The most accurate way to simulate gas expansion is conventional 3D full-field dynamic modelling where gas motion is treated as one of the fluid phases and accounts of geological gas fluid properties, relperm properties, heat exchange .

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:

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

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 Expansion @model

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