
The mth term of Eq. (12)
- t :
-
Real time
- t D :
-
Dimensionless time
- t*:
-
New scaled time
- V s :
-
The volume of sample pore
- V u :
-
The volume of upstream chamber
- V d :
-
The volume of downstream chamber
- x :
-
The distance along the sample from the upstream end
- z :
-
Gas compressibility factor
- μ :
-
Gas viscosity
- λ:
-
Klinkenberg coefficient
- ρ g :
-
Gas density
- ρ R :
-
Rock density
- ψ:
-
The mass of gas adsorbed per unit mass of rock
- ϕ :
-
True porosity
- ϕ a :
-
Apparent porosity
- ϕ ad :
-
The equivalent porosity due to gas adsorption
- θ m :
-
The roots of Eq. (13)
- η :
-
The contribution of first term in Eq. (12) to all terms
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Acknowledgements
This research was supported by the National Natural Science Foundation of China (Nos. 51374257 and 50804060). It was also supported by the China Scholarship Council (CSC) for the first author’s visit at Lawrence Berkeley National Laboratory.
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Appendix
Appendix
The main MATLAB code implemented for permeability and porosity calculation for pressure-pulse decay test is shown as below.
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Wang, C., Pan, L., Zhao, Y. et al. Analysis of the Pressure-Pulse Propagation in Rock: a New Approach to Simultaneously Determine Permeability, Porosity, and Adsorption Capacity. Rock Mech Rock Eng 52, 4301–4317 (2019). https://doi.org/10.1007/s00603-019-01874-w
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DOI: https://doi.org/10.1007/s00603-019-01874-w