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In many practical cases the reservoir fluid flow created  created by well is  is getting aligned with a radial direction towards or away from well.

This type of reservoir fluid flow is  is called radial fluid flow and corresponding pressure diffusion models provide a diagnostic basis for pressure-rate base reservoir flow analysis.

The radial flow can be infinite acting or boundary dominated or  or transiting from one to another.

Although the actual reservoir fluid flow may not have an axial symmetry around the well-reservoir contact or reservoir inhomogeneities (like boundary and faults and composite areas) but still:


Formation pressure pressure 

LaTeX Math Inline
body{p_i}
, skin-factor factor 
LaTeX Math Inline
bodyS
, transmissibility  transmissibility 
LaTeX Math Inline
body\sigma
 and pressure diffusivity diffusivity 
LaTeX Math Inline
body\chi
 are called basic diffusion model parameters as they are essential components of all diffusion models.

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InputsOutputs

LaTeX Math Inline
bodyq_t

total sandface rate

LaTeX Math Inline
bodyp(t,r)

reservoir pressure

LaTeX Math Inline
body{p_i}

initial formation pressure

LaTeX Math Inline
body{p_{wf}(t)}

well bottomhole pressure

LaTeX Math Inline
body\sigma

transmissibility

LaTeX Math Inline
body\chi

pressure diffusivity

LaTeX Math Inline
bodyS

skin-factor


Expand
titleDetailing


LaTeX Math Inline
body\sigma = \frac{k \, h}{\mu}

transmissibility

LaTeX Math Inline
body\mu

dynamic fluid viscosity

LaTeX Math Inline
body\chi = \frac{k}{\mu} \, \frac{1}{\phi \, c_t}

pressure diffusivity

LaTeX Math Inline
bodyc_t = c_r + c

total compressibility

LaTeX Math Inline
bodyk

absolute permeability

LaTeX Math Inline
body{c_r}

pore compressibility

LaTeX Math Inline
body{\phi}

porosity

LaTeX Math Inline
bodyc

fluid compressibility


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Radial fluid flowHomogenous reservoirInfinite boundarySlightly compressible fluid flowConstant rateConstant Skin skin

LaTeX Math Inline
bodyp(t, r)

LaTeX Math Inline
bodyM(r, p)=M =\rm const

LaTeX Math Inline
body\phi(r, p)=\phi =\rm const

LaTeX Math Inline
bodyh(r)=h =\rm const

LaTeX Math Inline
bodyc_r(r)=c_r =\rm const

LaTeX Math Inline
bodyr \rightarrow \infty

LaTeX Math Inline
bodyr_w = 0

LaTeX Math Inline
bodyc_t(r,p) = \rm const

LaTeX Math Inline
bodyq_t = \rm const

LaTeX Math Inline
bodyS = \rm const

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