Motivation

The most accurate way to simulate Gas Cap expansion (or shrinkage) is full-field 3D Dynamic Flow Model where Gas Cap 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 Gas Cap is not available.

Besides many practical applications require only knowledge of one element of the Gas Cap expansion process – a pressure support and not the sweep in the invaded zones.

This allows building a Gas Cap Drive @model using analytical methods.

Inputs & Outputs

Inputs		Outputs
$\begin{array}{l}p(t)\end{array}$	field-average formation pressure at time moment $\begin{array}{l}t\end{array}$	$\begin{array}{l}Q_{GC}(t)\end{array}$	Cumulative Gas Cap expansion at surface conditions
$\begin{array}{l}p_i\end{array}$	Initial formation pressure	$\begin{array}{l}\displaystyle q_{GC}(t) = \frac{dQ_{GC}}{dt}\end{array}$	Instantaneous Gas Cap expansion flowrate at surface conditions
$\begin{array}{l}V_{GC}\end{array}$	Initial Gas Cap reserves at surface conditions
$\begin{array}{l}Z(p)\end{array}$	Gas Cap compressibility factor at pressure $\begin{array}{l}p\end{array}$

Physical Model

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

Mathematical Model

(1)	$\begin{array}{l}\displaystyle Q_{GC}(t) = V_{GC} \cdot \left( 1- \frac{B_{gi}}{B_g(p)} \right) = V_{GC} \cdot \left( 1 - \frac{Z_i}{p_i} \, \frac{p}{Z(p)} \right)\end{array}$

(2)	$\begin{array}{l}\displaystyle q_{GC}(t) = \frac{dQ_{GC}}{dt}\end{array}$

where

$\begin{array}{l}B_g(p)\end{array}$	Gas formation volume factor at pressure $\begin{array}{l}p\end{array}$
$\begin{array}{l}B_{gi} = B_g(p_i)\end{array}$	Gas formation volume factor at Initial formation pressure $\begin{array}{l}p_i\end{array}$
$\begin{array}{l}Z_i = Z(p_i)\end{array}$	Gas Cap compressibility factor at Initial formation pressure $\begin{array}{l}p_i\end{array}$

Proxy Models

Ideal Gas ( $\begin{array}{l}Z(p)=1\end{array}$ )

(3)	$\begin{array}{l}\displaystyle Q_{GC}(t) = V_{GC} \, \left( 1 - \frac{p}{p_i}\right)\end{array}$

(4)	$\begin{array}{l}\displaystyle q_{GC}(t) = - \frac{V_{GC}\cdot p_i}{p^2(t)}\cdot \frac{d p}{dt}\end{array}$

In this case the only parameter of the gas cap model is its initial volume $\begin{array}{l}V_{gi}\end{array}$

Page tree

Motivation

Physical Model

Mathematical Model

Proxy Models

See Also