Fig. 1. Multi-rate drawdown test |
Given:
the superposition time is defined as:
\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 will be given by formula:
p_{wf}(t_s) = p_i + \frac{q_N B}{4 \pi \sigma} \ \ln t_s |
which has the same format as for a single rate drawdown test with flowrate , and duration and can be interpreted using Type-Curve Matching.
Fig. 2. Multi-rate build-up test |
Given:
the superposition time is defined as:
\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 will be given by formula:
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 , and duration and can be interpreted using Type-Curve Matching.
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