Abstract
Due to the intricate structure of carbonate rocks, relationships between porosity or saturation and petrophysical transport properties classically used for reservoir estimation and recovery strategies are either very complex or nonexistent. Thus, further understanding of the influence of the rock structure on the petrophysical transport properties becomes relevant. We therefore present a Dual Pore Network approach (D-PNM) applied to μ-CT images of bimodal porous media. The major advantage of this method lies in the fact that it takes into account the real architecture of the connected macropore network as well as the microporosity unresolved by μ-CT imaging. Whereas governing equations are solved in each individual macropore, transport behavior of microporosity is simulated by average quantities. Thus, D-PNM is particularly suited for the investigation of carbonate rocks, characterized by broad pore size distributions. We describe the principles of the image acquisition and network extraction procedure and the governing equations of D-PNM. The model is tested on three carbonate samples, two outcrop, and one reservoir carbonate. Calculated petrophysical transport properties are compared to experimental data and we show that D-PNM correctly reproduces conventional as well as unconventional electrical transport behavior. A major restriction of D-PNM is the requirement of a connected macropore network, that is, especially in the case of carbonates, not always available. Solutions to that are presented.
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Abbreviations
- α:
-
Half angle of the polygon describing the throat or pore
- θ:
-
Contact angle
- ρ :
-
Radius of the curvature of the oil–water interface, depending on the applied pressure
- μ :
-
Fluid viscosity
- σ w :
-
Electrical conductivity of bulk water
- \({\phi_{{\rm img}}}\) :
-
Global porosity of the 3D image
- \({\phi_{{\rm mi}}}\) :
-
Mean porosity of the microporous phase
- A :
-
Cross-section of the network
- A con :
-
Cross-section of the cuboid perpendicular to the flow direction
- A w :
-
Area of the wetting phase occupying the corners of the pores and throats
- A w,s :
-
Cross-sectional area occupied by the water phase
- FF:
-
Formation factor
- FFmi :
-
Formation factor of the microporous phase
- F ma :
-
Fraction of the macroporous phase (resolved porosity)
- F mi :
-
Fraction of the microporous phase
- F surf :
-
Fraction of the macropore surface in contact with the microporous phase
- g h :
-
Hydraulic conductance
- g e :
-
Electrical conductance
- G m :
-
Mean grey level of the image
- G s :
-
Peak grey levels of the solid phase
- G v :
-
Peak grey level of the void phase
- i, j :
-
Pore labels
- K :
-
Permeability
- K r :
-
Relative permeability
- L :
-
Length of the network
- I ij :
-
Electrical current
- l con :
-
Length of the microporous cuboid lining the macropore segments along the flow direction
- l ff :
-
Equivalent electrical throat length
- l h :
-
Equivalent hydraulic throat length
- m :
-
Cementation exponent
- m mi :
-
Cementation exponent of the microporous phase
- n :
-
Saturation exponent
- n c :
-
Number of corners of the pore or throat polygon
- n mi :
-
Cementation exponent of the microporous phase
- N ma :
-
Number of voxels of the resolved porosity
- N img :
-
Total number of voxels in the image
- N mi :
-
Number of voxels of the microporous phase
- N seg :
-
Number of segments
- P :
-
Pressure
- P c :
-
Capillary pressure
- Q :
-
Macroscopic flow rate
- q ij :
-
Flow rate in the throat between pore i and j
- p seg :
-
Percentage of pore segments with microporosity acting in parallel
- r h :
-
Hydraulic radius
- R 0 :
-
Resistivity of the saturated porous media
- RI:
-
Resistivity index
- R t :
-
Resistivity of the partially saturated porous media
- S w :
-
Water saturation
- U i , U j :
-
Electrical potential in the neighboring pores
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Bauer, D., Youssef, S., Fleury, M. et al. Improving the Estimations of Petrophysical Transport Behavior of Carbonate Rocks Using a Dual Pore Network Approach Combined with Computed Microtomography. Transp Porous Med 94, 505–524 (2012). https://doi.org/10.1007/s11242-012-9941-z
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DOI: https://doi.org/10.1007/s11242-012-9941-z