Multi-rate Shut-in Build-up Test
(1) | \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) |
Multi-rate Shut-in Build-up Test
(1) | \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) |