Motivation

Inputs & Outputs

Inputs		Outputs
	field-average formation pressure at time moment		Cumulative subsurface water influx from aquifer
	initial formation pressure		Subsurface water flowrate from aquifer
	water influx constant
	aquifer diffusivity
	net pay area

Detailing Inputs
	water influx constant
	central angle of net pay area ↔ aquifer contact
	aquifer effective thickness
	aquifer porosity
	aquifer total compressibility
	aquifer pore compressibility
	aquifer water compressibility

Transient flow in Radial Composite Reservoir

\frac{d Q^{\downarrow}_{AQ}}{dt} = q^{\downarrow}_{AQ}(t)

q^{\downarrow}_{AQ}(t)= C_a \cdot \frac{\partial p_a(t,r)}{\partial r} \bigg|_{r=r_e}

p_a(t, r)= p(0) + \int_0^t p_1 \left(\frac{(t-\tau) \cdot \chi}{r_e^2}, \frac{r}{r_e} \right) \dot p(\tau) d\tau

\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}

p_1(t = 0, r_D)= 0

p_1(t, r_D=1) = 1

\frac{\partial p_1}{\partial r_D} \bigg|_ {r_D=r_a/r_e} = 0

Transient flow in Radial Composite Reservoir:

\frac{\partial p_a}{\partial t} = \chi \cdot \left[ \frac{\partial^2 p_a}{\partial r^2} + \frac{1}{r}\cdot \frac{\partial p_a}{\partial r} \right]

p_a(t = 0, r)= p(0)

p_a(t, r=r_e) = p(t)

\frac{\partial p_a}{\partial r} \bigg|_ {r=r_a} = 0

1. van Everdingen, A.F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoirs. Trans., AIME 186, 305.