Unconventional hydrocarbon reservoirs consist of tight porous rocks which are characterised
by nano-scale size porous networks with ultra-low permeability [1,2]. Transport of gas
through them is not well understood at the present time, and realistic transport models are
needed in order to determine rock properties and for estimating future gas pressure
distribution in the reservoirs. Here, we consider a recently developed non-linear gas transport
equation [3],
∂p-+ U ∂p- = D ∂2p-, t > 0, (1)
∂t ∂x ∂x2
complimented with suitable initial and boundary conditions, in order to determine shale
rock properties such as the permeability K, the porosity φ and the tortuosity, τ. In our new
model, the apparent convection velocity, U = U(p,px), and the apparent diffusivity
D = D(p), are both highly non-linear functions of the pressure. The model incorporate
various flow regimes (slip, surface diffusion, transition, continuum) based upon the
Knudsen number Kn, and also includes Forchchiemers turbulence correction terms.
In application, the model parameters and associated compressibility factors are
fully pressure dependent, giving the model more realism than previous models. See
[4].
Rock properties are determined by solving an inverse problem, with model parameters
adjustment to minimise the error between the model simulation and available data. It is has
been found that the proposed model performs better than previous models. Results and details
of the model will be presented at the conference.
Corresponding author: namalik@kfupm.edu.sa and nadeem_malik@cantab.net
References
[1] Cui, X., Bustin, A.M. and Bustin, R., “Measurements of gas permeability and
diffusivity of tight reservoir rocks: different approaches and their applications”, Geofluids 9,
208-223 (2009).
[2] Chiba R., Fomin S., Chugunov V., Niibori Y. and Hashida T., “Numerical Simulation
of Non Fickian Diffusion and Advection in a Fractured Porous Aquifer”, AIP Conference
Proceedings 898, 75 (2007); doi: 10.1063/1.2721253
[3] Ali, I. “A numerical study of shale gas flow in tight porous media through non-linear
transport model”, PhD Dissertation, King Fahd University of Petroleum and Minerals.
Submitted (2016).
[4]. Civan, F., Rai, C.S., Sondergeld, C.H.: Shale-gas permeability and diffusivity inferred
by improved formulation of relevant retention and transport mechanisms. Transport in Porous
Media, 86(3), 925–944 (2011).
Acknowledgement: The authors would like to acknowledge the support provided by King
Abdulaziz City for Science and Technology (KACST) through the Science Technology Unit
at King Fahd University of Petroleum and Minerals (KFUPM) for funding this work through
project No. 14-OIL280-04. |