The effect of pressure on porosity and the transport properties of rock

TLDR

The study reexamines Wyllie and Rose’s 1950 flow model, simplifying the complex pore network into a single representative conduit. The authors derive expressions linking fluid permeability k and formation factor F to the mean hydraulic radius, then use this radius to estimate crack area per unit volume and asperity height variability in two granite samples, thereby simplifying the pore network into a single conduit representation. The simplified model accurately simulates pressure‑dependent transport properties, shows that the exponent r in k ∝ F^−r lies between 1 and 3, and its estimates agree reasonably with previous studies.

Abstract

We reanalyze the flow model proposed by Wyllie and Rose (1950) in which the complicated flow network through the pore phase of rock is replaced by a single representative conduit. Although the model is a very simple representation of the complicated pore phase in rock, we find that it provides an adequate simulation of how the transport properties vary with external pressure. Expressions derived for fluid permeability k and formation factor F are combined to give an expression for the mean hydraulic radius of the pore phase. Using this expression, we show that the exponent r in the empirical relationship k ∝ F −r must fall in the range 1≤r≤3. Also, we use the expression for hydraulic radius to estimate the crack area per unit volume and the standard deviation of the height of the asperities on the rhicrocrack surfaces for two granites. The values are in reasonable agreement with other estimates.