Motivation
In many practical cases the reservoir flow created by well or group of wells is getting aligned with a specific linear direction away from well.
This happens when well is placed in a channel or a narrow compartment. It also happens around fracture planes and conductive faults.
This type of flow is called linear fluid flow and a type library model provides a reference for linear fluid flow diagnostics.
Inputs & Outputs
Inputs | Outputs | ||
---|---|---|---|
q_t | total sandface rate | p(t,x) | reservoir pressure |
p_i | initial formation pressure | p_{wf}(t) | well bottomhole pressure |
d | reservoir channel width | ||
\sigma | transmissibility | ||
\chi | pressure diffusivity |
Physical Model
Linear fluid flow | Homogenous reservoir | Infinite boundary | Zero wellbore radius | Slightly compressible fluid flow | Constant rate production |
---|---|---|---|---|---|
p(t, {\bf r}) \rightarrow p(t, x) | M(x, p)=M =\rm const \phi(x, p)=\phi =\rm const h(x)=h =\rm const | x \rightarrow \infty | r_w = 0 | c_t(p) = c_r +c = \rm const | q_t = \rm const |
Mathematical Model
Applications
Pressure Testing – Channel or Narrow reservoir compartment
Pressure Drop |
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Log derivative |
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Fig. 2. PTA Diagnostic plot for linear fluid flow in reservoir channel |
Pressure Testing – Infinite conductivity fracture
Pressure Drop |
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Log derivative |
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Fig. 2. PTA Diagnostic plot for linear fluid flow in infinite conductivity fracture |
See also
Physics / Fluid Dynamics / Linear fluid flow
[ Radial Flow Pressure Diffusion @model ]