  Solid particles can be transported as a mobile granular bed, known as
bed-load, by pressure-driven flows. A common case in industry is the presence
of bed-load in stratified gas-liquid flows in horizontal ducts. In this case,
an initially flat granular bed may be unstable, generating ripples and dunes.
This three-phase flow, although complex, can be modeled under some simplifying
assumptions. This paper presents a model for the estimation of some bed-load
characteristics. Based on parameters easily measurable in industry, the model
can predict the local bed-load flow rates and the celerity and the wavelength
of instabilities appearing on the granular bed.
