• Net effective stress • Biot’s constant, 0 ≤ a ≤ 1 Porosity - compressibility ppea)u1)(21(B)u(3a)flc/mc1(1BB = 0 dry rock B < 1 partially saturated B = 1 liquid saturated, compressible rockPorosity - compressibilityPorosity - compressibility Step (Pov),psi pp,psi e,psi 1 200 0 200 2 400 200 200 0)( ppd 3 1000 800 200 4 1000 600 400 5 1000 400 600 pdpedd ;0 6 1000 200 800 ppdbcpdpmcbVbdVepdPbdVbV1mcGeertsma’s relations for elastic deformation and fluid pressure decline ppdmcbcpdpmcpVpdV1Hypothetical triaxial testPorosity - compressibility Step (Pov),psi pp,psi e,psi 1 200 0 200 2 400 200 200 0)( ppd 3 1000 800 200 4 1000 600 400 5 1000 400 600 pdpedd ;0 6 1000 200 800 ppdbcpdpmcbVbdVGeertsma’s relations for elastic deformation and fluid pressure decline ppdmcbcpdpmcpVpdV1Hypothetical triaxial test pdPpdVpV1pcPorosity - compressibility ppdbcpdpmcbVbdVGeertsma’s relations for elastic deformation and fluid pressure decline ppdmcbcpdpmcpVpdV1Hypothetical triaxial test Step (Pov),psi pp,psi e,psi 1 200 200 0 2 400 200 200 3 600 200 400 0pdp 4 1000 200 800 ppedbdVbV1bcDetermination of pore compressibility by: 1. Lab measurements 2. correlations Porosity - compressibilityPorosity - compressibility = external confining pressure - Pore pressurePorosity - compressibility Hall’s (1953) correlation of porosity and cp. Cp at 75% lithostatic pressure vs. initial sample porosity for limestones [Newman, 1973] • decrease in rock compressibility as porosity increases • Accepted for consolidated rocks • compressibility is f(net effective stress)Porosity – compressibility Newman’s (1973) data and correlations for pore compressibility • includes consolidated, friable and unconsolidated samples •Considered most reliable, but results can be an order of magnitufde in
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