Motivation
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| Aquifer Drive |
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| Aquifer Drive |
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| nopanel | true |
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Assumptions
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| Transient flow in Radial Composite Reservoir |
Equations
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| \frac{d Q^{\downarrow}_{AQ}}{dt} = q^{\downarrow}_{AQ}(t) |
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| q^{\downarrow}_{AQ}(t)= C_a \cdot \frac{\partial p_a(t,r)}{\partial r} \bigg|_{r=r_e} |
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| p_a(t, r)= p(0) + \int_0^t p_1 \left(\frac{(t-\tau) \cdot \chi}{r_e^2}, \frac{r}{r_e} \right) \dot p(\tau) d\tau |
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| \frac{\partial p_1}{\partial t_D} = \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D} |
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| p_1(t = 0, r_D)= 0 |
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| p_1(t, r_D=1) = 1 |
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| \frac{\partial p_1}{\partial r_D} \bigg|_ {r_D=r_a/r_e} = 0 |
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Transient flow in Radial Composite Reservoir:
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| \frac{\partial p_a}{\partial t} = \chi \cdot \left[ \frac{\partial^2 p_a}{\partial r^2} + \frac{1}{r}\cdot \frac{\partial p_a}{\partial r} \right] |
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| p_a(t = 0, r)= p(0) |
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| p_a(t, r=r_e) = p(t) |
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| anchor | p1_PSS |
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| alignment | left |
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| \frac{\partial p_a}{\partial r} \bigg|_ {r=r_a} = 0 |
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One can easily check that pressure from | LaTeX Math Block Reference |
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honors the whole set of equations | LaTeX Math Block Reference |
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–| LaTeX Math Block Reference |
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and as such defines a unique solution of the above problem. |
See Also
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Petroleum Industry / Upstream / Subsurface E&P Disciplines / Field Study & Modelling / Aquifer Drive / Aquifer Drive Models
Reference
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1. van Everdingen, A.F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoirs. Trans., AIME 186, 305.
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