Asphaltene deposition in wellbores has been recognized as the cholesterol of petroleum for decades causing billions of dollars in losses to the oil and gas industry every year. This necessitates great efforts in precise and fast forecasting of the production problems induced by asphaltene deposition.From perspective of the large length-to-diameter ratios of wellbores and the unidirectional nature of the crude oil flow, this work presents a numerical procedure to predict the coupled velocity,pressure and concentration distribution in a transient one-dimensional one-way framework. This procedure is general-purpose for flow passages of large aspect ratios with the precipitation rate, aggregation rate and deposition rate embedded in known forms. In this numerical procedure, the governing equations are solved using the finite volume method on a regular mesh arrangement with fully implicit spatial and temporal schemes. For verification purpose, a few cases having exact solutions are studied. Then, application of the presented procedure to capillary asphaltene deposition is illustrated where good agreement is achieved between the simulation results and the experimental measurements. This case demonstrates that the proposed procedure can be used to investigate oilfield asphaltene problems and assist reservoir engineers in assessing the potential asphaltene deposition risk in wellbores.