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The equations | LaTeX Math Block Reference |
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, | LaTeX Math Block Reference |
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and | LaTeX Math Block Reference |
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make one of the key assumptions in Capacitance Resistance Model (CRM).
It is important to note that assumption that CRM assumption that injector W0 may drain bigger volume than volume than producer W1 | LaTeX Math Inline |
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| body | V_{\phi, 0}> V_{\phi, 1} |
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is a misnomer in most practical cases.
When wells (producers and injectors) are placed into interconnected the same connected reservoir volume they drain the same total volume alltogether and the DTR/CTR all together and all UTRs will have the same same LTR asymptotic asymptotic:
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p_{u,\rm ik}(t \rightarrow \infty ) \rightarrow \frac{t}{c_t \, V_\phi}, \quad \forall i \in N_{\rm inj}, k \in N. |
where is reservoir storage.
Moreover, if each well is placed in different reservoir volumes which are only connected through wellbores then again they will all drain the same volume which is the sum of all connected volumes through the wellbores and the DTR/CTR all UTRs will again trend to the same same LTR asymptotic.
In order to relate the UTR UTR from numerical grid simulations or from deconvolution theory to the the CRM injection share constants one need to implement a following trick.
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