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| Titel |
A Realistic Gas Transport Model with application to Determining Shale Rock Characteristics |
| VerfasserIn |
Iftikhar Ali, Nadeem Malik |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250143050
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| Publikation (Nr.) |
 EGU/EGU2017-6739.pdf |
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| Zusammenfassung |
| A nonlinear transport model with pressure-dependent parameters for the flow
of shale gas in tight porous media, accounting for important physical
processes such as continuous flow, transition flow, slip flow, Knudsen
diffusion, surface diffusion, adsorption and desorption in to the rock
material, and also including a nonlinear Forchheimer correction term for
high flow rates (turbulence), has been developed [1,2]. The transport model
is an advection-diffusion type of partial differential equation with
pressure dependent model parameters and associated compressibility
coefficients, and with nonlinear pressure-dependent apparent convective
velocity $U(p,p_x)$ and apparent diffusivity $D(p)$
where $p$ is the pressure field. The transient one-dimensional model without gravity and without external source is,
\begin{equation}
\frac{\partial p}{\partial t}+U\frac{\partial p}{\partial x} &=&
D\frac{\partial^2 p}{\partial x^2}
\end{equation}
where,
\begin{equation}
D &=& \frac{\rho}{\mu} \frac{FK_a}{\rho\phi\zeta_1 +(1-\phi)\zeta_2}
\end{equation}
\begin{equation}
U &=& -D\zeta_3\frac{\partial p}{\partial x}
\end{equation}
and, $\rho$ is the fluid density, $\mu$ is the fluid viscosity, $K_a$
is the apparent rock permeability, $\phi$ is the rock porosity, and
$\zeta_1(p),\ \zeta_2(p),\ \zeta_3(p)$ are various pressure dependent compressibility factors, and $F$ is a factor incorporating the effects of high flow rates -- see [1, 2] for details.
The steady-state 1D model was used to determine the shale rock
charcateristics by history matching the pressure distribution across a shale
rock core sample obtained from pressure-pulse decay tests for different
inflow pressure conditions [3]. The best results were obtained when
the high flow rate Forchheimer correction term is included in the model; the
estimates for the porosity and permeability are then much more realistic
than previous models [4], which is a notable achievement. In the case considered, the porosity was determined to lie in the range, $0.1 |
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