...
LaTeX Math Block |
---|
|
\delta q_1 =-\sum_k f_{i1} \delta q_i
|
with constant coefficients LaTeX Math Inline |
---|
body | f_{i1} \geq 0, \ {k=\{i..N_{\rm inj} \} } |
---|
|
.
...
- 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:
LaTeX Math Inline |
---|
body | \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) |
---|
|
- Calculate DTR_11:
LaTeX Math Inline |
---|
body | \displaystyle p^*_{u, 11}(t) = p_{u, 11}(t) + \sum_{k \neq 1} p_{u, k1}(t) \cdot q^*_k |
---|
|
(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 |
---|
body | \displaystyle q^*_k = \frac{1}{N_k} \sum_{m=1}^{N_k} q_k(t_m) |
---|
|
- Calculate CTR_01:
LaTeX Math Inline |
---|
body | \displaystyle p^*_{u, 01}(t) = p_{u, 01}(t) + \sum_{k} p_{u, k1}(t) \cdot q^*_k |
---|
|
(meaning that injector W0 is working with unit-rate and all producers are working with constant rates )
- Calculate injection share constant as:
LaTeX Math Inline |
---|
body | \displaystyle f_{01} = - \frac{\dot p^*_{01}(t)}{\dot p^*_{11}(t)} \Bigg|_{t \rightarrow \infty} |
---|
|
...