BHA design: stabilizer placement, side forces and bit tilt

A vertical well through steeply dipping, hard rock does not stay vertical by itself. The formation pushes the bit, and the bottom-hole assembly either resists that push or adds to it, depending on where its stabilizers sit. This article works through how a BHA model finds the bit's side force, its tilt and the rate the assembly holds, and uses them to compare a packed and a pendulum assembly in a 12¼″ section that has started to drift.

What steers a rotary assembly

A rotary BHA with no bend has only three ways to change the hole's direction. The bit pushes sideways on the formation, with a side force. The bit's axis can point away from the hole's axis, a tilt of a fraction of a degree. And the formation itself deflects the bit: in layered rock it drills more easily across the beds than along them, so in beds dipping less than about 45° the bit tends to turn up-dip.

Stabilizers set the first two. Each one centres the string at a point, and between those points the collars bend under their own weight and the weight on bit. A packed assembly puts stabilizers close together near the bit, so the collars have no room to bend and the bit has almost no side force or tilt: it holds the angle it has. A pendulum leaves a long stretch of collar between the bit and the first stabilizer. In an inclined hole that stretch hangs towards the low side and pulls the bit down: it drops angle. A fulcrum, with a near-bit stabilizer and a long collar above it, levers the bit upwards and builds.

The sizes are small. A few hundred pounds of side force and a tilt of 0.1–0.2° decide whether a well drops a degree per hundred feet or holds. That is why stabilizer placement is worth modelling.

The beam-column model

The standard way to compute these forces treats the BHA as an elastic beam lying in the hole, loaded by gravity and by the weight on bit, and touching the wall where it runs out of clearance. In the plane of the hole's inclination, with u the offset from the hole's axis:

EI

bending stiffness of each tool (lbf·in²)

P

axial compression: the weight on bit less the buoyed weight carried along the hole

w, BF, θ

weight per unit length in air, buoyancy factor, hole inclination

κ

hole curvature (build positive): compression pushes the BHA to the outside of a curve

q_contact

wall reactions where a stabilizer blade or a collar touches the wall

The bit is a pin at the centre of the hole. Its reaction is the side force; its slope is the tilt. Solving the same BHA at a range of curvatures gives the equilibrium curvature: the hole curvature the BHA would drill by itself. There are two versions. A bit that cuts sideways as easily as ahead drills where its side force is zero; a bit that only drills along its axis drills where its tilt is zero. Real bits sit between those two bounds. A bit with a short, active gauge lets the side force work; a long, passive gauge makes it follow its tilt.

This is the finite-element method published by Millheim and colleagues in 1978, after Lubinski and Woods' analytical pendulum work of 1953. DrillIQ's BHA Design module solves it with beam-column elements and an active-set wall-contact search, from the bit to 90 ft above the highest stabilizer, where the collars rest on the low side. It is planar and static, and it has no term for the formation: the formation's push has to come from the surveys.

The example well

The example is a vertical exploration well in conditions typical of the Llanos foothills, Colombia: a thrust belt where hard, abrasive sandstones and shales dip at 30–60°, deep below thick overburden. The 12¼″ section runs from the 13⅜″ shoe at 2,900 m to 4,400 m in beds dipping 35°. It was started with a packed assembly, and by 3,600 m the survey shows 5°. Held at 5° for the remaining 800 m, the bit would move another 800 × sin 5° = 70 m sideways. The team wants the angle back down.

A hand check on the pendulum

The pendulum's drop force can be bracketed by hand. Treat the 66 ft of collar between the bit and the first stabilizer as a beam loaded by the part of its weight that acts across the hole.

1. Buoyancy. BF = 1 − 12.0 / 65.5 = 0.817.
2. Load across the hole. 150 × 0.817 × sin 5° = 10.68 lb/ft.
3. Two limits on the bit's reaction. If the stabilizer were a simple support, the bit would carry half the span: 10.68 × 66 / 2 = 352 lbf. If the collar were held straight at the stabilizer, the bit would carry three-eighths: 3 × 10.68 × 66 / 8 = 264 lbf. The collar continues above the stabilizer, so the truth lies between.
4. The engine. DrillIQ's beam model gives a drop force of 304 lbf at 5 klbf, inside the bracket, and 296 lbf at 25 klbf.
5. When the collar touches. A simply supported span sags 5wL⁴/384EI. With EI = 30 × 10⁶ × 198.0 in⁴ and 2.125 in of clearance around the collar, the sag reaches the wall at 85 ft. Our 66 ft span sags 0.77 in by this formula, so it hangs free.
6. Whirl. The same span's first bending critical speed, (π/L)²√(EI/m), is 64 rpm; the engine, using the span's actual tools, gives 66 rpm.

