By Robert W. Zimmerman
This e-book is a entire therapy of the elastic volumetric reaction of sandstones to diversifications in pressure. the speculation and knowledge provided practice to the deformations that take place, for instance, because of withdrawal of fluid from a reservoir, or a result of redistribution of stresses as a result of the drilling of a borehole. even though the emphasis is on reservoir-type sandstones, effects and techniques mentioned also are appropriate to different porous rocks. half One matters the impression of tension on deformation and discusses porous rock compressibility coefficients. Elasticity idea is used to derive relationships among the porous rock compressibility coefficients, the porosity, and the mineral grain compressibility. Theoretical bounds at the compressibility coefficients are derived. the concept that of potent pressure coefficients is tested, as is the built-in kind of the stress-strain relationships. Undrained compression and brought about pore pressures are handled in the comparable normal framework. half One is concluded with a quick, user-friendly advent to Biot's thought of poroelasticity. the entire leads to half One are illustrated and validated with vast references to released compressibility info. half bargains with the connection among pore constitution and compressibility, and provides equipment that allow quantitative prediction of the compressibility coefficients. - and third-dimensional versions of tubular pores, spheroidal pores, and crack-like "grain boundary" voids are analyzed. A serious evaluate is made up of a variety of equipment which were proposed to narrate the powerful elastic moduli (bulk and shear) of a porous fabric to its pore constitution. tools for extracting pore point ratio distributions from stress-strain facts or from acoustic measurements are offered, in addition to functions to genuine sandstone information. half 3 is a short precis of experimental options which are used to degree porous rock compressibilities within the laboratory. the knowledge contained during this quantity is of curiosity to petroleum engineers, particularly these concerned with reservoir modeling, petroleum geologists, geotechnical engineers, hydrologists and geophysicists.
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Extra resources for Compressibility of Sandstones
A , B and D were found for fixed values of F, after which an optimum value of p was found by minimizing the variance between the measured strains and the fitted curve. In each case, the standard deviation between the optimum curve and the data was no more than about 1%. 9990. The pore compressibility Cpc is then found by differentiating eqn. 8) with respect to P, : cPc= A +(B/F)e-PJP . 01 0 0 10 20 30 40 CONFINING STRESS, pC (MPa) 50 Fig. 1. , 1986aJ. Curves are found from least-squares fits to functions of the form given in eqn.
The excellent agreement (Fig. 4) not only verifies eqn. 7), but also illustrates that the dynamic compressibility of a dry sandstone is equivalent to the static value. This issue has often led to confusion, mostly caused by the fact that when acoustic waves travel through a fluid-sururured rock, the proper dynamic compressibility is nor equal simply to C, (see Chapter 6). o 0 0 I I 2 000 Pc I 0 4000 - Pp (PSI) Fig. 5. Measured values [Greenwald, 19801 of cbp for a Boise sandstone, compared with the .
8). (Note that almost all laboratory measurements of physical properties of reservoir rocks have been conducted under positive differential pressures, i . e . , P , > P p , which fall below the 45O line in Fig. 8. ) For the first stage of this path, P p =0, so (P, - P p ) = P,, and dEb = - C k ( P c ) d P , . Using P without a subscript as a dummy variable of integration, 46 20 I I I I 0 0 10 20 30 40 CONFINING STRESS, Pc (MPa) 50 Fig. 2. Pore compressibility C of a Boise sandstone as a function of confining pressure, at F.