Modeling of Sand and Crude Oil Flow in Horizontal Pipes during Crude Oil Transportation

Table 2

Similarities and differences between the new model and Doan et al.’s model.

Serial number	Condition	Doan et al. models	The modified Doan et al. model
(1)	Mass transport	1 solid phase equation + 1 liquid phase equation without eddies	2 solid phase equations + 1 liquid phase equation which include eddy parameter
(2)	Momentum transport	Including a fluid parameter and suspension parameter for sand	Including a fluid parameter and suspension and deposition parameters for sand
(3)	Mathematical solution	Considering molecular diffusivity term in its solution	Including both molecular and eddy diffusivity terms in the solution
(4)	Number of equations	(4)	(5)