Integral-average Average reservoir pressure over the drainage volume
:
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p_r = \frac{1}{V_e} \iint_{A_e} p(x,y,z) dSdV |
For the steady state flow in Steady State Radial Flow in finite reservoir the relationship between Boundary-average formation pressure
and
Field-average Drainarea formation pressure is going to be:
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p_r = p_i +- \frac{q_t}{24 \pi \sigma} \bigg[ \ln \frac{r_e}{r_w} -0.5 \bigg] |
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| V_e = \pi r_e^2 h, \quad dV = 2\pi r \, h |
, | BXEPW | p_r = \frac{1}{V_e} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr |
For the Steady State Radial Flow in finite reservoir the reservoir pressure is going to be: | LaTeX Math Block |
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| p(t,r) = p_e(t) + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_e} = p_i + \frac{q_t}{2 \pi \sigma} \, \ln \frac{r}{r_e} |
and substituting the above to | LaTeX Math Block Reference |
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and integrating:| LaTeX Math Block |
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| p_r = \frac{2}{r_e^2} \int \bigg[ p_i |
-+ \frac{q_t}{2\pi \sigma} \ln \frac{r}{r_ |
we} \bigg] \, r \, dr = p_i - \frac{q_t}{4\pi \sigma} |
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For the Pseudo-Steady State Radial Flow in finite reservoir the relationship between Boundary-average formation pressure
and Drainarea formation pressure is going to be:| LaTeX Math Block |
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p_r(t)= p_e(t) - 0.75 \cdot \frac{q_t}{2 \pi \sigma} |
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| V_e = \pi r_e^2 h, \quad dV = 2\pi r \, h dr |
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| p_r = \frac{1}{V_e} \int p(r) dV = \frac{2}{r_e^2} \int p(r) \, r \, dr |
For the Pseudo-Steady State Radial Flow in finite reservoir the reservoir pressure is going to be: | LaTeX Math Block |
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| p(r) = p_i + \frac{q_t}{4 \pi \sigma} \, \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_e^2} \right] |
and substituting the above to | LaTeX Math Block Reference |
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and integrating:| LaTeX Math Block |
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| p_r(t) = \frac{2}{r_e^2} \int \bigg[ p_e(t) + \frac{q_t}{4\pi \sigma} \left[ 2 \ln \frac{r}{r_e} - \frac{r^2}{r_ |
w-1\right] \bigg] \, r \, dr = p_i - 0.75 \cdot \frac{q_t}{2\pi \sigma} |
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See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Well & Reservoir Management / Formation pressure (Pe)
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