Table 1 Summary of the variables in the model.
From: A new analytical model for flow in acidized fractured-vuggy porous media
Defined parameters | Expressions |
|---|---|
Dimensionless time, tD | \({t}_{{\rm{D}}}={k}_{{\rm{F}}}t/[({\phi }_{{\rm{M}}}{C}_{{\rm{M}}}+{\phi }_{{\rm{F}}}{C}_{{\rm{F}}}+{\phi }_{{\rm{v}}}{C}_{{\rm{v}}})\mu {r}_{{\rm{w}}}^{2}]\) |
Dimensionless pressure, pD | \({p}_{{\rm{D}}}=2{\rm{\pi }}{k}_{{\rm{F}}}h({p}_{{\rm{0}}}-p)/(qB\mu )\) |
Dimensionless radius, rD | \({r}_{{\rm{D}}}=r/{r}_{{\rm{w}}}\) |
Diffusivity ratio between the two regions, η1D | \({\eta }_{{\rm{1D}}}={C}_{{\rm{t1}}}{\phi }_{1}/({\phi }_{{\rm{M}}}{C}_{{\rm{M}}}+{\phi }_{{\rm{F}}}{C}_{{\rm{F}}}+{\phi }_{{\rm{v}}}{C}_{{\rm{v}}})\) |
Fracture storage capacitance coefficient, ηFD | \({\eta }_{{\rm{FD}}}={C}_{{\rm{F}}}{\phi }_{{\rm{F}}}/({\phi }_{{\rm{M}}}{C}_{{\rm{M}}}+{\phi }_{{\rm{F}}}{C}_{{\rm{F}}}+{\phi }_{{\rm{v}}}{C}_{{\rm{v}}})\) |
Matrix storage capacitance coefficient, ηMD | \({\eta }_{{\rm{MD}}}={C}_{{\rm{M}}}{\phi }_{{\rm{M}}}/({\phi }_{{\rm{M}}}{C}_{{\rm{M}}}+{\phi }_{{\rm{F}}}{C}_{{\rm{F}}}+{\phi }_{{\rm{v}}}{C}_{{\rm{v}}})\) |
Vug storage capacitance coefficient, ηvD | \({\eta }_{{\rm{vD}}}={C}_{{\rm{v}}}{\phi }_{{\rm{v}}}/({\phi }_{{\rm{M}}}{C}_{{\rm{M}}}+{\phi }_{{\rm{F}}}{C}_{{\rm{F}}}+{\phi }_{{\rm{v}}}{C}_{{\rm{v}}})\) |
Permeability ratio, M1 | \({M}_{1}={k}_{{\rm{1}}}/{k}_{{\rm{F}}}\) |
Fracture-matrix inter-porosity coefficient, λFM | \({\lambda }_{{\rm{FM}}}={\alpha }_{{\rm{FM}}}{r}_{{\rm{w}}}^{2}{k}_{{\rm{M}}}/{k}_{{\rm{F}}}\) |
Fracture-vug inter-porosity coefficient, λFv | \({\lambda }_{{\rm{Fv}}}={\alpha }_{{\rm{Fv}}}{r}_{{\rm{w}}}^{2}{k}_{{\rm{v}}}/{k}_{{\rm{F}}}\) |
