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In order to relate true UTRs (from numerical grid simulations or from deconvolution) to the CRM injection share constants one needs to implement a certain workflow.:
- Collect Start with true UTRs
LaTeX Math Inline |
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body | \displaystyle p_{u, ik}(t) |
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with the same LTR asymptotic LaTeX Math Inline |
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body | \displaystyle p_{u, ik}(t) \rightarrow \frac{t}{RS} |
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. - Select injector W0
- Select producer W1
- Perform two convolution tests in virtual space:
- Test #1 – DTR_11
- Calculate historically-averaged rate for each producer:
LaTeX Math Inline |
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body | \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) |
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- Calculate DTR_11:
LaTeX Math Inline |
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body | \displaystyle p^*_{u, 11}(t) = p_{u, 11}(t) + \sum_{k \neq 1} p_{u, k1}(t) \cdot q^*_k |
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(meaning that injector W0 is shut-down and all producers are working with constant rates , except producer W1 which is working with unit-rate)
- Test #2 – CTR_01
- Calculate historically-averaged rate for each producer:
LaTeX Math Inline |
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body | \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) |
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- Calculate CTR_01:
LaTeX Math Inline |
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body | \displaystyle p^*_{u, 01}(t) = p_{u, 01}(t) + \sum_{k} p_{u, k1}(t) \cdot q^*_k |
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(meaning that injector W0 is working with unit-rate and all producers are working with constant rates )
- Calculate injection share constant:
LaTeX Math Inline |
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body | \displaystyle f_{01} = \frac{\dot p^*_{01}(t)}{\dot p^*_{11}(t)} \Bigg|_{t \rightarrow \infty} |
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as LLS over equation: LaTeX Math Inline |
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body | \displaystyle \dot p^*_{01}(t) = f_{01} \cdot \dot p^*_{11}(t) |
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- Repeat the same for other producers (starting from point 3 onwards)
- Repeat the same for other injectors (starting from point 2 onwards)
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