Hydraulics, ECD and hole cleaning, worked through

Drilling hydraulics is a budget. The pumps deliver a fixed pressure, and the string, the motor, the bit and the annulus each take a share. The annulus takes the smallest share and matters most: it sets the ECD the formation feels and the velocity that carries the cuttings out. This article works the budget through on a 60° 12¼″ tangent, from the rheology to the flow rate that hole cleaning asks for.

What the pumps pay for

Standpipe pressure is the sum of every friction loss on the way round: surface lines, drill string, motor and MWD, bit nozzles and the annulus. Only the annulus acts on the open hole. The hydrostatic of the mud column plus the annular friction above a depth, expressed as a density, is the equivalent circulating density, the ECD.

The annulus also cleans the hole. Cuttings sink through the mud at a slip velocity set by their size, the mud's viscosity at low shear and the density difference, and the mud has to rise faster than that. Between about 40° and 65° cuttings settle a short distance onto the low side, form a bed, and the bed can slide back down. A 60° tangent sits in the hardest part of that range, so hole cleaning usually sets the flow rate there. Every decision trades pump pressure, ECD and cuttings transport; flow rate, nozzles, rotary speed, drilling rate and rheology are the levers.

The method

Everything starts with the six Fann viscometer readings. The Bingham model draws a straight line through the 600 and 300 rpm readings: its slope is the plastic viscosity (PV), its intercept the yield point (YP). API RP 13D recommends the Herschel–Bulkley model, which keeps a yield stress but lets the curve bend:

τ, τ_y

shear stress and yield stress (lbf/100 ft²)

γ̇

shear rate (1/s)

θ₆₀₀ … θ₃

Fann dial readings at 600, 300, 6 and 3 rpm

n, K

flow index and consistency (lbf·sⁿ/100 ft²)

In this well's open annulus the wall shear rate is about 90 s⁻¹, far below the 511 and 1,022 s⁻¹ of the 300 and 600 rpm readings. Bingham extrapolates the high-shear line down to a yield point the mud does not have at low shear, so it overstates annular friction. ECD, the bit and the cuttings then follow from standard relations:

ρ_static

average density of the static mud column (ppg)

ΔP_ann

annular friction above the depth (psi); TVD in feet

Q, A, C_d

flow (gpm), total nozzle area (in²), nozzle discharge coefficient (0.95)

HSI

bit hydraulic horsepower per square inch of hole, D the bit diameter (in)

TR

transport ratio: the share of the annular velocity left to lift the cuttings

DrillIQ takes the slip velocity from Moore's correlation, corrected for hole angle and rotary speed, and above 30° also runs Larsen's correlation for the velocity at which no bed forms. The ECD with cuttings adds the rock in the annulus: it enters at the drilling rate and leaves at the transport ratio.

The example well

The example is a directional well in a mature oil area, set in conditions typical of the Llanos Basin, Colombia: a normally pressured Tertiary section of reactive shales and sands, drilled with an inhibitive water-based mud in a long 12¼″ section above the reservoir. The well kicks off at 700 m, builds at 3°/30 m to 60° and holds to the 9⅝″ casing point at 3,600 m MD, 2,346 m TVD. Near the bottom it crosses a sand that offset production has partly depleted, the weak point of the section.

Two options are on the table: 6 × 14/32 nozzles at 900 gpm, and 6 × 16/32 at 1,050 gpm.

A hand check at 1,050 gpm

Check the model's size by hand first. Take the 2,782 m of drill pipe in open hole, 6 × 16/32 nozzles and 1,050 gpm.

