In case the stress on rock and saturated fluids are in pressure equilibrium the total compressibility of formation can be expressed via fluid compressibility c_f and reservoir pore compressibility c_\phi as:
| (1) | c_t = c_\phi + c_f |
See Total compressibility @model for derivation.
In most popular practical case of a 3-phase fluid model the fluid compressibility will be:
| (2) | c_f = c_w \, s_w + c_o \, s_o + c_g \, s_g |
where {w, \, o, \, g} mean water phase, oil phase and gas phase.
Some applications (like multi-phase pressure diffusion) account for the impact of cross-phase fluid exchange on total compressibility which require some corrections to equation (1) and (2):
| (3) | c_t(s,p) = c_\phi + c_w s_w + c_o s_o + c_g s_g + s_o [ R_{sp} + (c_r + c_o) R_{sn} ] + s_g [ R_{vp} + R_{vn}(c_r + c_g) ] |
where
R_{sn}, \; R_{vn} | normalized cross-phase exchange ratios as functions of reservoir pressure p and temperature T |
R_{sp}, \; R_{vp} | normalized cross-phase exchange derivatives as functions of reservoir pressure p and temperature T |
See Non-linear multi-phase pressure diffusion @model for derivation of (3).
See also
Petroleum Industry / Upstream / Subsurface E&P Disciplines / Petrophysics (PP) / Volumetric Rock Model
[Compressibility] [Single-phase fluid compressibility] [Multi-phase fluid compressibility] [Pore compressibility (cr)]
[Total compressibility @model]