Phase Behaviour Modelling for Fluids from Unconventional Reservoirs
One of the challenges in the modelling of unconventional reservoirs is the alteration of the Pressure, Volume and Temperature (PVT) behaviour in confinement, this alteration is mainly dictated by the size of the reservoir pores. While pore sizes are smaller, the fluid-wall interactions are increasing; as a result, the adsorbed layer of the molecules on the wall occupies a considerable volume of the pore compared to the bulk (not adsorbed) portion. The adsorbed layer has a higher density and viscosity leading to a heterogeneous distribution of fluid properties. In addition, capillary pressure is not negligible in these reservoirs. The capillary effect produces different pressures in vapour and liquid phases which shift the fugacity values in the flash calculation. Because of these phenomena, saturation pressure is decreased, meaning that light components stay in the oil phase for a longer time. This causes that the oil phase would have a lower viscosity; the formation volume factor would be higher and the Gas to Oil ratio (GOR) is going to stay constant for a wider pressure range before it drops.
To overcome this challenge, our thermodynamic development group has started new efforts with the purpose of providing accurate phase behaviour and physical properties prediction for confined reservoir fluids in the Symmetry process software platform.
The objective of this communication is to show the capillary pressure effect and critical properties shift in the PVT behaviour from a cubic equation of state.
Critical properties shifts are captured through applying Zarragoicoechea and Kuz (2004) correlation:
In this correlation, Tcb and pcb are critical temperature and pressure at bulk condition. rp is pore radius and ΔT*c and Δp*c are shifts in critical temperature and pressure.
Figure 1: Shift in critical pressure for some hydrocarbons
Figure 2: Shift in critical temperature for some hydrocarbons
As it can be seen in Figures 1 and 2, the critical properties decrease by reducing the pore sizes. Capillary pressure is calculated using Young-Laplace equation (Ibach (2006)).
In this equation, pv and pL are vapour and liquid phases pressures. and are interfacial tension and pore radius. xi, yi, pL, pv, are liquid and vapour compositions, and liquid and vapour densities, respectively. The Parachor (Px) parameter is calculated based on two correlations from Fanchi (1985) and API Handbook (1992). In addition to abovementioned correlations, an alternative is to use a combination of both correlations based on the molecular weight of the component.
Figure 3: Change in envelope for binary mixture of 70% mol methane and 30% mol hexane
By applying the new alternative calculation to a cubic EOS (Advanced Peng-Robinson) the bubble point pressure decreases in confinement as compared to a bulk fluid for binary system of 70% mol methane and 30% mol hexane (Figure 3). The bubble point pressure also decreases with the pore size, this slows down the gas evolution from the oil phase, which can delay the GOR blow out in the reservoir history matching and prediction. Note that the dew curve is not changing with the pore size significantly in contrast with bubble curve for this system.
The presented analysis is a step towards being able to model confined reservoir fluid properties in the Symmetry process software platform. This will be achieved with the development of a comprehensive set of tools which will provide the capability of calculating not only saturation temperature and pressure, but also other type of flash and envelope calculations along with physical properties estimation.
Bita Bayestehparvin, Ph. D., Herbert Loria, Ph.D, P.Eng, VMG Calgary
Please contact your local VMG office for more information.
American Petroleum Institute, Technical Data Book - Petroleum Refining, 5th Ed. Washington, DC: American Petroleum Institute, 1992
Fanchi, J.R., 1985. Calculation of parachors for compositional simulation. Journal of petroleum technology, 37(11), pp.2-049.
Ibach, H., 2006. Physics of surfaces and interfaces (Vol. 12). Berlin: Springer.
Zarragoicoechea, G.J. and Kuz, V.A., 2004. Critical shift of a confined fluid in a nanopore. Fluid phase equilibria, 220(1), pp.7-9.