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This type of flow 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 transiting from one to another.

Although the actual 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 

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

Inputs & Outputs

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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

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Equations 

LaTeX Math Block Reference
anchorp_F
 and   and 
LaTeX Math Block Reference
anchorpwf
play
 show how the basic diffusion model parameters impact the pressure response while other diffusion parameters are encoded in 
LaTeX Math Inline
bodyF
 function and play important methodological role as they are used in many algorithms and express-methods of of Pressure Testing.


Expand
titleLine Source Solution


In simplest case of infinite homogeneous reservoir, produced by a vertical well the 

LaTeX Math Inline
bodyF
 function has an exact analytical formula, given by exponential integral 
LaTeX Math Inline
bodyF(z) = {\rm Ei}_1 (z)
 (see Line Source Solution (LSS) @model).


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