Cuttings Slip Velocity and Transport Ratio (Moore)
How fast a drilled cutting falls back through the mud, and how much of the annular velocity it keeps.
Example
You enter
- Cutting equivalent diameter (in) 0.25
- Cutting specific gravity (2.6 typical) 2.6
- Mud weight (ppg) 9.5
- Mud viscosity from power_law
- Apparent viscosity (cP, when entered) 0
- Flow behavior index n (power law) 0.7
- Consistency index K (equivalent cP, power law) 200
- Hole or casing inside diameter (in) 8.75
- Pipe outside diameter (in) 5
- Annular velocity (ft/min) 200
You get
- Slip velocity (ft/min) 29.3
- Apparent viscosity used cp 51.2
- Transport ratio 0.853
Checked against published worked examples from: Moore, Drilling Practices Manual (1974), as given in Bourgoyne et al., Applied...
Details, formula, and sources
ScopeMoore's correlation: the mud's apparent viscosity in the annulus from its power-law n and K, a particle Reynolds number, and the slip velocity for laminar, transitional or turbulent slip. A quarter-inch cutting in 9.5 ppg mud (n 0.7, K 200) at 200 ft/min in an 8.75 by 5 in annulus slips 29 ft/min, a transport ratio of 0.85. Vertical hole only. The mud engineer governs.
Formula or tableApparent viscosity mu_a = (K/144) ((d2 - d1)/v_a)^(1-n) ((2 + 1/n)/0.0208)^n, v_a in ft/s, diameters in inches, K in equivalent cP. Particle Re = 928 rho_f v_s d/mu_a (ppg, ft/s, in, cP). v_s = 82.87 d^2 (rho_s - rho_f)/mu_a for Re under 3; 2.90 d (rho_s - rho_f)^0.667/(rho_f^0.333 mu_a^0.333) for 3 to 300; 1.54 sqrt(d (rho_s - rho_f)/rho_f) over 300. rho_s = SG x 8.3454 ppg. Transport ratio = (v_a - v_s)/v_a.
Source and editionMoore's correlation for cuttings slip velocity: P. L. Moore, Drilling Practices Manual (1974), as presented in Bourgoyne, Millheim, Chenevert and Young, Applied Drilling Engineering (SPE Textbook Series), cited by name.
Free accessThe three slip-velocity forms follow from the force balance v^2 = 4 g d (rho_s - rho_f)/(3 f rho_f) with friction factors 40/Re, 22/sqrt(Re) and 1.5; worked in field units that derivation gives 82.91, 2.904, 1.544 and a Reynolds constant of 927.7, which round to the published 82.87, 2.90, 1.54 and 928. The tile computes with the derived values.
What governsEstimate. AHJ and licensed professional govern.
API field namescutting_diameter_in, cutting_sg, mud_weight_ppg, viscosity_mode, apparent_viscosity_cp, flow_index_n, consistency_k, hole_dia_in, pipe_od_in, annular_velocity_ft_min, slip_velocity_ft_min, apparent_viscosity_used_cp, transport_ratio
- Friction factors 40/Re laminar, 22/sqrt(Re) transitional, 1.5 turbulent, for an irregular cuttingMoore (1974)
- Regime the largest of the three friction factors governs, so the smallest of the three velocities; the curves cross at Re 3.3 and 215, close to the published limits of 3 and 300, and the result is continuous and falls as the mud thickensscope of this tile
- Apparent viscosity the Newtonian viscosity giving the same annular friction as the power-law mud, or an entered valueBourgoyne et al.