1. Rheology. PV = 70 − 48 = 22 cP and YP = 48 − 22 = 26 lbf/100 ft². The Herschel–Bulkley fit gives τ_y = 2 × 9 − 11 = 7 lbf/100 ft², n = 0.619 and K = 0.862 lbf·sⁿ/100 ft². The yield stress is about a quarter of the YP.
2. Annular velocity. 24.51 × 1,050 / (12.25² − 5.5²) = 214.8 ft/min.
3. Bingham annular loss. The laminar slot formula gives 22 × 214.8 / (60,000 × 6.75²) + 26 / (200 × 6.75) = 0.0017 + 0.0193 = 0.0210 psi/ft. The yield term is 92 % of it. Over 9,127 ft that is 192 psi. DrillIQ's engine on Bingham gives 183 psi, because it thins the mud as it heats and adds a small rotation term. On Herschel–Bulkley it gives 110 psi.
4. ECD at the sand. Take the sand at 3,180 m MD, 2,136 m TVD, or 7,009 ft. The static column above it averages 10.08 ppg against 10.2 ppg at surface, because hot mud expands. With 126 psi of annular friction above the sand, ECD = 10.08 + 126 / (0.052 × 7,009) = 10.42 ppg, the engine's clean figure.
5. Cuttings load. At 35 m/h the bit makes 11.7 gpm of rock. With a transport ratio of 0.79 the annulus holds 11.7 / (11.7 + 0.79 × 1,050) = 1.39 % cuttings by volume. At 21 ppg that adds 0.0139 × (21 − 10.2) = 0.15 ppg: 10.57 ppg with cuttings, as the engine reports.
6. Bit. The nozzle area is 6 × π/4 × 0.5² = 1.178 in². At 10.2 ppg, ΔP_bit = 10.2 × 1,050² / (12,032 × 0.95² × 1.178²) = 746 psi. The engine, using the mud's density at 91 °C, gets 726 psi: 726 × 1,050 / 1,714 = 445 hp, or 3.77 hp/in² of hole.

Every step lands within 5 % of the engine, and step 3 shows the main point: the rheology model decides how much friction the annulus carries.

Where the pressure goes

With 6 × 14/32 at 900 gpm the pumps need 3,461 psi: 1,716 psi through the surface lines and drill string, 696 psi through the motor and MWD, 910 psi (26 %) through the bit and 139 psi (4 %) in the annulus. That 4 % is all the friction the open hole feels.

The classic bit optimisation puts about 65 % of the pump pressure across the bit for maximum hydraulic horsepower, or about 48 % for maximum impact force. This well cannot get near either: 3,600 m of string at high flow leave little for the bit, and in a high-angle 12¼″ hole flow is the scarce resource. The useful question is how much flow the pumps can deliver with nozzles that still keep the bit clean.

Opening the nozzles to 6 × 16/32 moves pressure from the bit to the flow. At 1,050 gpm the pumps need 3,789 psi, 411 psi under the limit. HSI falls from 4.06 to 3.77 hp/in², while impact force rises from 1,482 to 1,544 lbf. The third bar is the same case on the Bingham model: 4,462 psi, over the limit, a plan nobody would choose.

ECD against the window

The static column falls from 10.2 ppg at surface to 10.06 ppg at TD as the mud heats. That clears the 9.8 ppg the shales need at 60° by only 0.26 ppg. With 1,050 gpm and cuttings, the Herschel–Bulkley ECD is 10.53 ppg at the shoe, far below its 13.3 ppg fracture gradient, and 10.57 ppg at the depleted sand, against 11.2 ppg. That 0.63 ppg margin is the one to manage.

Bingham puts the ECD at the sand at 10.79 ppg, a margin of 0.41 ppg; the API RP 13D power-law model gives 10.60 ppg. Two models agree within 0.03 ppg, and the third differs by more than a third of the margin. So calibrate on the first stands: compare calculated and measured standpipe pressure, and ECD directly if a pressure-while-drilling sub is in the string.

Flow barely moves the ECD here. From 900 to 1,050 gpm the annular friction rises 7 psi, but the faster annulus carries fewer cuttings, and the ECD at the sand falls from 10.58 to 10.57 ppg. The drilling rate moves it more: 10.51 ppg at 20 m/h, 10.63 ppg at 50 m/h. For the pore and fracture side of the window, see the mud-weight window article.

Flow rate, nozzles and hole cleaning

The transport ratio in the tangent rises slowly with flow: 71.2 % at 700 gpm, 76.2 % at 900, 78.8 % at 1,050. DrillIQ's hole-cleaning map calls 80 % and above comfortable and 65–80 % tight. At 120 rpm the tangent reaches 80 % at 1,130 gpm. With 6 × 14/32 nozzles the pumps hit 4,200 psi at 1,033 gpm. With 6 × 16/32 the limit moves to 1,131 gpm, the same flow, with no headroom left.

