We consider second migration of hydrocarbons and analyse the effect of the uncertainty associated with three-phase relative permeability on reservoir simulation results. The two-dimensional vertical reservoir has a size of 5000 m × 5000 m and it is discretized by 50 × 50 uniform cells.

Parameters of relative permeability models are evaluated via a Maximum Likelihood (ML) approach, relying on a set of coreflooding data available from the literature. Uncertainty in ML calibration of the relative permeability model parameters is propagated to the outputs of reservoir simulations within a Monte Carlo (MC) framework. Results are discussed in terms of time evolution of pressure, saturation (of all three phases) values as well as concentrations of the hydrocarbon components. Our results document a clear influence of the ML parameter estimation uncertainties on the reservoir simulations, especially considering local concentrations of hydrocarbon components. Moreover, even though the uncertain parameters follow a Gaussian distribution, outputs of the MC simulations are generally non-Gaussian and display long (positive and/or negative) tails.


Secondary migration typically refers to the movement of hydrocarbons along a carrier bed from the source rock to the trap. The hydrocarbons originated from kerogen faces a limited available spaces of accumulation in source rock, so they are forced (through capillaries) to move from the source rock toward more superficial layers, characterized by larger porosity. This process, called primary migration, is mainly governed by pressure gradients from the centre of the source rock towards the reservoir [2]. After the hydrocarbon has reached the reservoir, a secondary migration occurs and the hydrocarbon migrates versus more permeable facies. An active flow of oil can appear only if an interconnected network of oil saturated pores exists [2]. The significantly high porosities, permeabilities and pore sizes of the rock permit the formation of tiny oil stringers which are mainly controlled by buoyancy [2].

Previous works show that almost 60% of the oil movements from the source rock to the reservoir are displayed along the vertical direction [3]. During the vertical migration, due to pressure difference between the source rock and the reservoir, physic-chemical properties (i.e. pressure-volume-temperature, PVT) of the fluids may change [4].

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