By Robert W. Zimmerman
This e-book is a complete remedy of the elastic volumetric reaction of sandstones to adaptations in pressure. the idea and knowledge offered practice to the deformations that take place, for instance, because of withdrawal of fluid from a reservoir, or a result of redistribution of stresses because of the drilling of a borehole. even supposing the emphasis is on reservoir-type sandstones, effects and techniques mentioned also are acceptable to different porous rocks. half One issues the influence of pressure 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 idea that of powerful tension coefficients is tested, as is the built-in kind of the stress-strain relationships. Undrained compression and triggered pore pressures are handled in the comparable common framework. half One is concluded with a quick, common advent to Biot's idea of poroelasticity. all of the ends up in half One are illustrated and confirmed with large references to released compressibility info. half bargains with the connection among pore constitution and compressibility, and offers tools that allow quantitative prediction of the compressibility coefficients. - and third-dimensional types of tubular pores, spheroidal pores, and crack-like "grain boundary" voids are analyzed. A serious evaluate is made up of quite a few tools which have been 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 info or from acoustic measurements are provided, besides functions to real sandstone info. half 3 is a short precis of experimental innovations which are used to degree porous rock compressibilities within the laboratory. the data 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 info for Compressibility of Sandstones
6. Range of bulk compressibilities C , of twenty-four sandstones [after Fatt, 19581. The upper end of each vertical line represents the value at P,=O, while the lower end represents the value at (a) 15,000 psi, or (b) 7000 psi. 1. 31 As an example of this behavior, consider the compressibilities measured by Fatt [1958al. Fatt measured the pore compressibilities Cpc of twenty-four consolidated sandstones, and then converted these measurements to C , values through the (incorrect) equation C , = #Cpc.
Furthermore, since it directly utilizes the solid rock volume V , , this method is more readily generalized to inelastic behavior. Starting with the definition $= Vp/ v b , and using the rules for differentiating quotients, an analysis similar to that carried out for V p and v b can be carried out for changes in the porosity: so In+ = lnVp - 1 n V b . 0, and the incremental porosity change depends only on the change in the difference between P, and P p . The term [ C k ( l - @ ) - C r ] is necessarily positive, so the porosity is a decreasing function of the differential pressure P , = P, - P p .
6b, as functions of the initial porosity. The compressibilities for each core plot as vertical lines whose upper endpoints represent to compressibility at zero stress, and whose lower endpoints represent the high-stress asymptotes. The theoretical lower bound shown in the figures was calculated from eqn. 20. In each case, the compressibility starts at a high value at zero pressure, and decreases down towards the lower bound as the confining pressure increases. An interesting fact that also emerges from Fig.