The plan runs 1,050 gpm on 6 × 16/32, keeps 411 psi of headroom to see a pack-off coming, and accepts a transport ratio in the tight band. Rotation, drilling rate and circulating time do the rest. At 1,050 gpm the engine gives 77.3 % at 60 rpm, 78.8 % at 120 rpm and 80.4 % at 180 rpm. That counts only the slip correction; flow-loop work shows rotation also stirs a settled bed back into the flow, so treat it as a floor.

Larsen's correlation, which has no rotation term, puts the flow that leaves no bed at 2,629 gpm at 35 m/h, and 2,000 gpm at 20 m/h. No rig pumps that through a 12¼″ annulus, so in a hole like this the bed has to be managed. Circulating time matters too: the annulus holds 1,374 bbl, bottoms-up at 1,050 gpm takes 55 minutes, and the engine's circulate-clean time, which scales each interval's bottoms-up by its angle, is 103 minutes.

What to do on the rig

Calibrate early. After drilling out the shoe, record standpipe pressure at three flow rates off bottom and fit the model's friction to them. A model that matches within a few per cent can be trusted for ECD.

Read standpipe pressure as a trend. A slow rise at constant flow, with torque rising too, points to a growing bed or a pack-off. A sudden drop is a washout or a lost nozzle; a step up, a plugged nozzle. See torque and drag and the early signs of stuck pipe.

Protect the weak zone in transients. The 0.63 ppg margin is a steady circulating figure. Breaking circulation in gelled mud, a pack-off or running casing past the sand all spike the pressure. Stage the pumps up slowly and check surge speeds before trips; the surge and swab article works through that limit.

Watch the shakers against the drilling rate. If fewer cuttings come over the shakers than the bit makes, the hole is storing them. Slow down, rotate and circulate before the bed shows up as overpull.

A checklist for the rig team

• Fit Herschel–Bulkley to all six Fann readings; don't take ECD from Bingham YP alone.
• Calibrate the model against measured standpipe pressure, and PWD if you have it, on the first stands.
• Know the weakest point in the open hole and its margin to the ECD with cuttings.
• Set the flow rate for hole cleaning first, then choose nozzles that fit it under the pump limit.
• Keep pressure headroom below the pump limit to see a pack-off coming.
• Rotate at the highest speed the string and BHA allow, and control the drilling rate when cleaning is tight.
• Circulate the hole clean before tripping, by time and by what the shakers show.
• Remember the hot mud column is lighter than the flowline weight.

How DrillIQ handles it

In DrillIQ the Hydraulics & ECD module plans each section with Bingham, power-law, API RP 13D, Herschel–Bulkley and Unified rheology, splits the standpipe pressure into surface, string, tool, bit and annular losses, and computes ECD with cuttings and temperature against the window, transport ratio and Larsen beds, bit hydraulics, nozzle choice, and surge and swab. Its hole-cleaning map sweeps flow against drilling rate or rotary speed. While drilling, it runs the same engine on live rig data, compares calculated with measured standpipe pressure and PWD, fits friction to them, and alarms on ECD margin, pressure deviation and transport ratio. Everything above was worked out with the same engine.

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References

1. American Petroleum Institute. Recommended Practice 13D: Rheology and Hydraulics of Oil-well Drilling Fluids.
2. Bourgoyne, A.T., Millheim, K.K., Chenevert, M.E. and Young, F.S. Applied Drilling Engineering. SPE Textbook Series Vol. 2, 1986.
3. Luo, Y., Bern, P.A. and Chambers, B.D. Flow-Rate Predictions for Cleaning Deviated Wells. IADC/SPE 23884, 1992.
4. Larsen, T.I., Pilehvari, A.A. and Azar, J.J. Development of a New Cuttings-Transport Model for High-Angle Wellbores Including Horizontal Wells. SPE Drilling & Completion 12(2), 1997 (SPE 25872).
5. Sanchez, R.A., Azar, J.J., Bassal, A.A. and Martins, A.L. Effect of Drillpipe Rotation on Hole Cleaning During Directional-Well Drilling. SPE Journal 4(2), 1999 (SPE 56406).

About this example. The well in this article is a representative scenario set in typical Llanos Basin, Colombia conditions and worked through with DrillIQ's engines. It is not a client's well, and its figures are not field results.