Reservoir Engineering Aspects of Unconventional Oil and Gas

Posted by D Nathan Meehan January 19, 2015

Category: Oilfield economics, Production, Reserves, Reservoir, Reservoir monitoring, Shale, Uncategorized | Tags: advection, D'arcy, diffusion, fickian, flow mechanisms, gas, Oil, reservoir engineering, Shale, unconventional

Baker Hughes is publishing a book titled “Unconventional Resources: Exploitation and Development” covering a wide variety of topics central to optimizing recovery and profitability of these reservoirs. This blog entry includes extracts from the book which will be available in the next few months at http://www.shopbakerhughes.com/

As reservoir engineers, we can analyze most conventional oil and gas reservoirs and even tight gas plays by measuring or estimating the variables which constitute Darcy’s law and the material balance equation. These include:

- PVT properties such as viscosity, formation volume factor, isothermal compressibility,
- porosity and saturations,
- reservoir pressure and temperature,
- permeability including phase relative permeabilities,
- reservoir geometry including thickness and area, and
- in the case of hydraulic fractured wells, fracture geometry and permeability.

Complete descriptions of reservoir performance in conventional reservoirs and tight gas may further require knowledge of natural fractures and other detailed heterogeneities. The spatial variations of reservoir properties as dictated by geology represent the largest group of unknowns. The most critical aspect of this variability is often the spatial correlation of extreme values such as in natural fractures of faults. Conventional tools to address this problem includes 3-D or even 4-D seismic to improve the spatial model, integration of geological knowledge about the reservoir along with petrophysical (and less frequently but likely no less important geomechanical) information into an integrated earth model.

Baker Hughes’ JewelSuite software (Figure 1) is an example of such an earth model. The well and reservoir parameters from the earth model are then discretized into a reservoir simulation model. The reservoir simulation model simultaneously solves flow and material balance equations and can be used to match historical data or forecast reservoir performance under a variety of alternative development scenarios. These alternative development scenarios allow economic optimization of decisions including well spacing, hydraulic fracture stage spacing and locations, hydraulic fracture design parameters and operating conditions.

Figure 1 JewelSuite image

Unconventional reservoirs are not as easily addressed as conventional or tight gas reservoirs for the following reasons:

- Fluid flow mechanisms in unconventional are different.
- Storage mechanisms for hydrocarbons are different and difficult to characterize.
- The distribution of natural fractures is different and not susceptible to conventional natural fracture modeling.
- The interaction and characterization of multiple hydraulic fractures is not generally captured in unconventional models.

Flow rates and pressure drops for a single-phase fluid can be calculated rigorously only for simple geometries and fluid-wall interfaces. For example, the Hagen-Poiseiulle equation calculates steady-state laminar flow through a cylinder and if Newtonian fluids are used, the model predicts flow velocities that are linear with pressure drop. Such approaches would be extremely complex for real porous media. Darcy’s law is a phenomenologically derived constitutive equation to calculate flow velocity in porous media that presumes linearity and introduces permeability (k) as an empirical constant to approximate the aggregate complexities in cross-sectional area and connectedness of the reservoir pores. Although originally established empirically, it can be derived from the Navier-Stokes equation. The simplest form of Darcy’s law is:

where:

*u* = the apparent velocity, cm/s

*k* = permeability, D

μ = viscosity, cp

*P* = pressure, atm

*L* = length of cylinder, cm

Darcy’s law can be applied to most flow in porous media and forms the basis (along with material balance) of reservoir engineering. Even when reservoir conditions do not strictly show this linear relationship of flow rates with pressure drop, the standard approach is a modification of Darcy’s law to adapt for unique reservoir conditions. Relative permeability (for example) is a construct that allows us to model phase permeabilities as a function of saturation.

Unconventional reservoir pores are thought to be so small that Darcy’s law *may* not be applicable. In general, flow processes occur either as a result of advection or diffusion. Advection describes flow with a net mean fluid flow while diffusion represents more random flow behavior (even if driven by concentration gradients). Both models are represented by conservation of mass and constitutive laws. Diffusion equations generally incorporate stochastic models based on random walks and central limit theorems with constitutive equations either at the microscopic level or mesoscopic level.

In small pores, fluid flow can occur in a wide range of flow mechanisms including:

- Knudsen diffusion[1], where the mean free path of a particle is relatively long compared to the pore size. Collisions with the walls are frequent and Knudsen diffusion is common for pore sizes in the 2-50 nm range.
- Fickian Diffusion[2]
^{,[3]}, this model describes molecular diffusion driven by differences in concentration gradients. By contrast to Knudsen diffusion, the mean free path of particles is relatively low compared to pore scales and this diffusion model is applicable to Brownian motion. - Hydrodynamic flow[4] is driven by pressure gradients along a flow channel.
- Viscous flow[5] is flow in which the mean free path is small compared to the pore scale and pressure drops are determined mainly by the collisions of the molecules.
- Normal-mode diffusion[6] describes flow of Brownian particles in the presence of friction.
- Single-file diffusion[7] represents flow where flow paths are so small that they cannot pass each other in pore channels or throats.

Knudsen (diffusive flow) may be important in nanopores or in solid kerogen. Additionally, desorption from kerogen may contribute to production. Ozkan and Raghavan[8] illustrated the impact of integrating diffusive flow in nanopores in addition to Darcy flow in the fractures and matrix. When permeabilities are very low, Darcy flow becomes insignificant and diffusive flow dominates. They conclude that at very low permeabilities it is essential to incorporate diffusive flow.

The next blog entry will address storage and flow mechanisms for unconventional reservoirs.

[1] Malek, K. and M.O. Coppens, Knudsen self- and Fickian diffusion in rough nanoporous media. *Journal of Chemical Physics*, 2003. 119(5): p. 2801-2811.

[2] Hosticka, B., et al., Gas flow through aerogels. *Journal of Non-Crystalline Solids*, 1998. 225(1): p. 293-297.

[3] Singh, H. and Javadpour, F. Nonempirical Apparent Permeability of Shale, 168724-MS SPE Conference Paper – 2013.

[4] Weber, M. and R. Kimmich, Maps of electric current density and hydrodynamic flow in porous media: NMR experiments and numerical simulations. *Physical Review E*, 2002. 66(2): p. 026306.

[5] Andrade, J.S., et al., Inertial effects on fluid flow through disordered porous media. *Physical Review Letters*, 1999. 82(26): p. 5249-5252.

[6] Sholl, D.S. and K.A. Fichthorn, Normal, single-file, and dual-mode diffusion of binary adsorbate mixtures in AlPO4-5. *Journal of Chemical Physics*, 1997. 107(11): p. 4384-4389.

[7] Levitt, D.G., Dynamics of a Single-File Pore – Non-Fickian Behavior. *Physical Review A*, 1973. 8(6): p. 3050-3054.

[8] Ozkan, E. and Raghavan, R., “Modeling of Fluid transfer from Shale Matrix to Fracture Network,” Society of Petroleum Engineers 134830, presented at the ATCE in Florence, Italy September 2010.

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