Fluid Mud Underflow Models

ERDC TN-DOER-N7

August 2000

A Reynolds number (R) criteria for the turbulent-laminar transition has been proposed for Bingham

plastic materials (Liu and Mei 1990), and found to be applicable to mud flows. R is composed of

viscous (R)and yield-stress components (Rτ) depending on underflow conditions, and:

(1)

d1 R + 1 Rτ i

where

R = 4 ρ q and

Rτ = 8ρ q2 τ yh2

where

ρ = the underflow density, the overbar indicates a layer-averaged density

q = the underflow discharge per unit width

= the apparent viscosity

τy = the yield stress

h = the underflow thickness.

The yield stress is defined here as the stress below which no flow occurs, but in practice it is

dependent on the stress history of the material and flow conditions for the case at hand. Measured

values are method-depend. Experimental evidence indicates that the turbulent-laminar transition

occurs at R's of about 2,100 (Liu and Mei 1990; Van Kessel and Kranenburg 1997).

Fluid Mud Underflow Models. To predict underflow behavior, a set of equations must be solved

that is appropriate to its classification. The study of fluid mud flow properties is known as rheology,

and two notable flow features are plasticity and shear-thinning. Deformation in a plastic material

is limited to conditions where the imposed shear stress is greater than some threshold value, a yield

stress. A Bingham model is usually used to represent the stress-strain relationship of a plastic

material. A shear-thinning material's apparent viscosity decreases with increased shear-rate (Teeter

1992a). A Newtonian fluid such as water has a linear stress-strain relationship. Both yield stress

and shear thinning are non-Newtonian characteristics of fluid muds.

Recent studies on laminar fluid mud underflows have used Bingham (Liu and Mei 1990; Van Kessel

and Kranenburg 1997) or Herschel-Bulkley (Coussot and Proust 1996; Huang and Garcia 1998)

rheological models where shear stress (τ) is:

τ = τ y + γ n , τ > τ y

(2)