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| r_{wf} < r \leq r_e |
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| p(t, r ) = p(r) \Leftrightarrow \frac{\partial p}{\partial t} = 0 |
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| \frac{\partial^2 p}{\partial r^2} + \frac{1}{r} \frac{\partial p}{\partial r} =0 |
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| p(r_e ) = p_i |
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| \left[ r\frac{\partial p(r )}{\partial r} \right]_{r \rightarrow r_w} = \frac{q_t}{2 \pi \sigma} |
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| p_{wf}= p(r_w ) - S \cdot r_w \, \frac{\partial p}{\partial r} \Bigg|_{r=r_w} |
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Equation
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shows how the
basic diffusion model parameters impact the relation between
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body | \Delta p = p_i - p_{wf} |
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and
total sandface flowrate and plays important methodological role as they are used in many algorithms and express-methods of
Pressure Testing.
It also called Dupuis
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title | Productivity Index Analysis |
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The Total Sandface Productivity Index for low-compressibility fluid and low-compressibility rocks does not depend on formation pressure, bottomhole pressure and the flowrate and can be expressed as: LaTeX Math Block |
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| J_t = \frac{q_t}{p_i - p_{wf}(t)} =\frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} + S} = {\rm const} |
The Field-average Productivity Index for low-compressibility fluid and low-compressibility rocks does not depend on formation pressure, bottomhole pressure and the flowrate and can be expressed as: LaTeX Math Block |
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| J_t = \frac{q_t}{p_r(t) - p_{wf}(t)} =\frac{2 \pi \sigma}{\ln \frac{r_e}{r_w} + 0.5 +S} = {\rm const} |
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See Also
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Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Radial fluid flow / Pressure diffusion / Pressure Diffusion @model / Radial Flow Pressure Diffusion @model
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