In this paper, a one-dimensional three-fluid model is developed in Python. The physical model features a mass and momentum balance for each fluid. It allows to predict the pressure drop and flow patterns. The hydraulic transport of slurry system in horizontal tubes has been investigated. To simulate it dynamically, continuity and momentum equations used in applied engineering problem, are solved together. These equations are conveniently solved using the method of characteristics (MOC). The mumerical results from the numerical code model head and pressure losses. We test numerically the fitting of the model with the real physical problem.