A computing system includes a processor that estimates a pattern of a flow of a mixture of particles and a fluid in a tubular structure as a stationary bed flow, a dispersed flow, or a transitional flow that is relative to the stationary bed and dispersed flows. The processor estimates a plurality of parameters based on the estimated pattern. The processor determines a plurality of dimensionless parameters, based on the estimated parameters. The dimensionless parameters include a first dimensionless parameter corresponding to an effect of turbulence on the flow and a second dimensionless parameter corresponding to an effect of gravity on the flow. The processor characterizes the pattern of the flow as the stationary bed flow, the dispersed flow, or the transitional flow, based on the dimensionless parameters. The processor models the flow based on the estimated pattern if it is determined that the characterized pattern matches the estimated pattern.