The most accurate way to simulate gas expansion is conventional 3D full-field dynamic modelling where gas 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.

The analytical models usually assume:

Isothermal expansion	Uniform pressure depletion in Gas Cap
$\begin{array}{l}T = \rm const\end{array}$	$\begin{array}{l}p_{GC}(t) = p(t)\end{array}$

which leads to the following equation for Gas Cap volume:

$\begin{array}{l}\displaystyle V_{GC}(t) = V_{GC}(0) \cdot \exp \left[ - \int_{p_i}^{p(t)} c_g(p) dp \right]\end{array}$

and correspondingly to following Gas Cap Drive model:

$\begin{array}{l}\displaystyle Q_{GC}(t) = V_{GC}(t) - V_{GC}(0)= V_{GC}(0) \cdot \left( 1- \exp \left[ - \int_{p_i}^{p(t)} c_g(p) dp \right] \right)\end{array}$

$\begin{array}{l}\displaystyle q_{GC}(t) = \frac{dQ_{GC}}{dt} = - c_g V_{GC}(0) \frac{dp}{dt} \cdot \exp \left[ - \int_{p_i}^{p(t)} c_g(p) dp \right]\end{array}$

In simple case when Z-factor is constant (and $\begin{array}{l}\displaystyle c_g = \frac{1}{p}\end{array}$ ) then:

$\begin{array}{l}\displaystyle V_{GC}(t) = V_{GC}(0) \frac{p_i}{p(t)}\end{array}$

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Gas Cap Drive @model

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