Motivation

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.

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

Page tree

Motivation

Inputs & Outputs

Assumptions

Equations

Approximations

See Also

Page tree

Gas Cap Drive @model

Motivation

Inputs & Outputs

Assumptions

Equations

Approximations

See Also