GLOSSARY

Page tree

Versions Compared

Old Version 56

changes.mady.by.user Arthur Aslanyan (Nafta College)

Saved on

compared with

New Version 57

changes.mady.by.user Arthur Aslanyan (Nafta College)

Saved on

Key

  • This line was added.
  • This line was removed.
  • Formatting was changed.

...

LaTeX Math Block
anchorCase2
alignmentleft
\delta q_1(t) = - \frac{\dot p_{u,\rm 21}(t)}{\dot p_{u,\rm 11}(t)} \cdot \delta q_2

where

LaTeX Math Inline
bodyt

time

since the water injection

since injector's W2 rate has changed

by the 

by 

LaTeX Math Inline
body\delta q_2

in injector W2

.

LaTeX Math Inline
body\dot p_{u,\rm 21}(t)

cross
time derivative of cross-well pressure transient response (CTR) in producer W1 to the unit-rate production in injector W2

LaTeX Math Inline
body\dot p_{u,\rm 11}(t)

drawdown

time derivative of drawdown pressure transient response (DTR) in producer W1 to the unit-rate production in the same well


Expand
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-\tau) dq_1(\tau) - \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) = \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-\tau) dq_1(\tau) \right)^{\cdot} - \left( \int_0^t p_{u,\rm 21}(t-\tau) dq_2(\tau) \right)^{\cdot} = 0


LaTeX Math Block
anchorCase2_PSS_p11
alignmentleft
 p_{u,\rm 11}(0) \cdot q_1(t) + \int_0^t \dot p_{u,\rm 11}(t-\tau) dq_1(\tau)  = - p_{u,\rm 21}(0) \cdot q_2(t) -  \int_0^t \dot p_{u,\rm 21}(t-\tau) dq_2(\tau)


...