Timescales for the development of thermodynamic equilibrium in hydrocarbon reservoirs
Creators: name: Obidi, Onochie
Publisher: name: Imperial College London
Year: 2014

description: The full understanding of the initial state of petroleum reservoirs and the fluxes that lead to compositional variations have become of huge interest to the petroleum industry. The compositional variation of reservoir fluid has great commercial impact on reservoir management and field development as it affects the value of the hydrocarbon in place, what recovery mechanisms applied and the treatment process of the extracted fluid if necessary. Lateral and vertical variation in hydrocarbon density and composition between wells are observed in many oil reservoirs under appraisal. These gradations may be due to changes in reservoir filling over geological time, in which case the variations are not in an equilibrium state, or alternatively due to an equilibrium between chemical, thermal and gravity potentials. The mixing of non-equilibrium compositional distributions is affected by Darcy flows (if there is a resulting pressure gradient), gravitational overturning (if there is a density difference) and molecular diffusion. The diffusion flux may also be affected by gravitational and thermal effects. Previous work has focused primarily on convective mixing and simple models of mixing via molecular diffusion. This work focuses on the rate of mixing via molecular diffusion, including the effects of pressure and thermal diffusion, which are modelled using the thermodynamics of irreversible processes for a single phase system. The interaction of diffusional mixing and gravitational overturning is also examined. The timescales to attain steady state are analyzed as well as the resulting compositional profiles. The developed model has been validated using simple transient analytical solution proposed by Carslaw and Jaeger (1959) for the molecular diffusion flux and Gardner et al. (1962) for the natural convection process. The diffusive fluxes in our model are also validated by steady state analytical solutions for species segregating in a thermo-gravitational column. The developed model was used to analyze the experimental results obtained for two ternary mixtures of methane, n-pentane and 1-methylnapthalene; and methane, n-pentane and undecane by Ratulowski et al. (2003). Although 1-methylnapthalene and undecane have similar molar masses, the system containing 1-methylnapthalene resulted in a bigger grading (difference in mole fraction at the top and bottom of the system) than the latter. This analysis demonstrates the impact of real mixture modelling (as opposed to the case when an ideal fluid is assumed) on the segregation-mixing process. Finally, we show how the knowledge of the timescales for observed compositional variations to reach equilibrium can be used to estimate the time since a reservoir filled. The Madison formation in the LaBarge field in Wyoming, U.S.A was studied. This is an unusual gas reservoir, as non-hydrocarbons make up about 80% of the total gas composition, with methane constituting the remainder. The methane composition varies significantly, 22% at the crest of the formation to 5% near the GWC. There are several hypotheses in the literature behind the unusual gas composition and distribution in this formation (De Bruin, 2001; Stilwell, 1989; Huang et al., 2007). We use the fluid mixing model to test the various hypotheses. The results reveal that the geothermal gradient in this field is not sufficient to make the thermal diffusion and thermal convection process in this reservoir override the effect of the molecular diffusion. We conclude that the reservoir is not yet in compositional equilibrium as molecular diffusion will completely homogenize the composition variation in this field. We propose that the currently observe composition profile is as result of the formation being enriched with CO2 at approximately 3 million years ago. This timescale is contemporaneous with the volcanic activity proposed by De Bruin (2001) and Stilwell (1989).