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titleDerivation

Consider a pressure convolution equation for the above 2-wells system with constant BHP:

LaTeX Math Block
anchorCase2_PSS_p11
alignmentleft
p_1(t) = p_i - \int_0^t p_{u,\rm 11}(t) dq_1 - \int_0^t p_{u,\rm 21}(t) dq_2 = \rm const

The time derivative is going to be 

LaTeX Math Block
anchorCase2_PSS_p11
alignmentleft
\dot p_1(t) = - \left( \int_0^t p_{u,\rm 11}(t) dq_1 \right)^{\cdot} - \left( \int_0^t p_{u,\rm 21}(t) dq_2 \right)^{\cdot} = 0


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