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Stojan Petkovic Stojan Petkovic

CT Pressure Loss

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Hydraulics

CT Pressure Loss

Frictional pressure loss for fluids pumped through coiled tubing. Choose the rheology model, enter the fluid, the tubing and the flow rate, in oilfield or metric units.

Before you use the tools

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  • Results are approximate. They are not a design, a procedure or professional advice.
  • Do not use them as the only basis for work on wells, work under pressure, work with nitrogen or any other safety-critical action. Follow your company's procedures, the manufacturer's data and the instruction of the responsible person.
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Fluid

How the flow curve of the fluid is described

lb/gal
cP

For a Newtonian fluid, its viscosity

lbf/100 ft²

Yield stress of the fluid

Power-law exponent; 1 for a Newtonian fluid

lbf·sⁿ/100 ft²

Power-law consistency, from the rheology of the fluid

Fann readings

Dial readings θ of a Fann 35 viscometer at each speed. The standard R1-B1 rotor-bob combination and F1 torsion spring are assumed.

Temperature effects

For Newtonian and Bingham fluids PV and YP are interpolated between the rows at the fluid temperature. Leave the table empty to use the surface values.

°F

Temperature at which PV and YP are taken from the table; empty uses the values above

Rheology at different temperatures

Temp.

PV

YP

°F
cP
lbf/100 ft²
°F
cP
lbf/100 ft²
°F
cP
lbf/100 ft²
°F
cP
lbf/100 ft²
Tubing and reel
in

Diameter of the coil the tubing is wound on

in
in
in

Absolute roughness of the inside wall; 0 for smooth tubing. Only affects turbulent flow

ft
ft

Straight length, not wound on the reel

Flow
gal/min

Inputs

Result

Total friction pressure loss

– psi

Off the reel (straight)
– psi

Flow regime: –

On the reel (curved)
– psi

Flow regime: –

Velocity
– ft/min
Reynolds number
–
Equivalent flow index n′
–
Equivalent consistency K
– lbf·sⁿ/100 ft²
Dean number
–

Method

The loss is calculated separately for the part of the string off the reel (straight) and the part on the reel (curved), and the two are added.

  1. Rheology: the model gives the wall shear stress τ at a wall shear rate γ. Newtonian: τ = μγ. Bingham plastic: τ = YP + PV·γ. Power law: τ = Kγⁿ. Herschel–Bulkley: τ = τ₀ + Kγⁿ. Empirical: the measured Fann points joined by straight lines on log–log axes. Fann speed N rpm gives γ = 1.7023 N 1/s and τ = 1.0678 θ lbf/100 ft².
  2. Equivalent power law: at the flow in question the pseudo shear rate is Γ = 8V/D. The wall shear rate γw = Γ(3n′+1)/(4n′) is found by iterating with n′, the local slope of the flow curve, and the model's K and n′ are those that give the same wall stress and slope. A power-law fluid returns its own n and K.
  3. Fann fit: Bingham plastic PV = θ600 − θ300 and YP = θ300 − PV; Herschel–Bulkley τ₀ = 2τ3 − τ6 and a log–log fit for n and K; power law a log–log fit; Newtonian a fit through the origin. The deviation is the root-mean-square relative error of the model against the readings.
  4. Reynolds number (Metzner–Reed): Re = 31.042 ρ Q^(2−n) / (9.804^n K ID^(4−3n)) · (n/(1+3n))^n, with ρ in lb/gal, Q in gal/min, ID in inches and K in lbf·sⁿ/100 ft².
  5. Straight tubing: laminar below Re = 3470 − 1370n and turbulent above 4270 − 1370n. Laminar f = 16/Re. Turbulent f = a/Re^b, with a = (log n + 3.93)/50 and b = (1.75 − log n)/7.
  6. Coiled tubing: the laminar factor is multiplied by ψ·De^φ, where De = Re_g·(ID/D)^0.5 is the Dean number, ψ = 47.969 − 153.8n + 166.22n² − 60.132n³ and φ = 0.875n − 0.515. Turbulent: f = 1.069·a/Re^(0.8b)·(ID/D)^0.1. The laminar limit is (4n/(3n+1))^n · [2100 ψ (ID/D)^(0.5φ)]^(1/(1−φ)) and the turbulent limit is 800 above it.
  7. Pressure loss: ΔP = f ρ Q² L / (154.63 ID⁵) in oilfield units. Between the two limits the loss is interpolated linearly in Re, from the laminar loss at the lower limit to the turbulent loss at the upper limit.

Assumptions

  • Wall roughness enters only the turbulent friction factor, as the ratio of the Haaland factor with roughness to the one without, so a roughness of 0 gives the smooth-tube result. For n other than 1 this is an estimate.
  • For models with a yield stress the equivalent power law is evaluated at the flow rate entered. This is sound for laminar flow; turbulent and transitional values for such fluids are estimates, and the critical Reynolds numbers are those of a power-law fluid.
  • A single-phase power-law fluid without solids.
  • Smooth tubing and fully developed flow, with fluid properties constant along the string.
  • The curvature is that of the reel diameter you enter; tubing off the reel is straight.
  • The correlations cover a limited range of n and ID/D. Check results outside it.

Based on published correlations for power-law fluids in coiled tubing (Zhou and Shah), with the Metzner–Reed Reynolds number and Dodge–Metzner turbulent factors. The calculation reproduces a reference worksheet for its example case. Check the original papers before you rely on a result.

The tools are aids for engineers. Check the inputs and the results: responsibility for any decision stays with the user.