CFD Simulation of Pore Pressure Oscillation Method for the Measurement of Permeability in Tight Porous-Media
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1 CFD Simulation of Pore Pressure Oscillation Method for the Measurement of Permeability in Tight Porous-Media Seyed Armin Madani, M.S. Oil Center Research LLC, Lafayette, Louisiana, USA. Mehdi Mokhtari, Ph.D. Assistant Professor of Petroleum Engineering, University of Louisiana at Lafayette, Louisiana, USA. Abdennour Seibi, Ph.D. Associate Professor of Petroleum Engineering, University of Louisiana at Lafayette, Louisiana, USA. COMSOL CONFERENCE 2016 Boston, MA Oct 5-7, 2016
2 Unconventional Hydrocarbon Resources Source: Source:
3 Conventional vs. Unconventional Reservoirs K=1 Darcy K=1 Nano-Darcy BHP=1000 Pa Production BHP=1000 Pa Production
4 Effect of Fracturing on Production Intact Fractured Sad Pistachio Fracturing Smiley Pistachio
5 Outline Introduction Steady State Method of Permeability Measurement Unsteady State Method: Pulse Decay Method Unsteady State Method: Crushed Sample Method Unsteady State Method: Pressure Oscillation Method How it works? Theory Numerical Simulation Analyze of experimental parameters Preliminary results on Anisotropy
6 Steady State Method of Permeability Measurement Core analysis and permeability measurement techniques Steady state methods Constant flow or constant pressure head methods Darcy s equation Suitable for high permeability samples Time consuming for low permeability samples (days to weeks) k = qμl A P
7 Unsteady State Method of Permeability Measurement: Pulse Decay Method
8 Unsteady State Method of Permeability Measurement: Crushed Sample Method Permeability is Size-Dependent in GRI Method
9 Pressure Oscillation Method Schematic diagram of experimental setup Pressure data recorded at upstream and downstream reservoirs
10 Methodology (analytical formulation) Kranz et. al. at (1990) o Governing equations in pressure oscillation method (homogenous and isotropic sample) Conservation of mass Darcy s equation Combined together o Governing boundary conditions in pressure oscillation method o Governing initial condition
11 Methodology (analytical formulation) o Solution of governing partial differential equation Permanent solution Transient and temporary solution
12 Methodology (analytical formulation) Solution at location of downstream reservoir (x=0) Pressure wave amplitude attenuation from upstream to downstream Pressure wave phase shift from upstream to downstream Dimensionless porosity Dimensionless permeability
13 Methodology (CFD modeling ) COMSOL Geometry and computational mesh o o o Core length: 50 mm Core height: 10 mm Downstream reservoir length: variable o Mesh size: 1 mm (2D model quad mesh) o Aspect ratio: 1 o Time step size: 1 second o o o o Time dependent direct solver: Multifrontal Massively Parallel sparse direct Solver (MUMPS) Porous media fluid properties: Ideal gas Total simulation time: 36 times of pressure wave period (to have only the permanent part of solution) Initial pore pressure: 5e6 Pa
14 Results and Discussions Pressure response at downstream reservoir (CFD and analytical solution results) Transient and permanent parts of solution permanent part of solution
15 Analyzing Laboratory Data to Calculate Shale Permeability using Oscillation Method
16 Methodology (CFD modeling )
17 Anisotropy in Shales
18 Results and Discussions o Layer 1 Permeability: m 2 Porosity: 0.06 o Layer 2 Permeability: m 2 Porosity: 0.09 o Layer 3 Permeability: m 2 Porosity: 0.1
19 Conclusion Pressure oscillation method was successfully simulated by COMSOL CFD module to calculate the permeability of tight rocks in the range of nano-darcy. Excellent agreement between CFD and analytical formulation results was observed in isotropic models. Parametric study of simulations is in progress to optimize experiments for permeability measurement. Numerical simulation of anisotropic rocks is in progress to get more accurate interpretation of results in heterogeneous and anisotropic shale formations.
20 CFD Simulation of Pore Pressure Oscillation Method for the Measurement of Permeability in Tight Porous-Media Thank you! Any questions?
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