Particle-laden internal turbulent flows are very commonplace, for example, in petrochemical flow lines, oil wells and so on. From an engineering view point, modelling such flows in a 3D or even 2D fashion may not be reasonable in terms of computational cost, especially when the flow domain is sufficiently long, and a large number of grid cells are needed to resolve the flow field. On the other hand, ID models are quite fast but only take into account the stream-wise variations of the flow characteristics, without providing any information on their cross-sectional distribution. In this work, a novel quasi-ID modelling framework was introduced, which is able to capture the flow field in both stream-wise and cross-stream directions and yet stay computationally more efficient than the 3D or 2D models. The quasi-ID modelling framework was developed based on the one-way coupling of a RANS model for the single-phase turbulent flow with an Eulerian model for the transport of the dispersed particle phase. The nucleation, agglomeration and breakup events were also taken into considera¬tion through the generic population balance equation, the solution of which was provided using the direct quadrature method of moments. The results of the quasi-ID single-phase flow model were verified and shown to be in accordance with those of the AN SYS Fluent 2D model for different test cases. The computational cost analysis revealed that the simulation CPU time of the quasi-ID model increases linearly with the number of streamwise grid cells (Nx), whereas that of the 2D model scales with Nx1.6, implying that the quasi-ID model will perform faster than the 2D model from a certain number of grid cells on. The quasi-ID multi-phase-flow tool was then used to address the transport and deposition of asphaltenes in oil wells, as an example of particle-laden internal turbulent flows. To this end, a simulation test case was set up with several simplifications, and the results were compared with those of a simpler ID model in the literature, as the benchmark. Due to the lack of an appropriate model for the collision efficiency of asphaltene particles, a model associated with liquid droplets was adopted and tuned to obtain a match between the results of this study and the benchmark. The outcome of the sensitivity analysis demonstrated that the collision efficiency plays an important role in determining the asphaltenes deposition profile along the well bore and needs to be modeled accurately.