Dimensionless transient water flux response from aquifer to unit step change in net pay pressure:

(1)	$\begin{array}{l}\displaystyle W_{eD}(t, r_{aD}) = \int_0^{t} \frac{\partial p_1( t_D, r_D)}{\partial r_D} \Bigg\|_{r_D=1} dt_D\end{array}$

where

$\begin{array}{l}p_1(t_D, r_D)\end{array}$

solution of unit-pressure radial composite reservoir transient flow (2)– (5)

(2)	$\begin{array}{l}\displaystyle \frac{\partial p_1}{\partial t_D} = \frac{\partial^2 p_1}{\partial r_D^2} + \frac{1}{r_D}\cdot \frac{\partial p_1}{\partial r_D}\end{array}$

(3)	$\begin{array}{l}\displaystyle p_1(t_D = 0, r_D)= 0\end{array}$

(4)	$\begin{array}{l}\displaystyle p_1(t_D, r_D=1) = 1\end{array}$

(5)	$\begin{array}{l}\displaystyle \frac{\partial p_1(t_D, r_D)}{\partial r_D} \Bigg\|_{r_D=r_{aD}} = 0\end{array}$

or

(6)	$\begin{array}{l}\displaystyle p_1(t_D, r_D = \infty) = 0\end{array}$

The Dimensionless Water Influx $\begin{array}{l}W_{eD}(t)\end{array}$ is a unique function of time $\begin{array}{l}t\end{array}$ for each dimensionless value of $\begin{array}{l}r_{aD}\end{array}$ which represents the ratio of external aquifer size $\begin{array}{l}r_a\end{array}$ to net pay size $\begin{array}{l}r_e\end{array}$ :

(7)	$\begin{array}{l}\displaystyle r_{aD} = \frac{r_a}{r_e}\end{array}$

This function is readily tabulated for a wide range of $\begin{array}{l}r_{aD}\end{array}$ variations.

There are also polynomial approximations.

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Dimensionless Water Influx (WeD)

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