Abstract
Invasion percolation was studied on three-dimensional regular lattices of various node numbers. A new model has been developed to obtain the pore-size distribution from capillary pressure measurements. The new model is superior to the conventional percolation model, since it takes into account the physical trapping of the wetting phase. The irreducible wetting phase saturation includes the film of the wall of the pores, the dead-end pore volume, and the main contribution by pores isolated from the outlet of the medium by the nonwetting phase. This has been related to the node number and the sample 3dimensions. Over 100 capillary pressure curves of consolidated media have been collected. Good agreement was obtained between this data set out and our invasion percolation predictions using node numbers of 6–13, as reported by Mishra and Sharma. The pore-throat size distribution function estimated by our new model is broader than from the conventional percolation and the capillary tube models.
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Abbreviations
- c :
-
constant
- D :
-
pore throat diameter [m]
- D max :
-
maximum pore diameter [m]
- f(D) :
-
correlation function of pore throat size and pore body size
- L :
-
a parameter representing the dimension of a sample
- n :
-
node number
- p :
-
pressure [N/m2]
- S n :
-
the nonwetting phase saturation
- x :
-
random number ranging from 0 to 1.0
- X a :
-
∂X a t /∂X/ t
- X a e :
-
X a t −X i t
- X i :
-
∂X i t /∂X a t
- X nw :
-
fraction of pore volume occupied by the injected phase
- X t :
-
fraction of pores larger thanD
- X a t :
-
total accessibility of pores larger thanD
- X i t :
-
total isolation of pores larger thanD
- θ :
-
contact angle
- σ :
-
interfacial tension [N/m]
- α(D) :
-
pore throat size distribution
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Zhou, D., Stenby, E.H. Interpretation of capillary pressure curves using invasion percolation theory. Transp Porous Med 11, 17–31 (1993). https://doi.org/10.1007/BF00614632
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DOI: https://doi.org/10.1007/BF00614632