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 simplified modelling of the Gas Cap expansion using simple analytical methods.

Inputs & Outputs

Inputs		Outputs
$\begin{array}{l}p_i\end{array}$	Initial formation pressure	$\begin{array}{l}Q^{\downarrow}_{GC}(t)\end{array}$	Cumulative flux of gas from Gas Cap
$\begin{array}{l}V_{GC}(0)\end{array}$	Initial Gas Cap volume	$\begin{array}{l}q^{\downarrow}_{GC}(t) = \frac{dQ^{\downarrow}_{GC}}{dt}\end{array}$	Volumetric gas flowrate from Gas Cap
$\begin{array}{l}c_g(p)\end{array}$	Gas compressibility

Assumptions

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:

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

Equations

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

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

Approximations

In case when pressure depletion $\begin{array}{l}\displaystyle \frac{p(t)}{p_i}\end{array}$ is not severe then compressibility factor maybe considered as relatively constant $\begin{array}{l}Z = \rm const\end{array}$ which leads to $\begin{array}{l}\displaystyle c_g = \frac{1}{p}\end{array}$ and:

(4)	$\begin{array}{l}\displaystyle Q^{\downarrow}_{GC}(t) = V_{GC}(0) \cdot \left( \frac{p_i}{p(t)} -1 \right)\end{array}$

(5)	$\begin{array}{l}\displaystyle q^{\downarrow}_{GC}(t) = \frac{dQ_{GC}}{dt} = V_{GC}(0) \frac{p_i}{p^2(t)} \frac{dp}{dt}\end{array}$

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Motivation

Assumptions

Equations

Approximations

See Also

Page tree

Gas Cap Drive @model

Motivation

Assumptions

Equations

Approximations

See Also