Phenomenological Modeling of Catastrophic Dilute Gravity Flows

Abstract

Numerous hydrocarbon reservoirs originate from sediments deposited in deep water. This is why processes governing their settings have given rise to a growing interest, especially in the field of numerical simulation. Taking the problematic and constraints imposed by the geological data into account, the method that we have adopted to obtain a mathematical model for diluted and turbulent finite gravity flows is the following: the two-dimensional movement created by the instantaneous release of a finite volume of heavy fluid (suspension of sediment particles) into a lighter one (water), on variable slopes, is theoretically studied as a model for gravity flows. These flows develop a characteristic longitudinal structure, comparable to a deformable semi-lens, where the height is small relative to the length. This geometry is imposed on the gravity flow. Using the Boussinesq's approximation, the flow dynamics is supposed to be governed by a balance between gravity driving forces, inertia and turbulent friction. The study of the internal longitudinal flow velocity field allows a law of variation for the spreading velocity to be formulated. An equation, including effects of water incorporation at the suspension-ambient fluid interface, quantifies the variation of the total volume of the flow. Finally, a transport equation for the particles volume concentration is proposed assuming that: - turbulence creates a uniform density distribution in the flow; - particles are advected at the mean flow velocity; - particles fall out or are eroded in the viscous sublayer of the flow. The coupled system of the non-linear differential equations obtained is solved numerically. The model is then validated by experimental small-scale models realized by Laval (1988). The comparison between theoretical predictions and experimental results shows good agreement. An analytical study of the system, by local analysis methods for long times, shows the evolution of solutions when taking new physical phenomena into account and the consistency of the obtained numerical solutions. The obtained model leads to very low computational time on a microcomputer. Simple and complete, it constitutes a first step towards quantitative comprehension of the impact of external parameters-such as the nature and the amount of sediment supply and the geometry of the basin-on gravity flow dynamics and on the organization of subsequent depositional sequences (turbidites).