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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:
- the dominant part of wellbore and reservoir pressure variation is usually radial-flow or linear-flow and the two represent the basis for Pressure diffusion analysis
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- in most practical cases the long-term correlation between the flowrate and bottom-hole pressure response can be approximated by a radial flow
Inputs & Outputs
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| \frac{\partial p}{\partial t} = \chi \, \left( \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} \right) |
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| p(t = 0, {\bf r}) = p_i |
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| p(t, r \rightarrow \infty ) = p_i |
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| \left[ r\frac{\partial p(t, r )}{\partial r} \bigg|right]_{r \rightarrow 0r_w} = \frac{q_t}{2 \sigmapi \, dsigma} |
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| p(t,r) = p_i + \frac{q_t}{4 \pi \sigma} \, F \bigg( - \frac{r^2}{4 \chi t} \bigg) |
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| p_{wf}(t) = p_i + \frac{q_t}{4 \pi \sigma} \, \bigg[ - 2S + F \bigg( - \frac{r_w^2}{4 \chi t} \bigg) \bigg] |
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where a single-argument function describing the peculiarities of the diffusion model (well geometry, penetration geometry, formation inhomogeneities, hydraulic fractures, boundary conditions, etc.)
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