For a porous rock there exists two volume element (rocks&pores) and two pressure elements(confining&pore pressure). This leads to four different kinds of compressibilities(Change in bulk volume, when pore/confining pressure is changing and Change in pore volume, when pore/confining pressure is changing).
Cbc = bulk compressibility as if material was non porous, used in wave propogation problems.
Cbp=puesdo bulk compressibility, used in subsidance calculations.
Cpc =formation compaction. Used to convert laboratory values to insitu pore volume of a reservoir rock.
Cpp=effective pore compressibility, used in diffusivity equation when added with Cf (fluid compressibility). Ct = Cf+Cpp.
Two basic assumptions while deriving (or measuring) any of these compressibilities is (1) Temperature is held constant.(Experimentalist ignores this assumption most of the time) (2) All compressibilities are ‘drained compressibilities’ (we can have the undrained test if we want). The magnitudes of these compressibilities and their variation with stress(pressure) are determined by the geometry of void spaces in the rock.
Consider a coring operation where when core arrived at surface and core barrel is opened, it is found that the real core diameter is much less than the diameter of core barrel. As per general intuition, the core should expand as it is removed from overburden and constantly taken out from drilling hole (due to a reduction in overburden pressure), but simultaneously we will have expulsion of reservoir fluids (change in pore pressure). Hence, this observation can be attributed to this relationship of pore and rock compressibility. Also, this gives us an opportunity of measurement of the reduction in core diameter which makes it possible to directly deduce the quantitative values of these compressibilities, If we can develop an appropriate model for such a phenomenon.