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In case injector W0 supports only one producer W1 , then both wells drain the same reservoir volume
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| body | V_{\phi, 0} = V_{\phi, 1} |
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so that
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leads to:
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In order to relate the UTR from numerical grid simulations or from deconvolution theory to the CRM injection share constants one need needs to implement a following trick:certain workflow.
- Collect true UTRs with the same LTR asymptotic.
- Perform two convolution tests in virtual space:
- Test #1 – DTR 11
- Calculate historically-averaged rate for each producer:
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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:
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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 all producers are working with constant rates , except producer W1 which is working with unit-rate and injector W0 which is shut-down )
- Test #2 – CTR 01
- Calculate historically-averaged rate for each producer:
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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:
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| body | \displaystyle p^*_{u, 01}(t) = p_{u, 11}(t) + \sum_{k \neq 1} p_{u, k1}(t) \cdot q^*_k + p_{u, 01}(t) \cdot q^*_0 |
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(meaning that all producers are working with constant rates , except producer W1 which is working with unit-rate and injector W0 which is shut-down )
- qwe
Again it is important to note Again it is important to notew a difference between
- CRM assumptions (constant PI, constant drainage volumes with no flow boundaries and constant total compressibility) – which may or may not take place and hence may or may not make CRM applicable
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