Solids suspension has broad applications in the oil and gas industry (i.e., sand production, cuttings transportation during drilling, and barite sag in drilling fluids). The conventional modeling approaches for solids suspension and transportation include mechanics models (i.e., layer models) and computational fluid dynamics (CFD) based Eulerian-Lagrangian models. One of the most important assumptions for these approaches is that the solid particles have uniform size, which is not true in the actual applications. The computational fluid dynamics/discrete element method (CFD-DEM) approach can track each single particle in the system; however, the computational time is not practical for industrial applications.

This paper presents a relatively simple Eulerian approach for characterizing solids suspension in multiphase flow systems. The multiphase flow equations are derived by using a proper averaging procedure without considering interphase mass transfer. A proposed new solids suspension model, which is based on the fluid-solid interaction and kinetic theory, account for multiple solids sizes in the flow. The suspension characterizations for particles with different sizes are considered by introducing a particle size distribution function, which also captures detailed particle distribution and fluid/particle and particle/particle interactions. Therefore, a more realistic solids transportation prediction can be achieved. A simulation package is developed by solving the model using the finite difference method. The boundary-fitted coordinate system is applied to integrate the irregular geometry caused by drillpipe eccentricity and a packed solids bed. The influence of the solid phase on the carrier fluid is considered, and solid-liquid two-way coupling is implemented.

The simulation package has been used for transient hole cleaning simulations during drilling. Simulation results show that cuttings’ backsliding makes the hole cleaning process in intermediate inclined wells different from that in horizontal and highly inclined wells. The cuttings movement in this part of the well follows the two-steps-forward, one-step-back routine. Well packoff is also captured by the program for improper hole cleaning operations in an intermediated inclined position. Transient hole cleaning tests were conducted on a 90 ft long, 8 × 4.5 in. flow loop. Experimental data are compared with the simulation results, and good matching is obtained. This method can also be used as a general tool for solids suspension and transportation simulation in multiphase systems.

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