Motivation

The most accurate way to simulate Aquifer Expansion (or shrinkage) is full-field 3D Dynamic Flow Model where Aquifer Expansion is treated as one of the fluid phases and accounts of geological heterogeneities, gas fluid properties, relperm properties and heat exchange with surrounding rocks.

Unfortunately, in many practical cases the detailed information on the aquifer is not available which does not allow a proper modelling of aquifer expansion using a geological framework.

Besides many practical applications require only knowledge of cumulative water influx from aquifer under pressure depletion.

This allows building an Aquifer Drive Models using analytical methods.

Inputs & Outputs

Inputs		Outputs
$\begin{array}{l}p(t)\end{array}$	Formation pressure in the oil reservoir	$\begin{array}{l}Q^{\downarrow}_{AQ}(t)\end{array}$	Cumulative subsurface water influx from Aquifer
$\begin{array}{l}p_i\end{array}$	Initial formation pressure	$\begin{array}{l}q^{\downarrow}_{AQ}(t) = \frac{dQ^{\downarrow}_{AQ}}{dt}\end{array}$	Subsurface water flowrate from Aquifer
$\begin{array}{l}J_{AQ}\end{array}$	Aquifer Productivity Index

Assumptions

Steady-state flow
$\begin{array}{l}p_{AQ}(t)=p_i = \rm const\end{array}$	Aquifer pressure is constant
$\begin{array}{l}J_{AQ} = \rm const\end{array}$	Aquifer Productivity Index is constant

Equations

(1)	$\begin{array}{l}\displaystyle Q^{\downarrow}_{AQ}(t) = J_{AQ} \cdot \left[ p_i \cdot t - \int_0^t p(t) dt \right]\end{array}$

(2)	$\begin{array}{l}\displaystyle q^{\downarrow}_{AQ}(t) = J_{AQ} \cdot (p_i - p(t))\end{array}$

It maybe considered as partial case of Fetkovich PSS with infinite Aquifer volume.

Reference

1. Schilthuis, R.J. 1936. Active Oil and Reservoir Energy. Trans., AIME 118: 33. https://doi.org/10.2118/936033-G

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Motivation

Inputs & Outputs

Assumptions

Equations

See Also

Reference

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Schilthuis Aquifer expansion @model

Motivation

Inputs & Outputs

Assumptions

Equations

See Also

Reference