Multi-rate drawdown test
Fig. 1, . Multi-rate build-up drawdown test |
Given:
- a discrete flowrate history
followed by shut-in periodLaTeX Math Inline body \{ \, (\Delta t_1, q_1) , \, (\Delta t_2, q_2) , \, (\Delta t_3, q_3) , \, (\Delta t_{N-1}, q_{N-1}) , \, (\Delta t_N, q_N = 0) , \, \} mathinline
(see Fig. 1)body (\Delta t_N, q_N = 0) - vertical well and homogeneous reservoir with no boundaries
- The duration of the last shut-in
reaching radial flow regimeLaTeX Math Inline body \Delta t_N
the superosition time is defined as:
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\ln t_s = \ln (t-t_{N-1}) - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}} \ln (t-t_{i-1}) = \ln \Delta t - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}} \ln \left( \Delta t + \sum_{i=1}^{N-i} \Delta t_i \right) |
The pressure response at time moment
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p_{wf}(t_s) = p_i + \frac{q_{N-1} B}{4 \pi \sigma} \ \ln t_s |
which has the same format as for a single rate drawdown test with flowrate
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Multi-rate build-up test
Fig. 1, 2. Multi-rate build-up test |
Given:
- a discrete flowrate history
followed by shut-in periodLaTeX Math Inline body \{ \, (\Delta t_1, q_1) , \, (\Delta t_2, q_2) , \, (\Delta t_3, q_3) , \, (\Delta t_{N-1}, q_{N-1}) , \, (\Delta t_N, q_N = 0) , \, \}
(see Fig. 12)LaTeX Math Inline body (\Delta t_N, q_N = 0) - vertical well and homogeneous reservoir with no boundaries
- The duration of the last shut-in
reaching radial flow regimeLaTeX Math Inline body \Delta t_N
the superosition time is defined as:
LaTeX Math Block | ||||
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\ln t_s = \ln (t-t_{N-1}) - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}} \ln (t-t_{i-1}) = \ln \Delta t - \sum_{i=1}^{N-1} \frac{q_i - q_{i-1}}{q_{N-1}} \ln \left( \Delta t + \sum_{i=1}^{N-i} \Delta t_i \right) |
The pressure response at time moment
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p_{wf}(t_s) = p_i + \frac{q_{N-1} B}{4 \pi \sigma} \ \ln t_s |
which has the same format as for a single rate drawdown test with flowrate
LaTeX Math Inline | ||
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LaTeX Math Inline | ||
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