One of the well-known problems encountered in oil flow lines, oil reservoirs and completion strings, causing flow assurance issues, is the deposition of asphaltenes in these areas. The complications aroused due to asphaltenes deposition include, but are not limited to, permeability reduction, wettability reversal, pipeline and well plugging, increased pressure drop and an overall reduction in oil production. The problem is not only severe, but it occurs so abruptly that it can damage the formation in a few days if it proceeds unnoticed. The asphaltenes deposition for a given oil is measured by the use of high-tech and expensive apparatuses, particularly where multiphase flow occurs, which incurs additional costs. Multiphase flow combined with asphaltenes precipitation worsens the situation in well bores and affects the flow of crude oil. This paper presents a numerical modeling approach for prediction of asphaltenes deposition and precipitation in crude oil in multiphase flow by the use of governing equations calculated using finite difference discretization methods. These numerical models belong to the family of front-capturing-models which permit the capture of the depositing front on a fixed mesh. The paper also presents a model for studying the effect of CO2 injection on asphaltenes precipitation during enhanced oil recovery from the reservoir. The developed numerical models are validated against each other. The parametric effect on deposition of crude oil was modeled and studied against experimental values. The numerical models and resulting simulations were in good agreement with the steady-state solution of the asphaltenes onset curve.