The problem of cuttings transport in the inclined sections of ERW's is a major concern in the oil well drilling industry. This paper presents an innovative time dependent mathematical model, along with a computer implementation of it, which is based on the well-known two-layer model approach. An innovative feature of this model consists in the consideration of the added amount of solids that comes from the crumbling and cave-in of the well bore. The unstable effects of this added amount of solids is taken into account through a variable representing the added volume of cuttings per unit time and length. A finite volume approach is used to solve the system of differential equations. The paper represents a first step on the integrated analysis of cuttings transport and well bore stability problems.

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