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Although the actual reservoir fluid flow may not have an axial symmetry around the well-reservoir contact or around reservoir inhomogeneities (like boundary and faults and composite areas) but still  in still in many practical cases the long-term correlation between the flowrate and bottom-hole pressure response can be approximated by a radial flow pressure modelthe reservoir flow tends to become radial after some time which makes a Radial Flow Pressure Diffusion @model (in its general form or in particular BVP solution) a popular diagnostic tool. 


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\sigma = \frac{k \, h}{\mu}



LaTeX Math Inline
body\chi

pressure diffusivity,

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



LaTeX Math Inline
bodyS

skin-factor

LaTeX Math Inline
bodyr_w

wellbore radius

LaTeX Math Inline
bodyr_e

drainage radius (could be infinite)

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Equations 

LaTeX Math Block Reference
anchorp_F
 and 
LaTeX Math Block Reference
anchorpwf
 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 Pressure Testing.In many practical cases the reservoir flow tends to become radial after some time which makes a Radial Flow Pressure Diffusion @model (in its general form or in particular BVP solution) a popular diagnostic tool. 


Expand
titleLine Source Solution


In case of infinite homogeneous reservoir, produced by a infinitely small vertical well with no skin and no wellbore storage the 

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


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