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General case

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\delta q = \frac{p_{\rm DTR}(t)}{p_{\rm CTR}(t)} \cdot \delta q_I

where 

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 is time since the water injection rate has changed by the 
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body\delta q_I
value.


Pseudo-steady state flow

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\delta q = \frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I


Steady state flow

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\delta q = \frac{c_{t,I} V_{\phi, I}}{c_t V_{\phi}} \cdot \delta q_I