Motivation
Reservoir pressure dynamics away from wellbore and boundaries is representative of two very important complex reservoir properties: transmissibility \sigma and pressure diffusivity \chi.
In case the reservoir flow has been created by a well (vertical or horizontal) it will trend to form a radial flow away from boundaries and well itself.
In this case a pressure drop and well flowrate can be roughly related to each other by means of a simple analytical homogeneous reservoir flow model with wellbore and boundary effects neglected.
Inputs & Outputs
Inputs | Outputs | ||
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q_t | total sandface rate | p(t,r) | reservoir pressure |
{p_i} | initial formation pressure | ||
\sigma | transmissibility | ||
\chi | pressure diffusivity |
Physical Model
Radial fluid flow | Homogenous reservoir | Infinite boundary | Zero wellbore radius | Slightly compressible fluid flow | Constant rate production |
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p(t, r) | M(r, p)=M =\rm const \phi(r, p)=\phi =\rm const h(r)=h =\rm const c_r(r)=c_r =\rm const | r \rightarrow \infty | r_w = 0 | c_t(p) = c_r +c = \rm const | q_t = \rm const |
Mathematical Model
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Computational Model
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Approximations
Late-time response | ||
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See also
Physics / Fluid Dynamics / Radial fluid flow / Line Source Solution
[ Radial Flow Pressure @model ] [ 1DR pressure diffusion of low-compressibility fluid ] [ Exponential Integral ]