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- Start with true UTRs
with the same LTR asymptoticLaTeX Math Inline body \displaystyle p_{u, ik}(t)
.LaTeX Math Inline body \displaystyle p_{u, ik}(t) \rightarrow \frac{t}{RS} - Select injector W0
- Select producer W1
- Perform two convolution tests
- to account for the impact from {W2 .. WN} production on to DTR_11
and CTR_01LaTeX Math Inline body p_{u, 11}(t)
:LaTeX Math Inline body p_{u, 01}(t) - Test #1 – DTR_11
- Calculate historically-averaged rate for each producer:
LaTeX Math Inline body \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) - Calculate interfering DTR_11:
, meaning that injector W0 is shut-down and all producers are working with constant ratesLaTeX Math Inline body \displaystyle p^*_{u, 11}(t) = p_{u, 11}(t) + \sum_{k \neq 1} p_{u, k1}(t) \cdot q^*_k
, except producer W1 which is working with unit-rateLaTeX Math Inline body q^*_k
- Calculate historically-averaged rate for each producer:
- Test #2 – CTR_01
- Calculate historically-averaged rate for each producer:
LaTeX Math Inline body \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) - Calculate interfering CTR_01:
, meaning that injector W0 is working with unit-rate and all producers are working with constant ratesLaTeX Math Inline body \displaystyle p^*_{u, 01}(t) = p_{u, 01}(t) + \sum_{k} p_{u, k1}(t) \cdot q^*_k LaTeX Math Inline body q^*_k
- Calculate historically-averaged rate for each producer:
- Test #1 – DTR_11
- Calculate injection share constant:
as LLS over equation:LaTeX Math Inline body \displaystyle f_{01} = \frac{\dot p^*_{01}(t)}{\dot p^*_{11}(t)} \Bigg|_{t \rightarrow \infty} LaTeX Math Inline body \displaystyle \dot p^*_{01}(t) = f_{01} \cdot \dot p^*_{11}(t)
- to account for the impact from {W2 .. WN} production on to DTR_11
- Repeat the same for other producers (starting from point
- 2a onwards)
- Select producer W1
- Repeat the same for other injectors (starting from point 2 onwards)
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