The hand figures frame the engine's answer without replacing it. They can't give the tilt, the effect of weight on bit, or what happens once the collar touches the wall. Those need the full model.

Where each layout touches the wall

At 5° and 25 klbf the two layouts behave in opposite ways. The packed assembly's three stabilizers hold the collars almost straight. Its bit pushes 63 lbf towards the high side and points within a thousandth of a degree of the hole axis, and both of its equilibrium rates are within 0.03°/100 ft of zero: it holds 5°, no more and no less. Most of its contact load sits on the top stabilizer, 956 lbf on the low side, where the long collar column above it starts to lie on the wall.

The pendulum pushes on the low side at the bit, 296 lbf, and its two stabilizers carry 493 and 788 lbf. Its collars sag 0.64 in towards the low side halfway to the first stabilizer, and that sag tilts the bit 0.16° up. The side force says drop; the tilt says build. The two bounds put the pendulum's rate between a drop of 1.14°/100 ft and a build of 2.03°/100 ft, and the bit decides where in that band the well goes.

Where to put the first stabilizer

Moving the pendulum's first stabilizer up the string lengthens the hanging span, and the drop force grows: from 184 lbf with the stabilizer 24 ft from the bit to 363 lbf at 89 ft, at 25 klbf. One step further, at 94 ft, the collar below the stabilizer sags onto the low side. From then on the collar's own contact carries part of the weight, the effective pendulum gets shorter, and the drop force falls back to 254 lbf at 134 ft. At 10 klbf the collar is straighter, so the peak moves out to 94 ft and 401 lbf.

That is the classical pendulum rule, now with numbers for this BHA: place the first stabilizer just short of the point where the collar touches the low side, and remember that the point moves closer to the bit as weight on bit rises. The tilt sets a second limit. At 25 klbf the tilt bound climbs from a build of 0.24°/100 ft at 24 ft to 4.0°/100 ft at 84 ft, much faster than the drop force grows. A longer pendulum helps a bit that cuts sideways and hurts one that follows its axis.

Weight on bit and the drop rate

Weight on bit barely changes the pendulum's side force at 5°: 304 lbf at 5 klbf, 290 lbf at 35 klbf. It changes what that force achieves. Compression makes the collars easier to bend into a curve, so the same side force is balanced by a smaller drop. The side-force bound shrinks from a drop of 1.90°/100 ft at 5 klbf to 0.94°/100 ft at 35 klbf, while the tilt bound rises from a build of 1.79 to 2.26°/100 ft. The packed assembly stays within ±0.04°/100 ft of hold across the whole range.

Inclination matters as much as weight. The drop force scales with sin θ: 576 lbf at 10°, 296 lbf at 5°, 115 lbf at 2° and only 58 lbf at 1°. A pendulum works hardest when the hole has already drifted and fades as it nears vertical, so in a formation that keeps pushing, the hole settles at the angle where the two balance. This is where automated vertical-drilling systems, which push the bit back towards vertical at any angle, earn their cost.

Choosing and running the assembly

Measure the formation's push first. The model has no formation term. While the packed assembly holds by the model's account, any build in the surveys is the formation's. Here the packed BHA, at +0.03°/100 ft by itself, has built 5° in the 700 m since the shoe, about 0.22°/100 ft. That difference is the push the next BHA has to beat.

Match the bit to the layout. A pendulum is a side-force tool. Run it with a bit that cuts readily at its gauge, or its upward tilt will cancel the drop. With a long-gauge bit, a packed assembly that holds may be the better choice until a steerable tool is available.

Trade weight for angle deliberately. In hard sandstone, every klbf taken off the bit costs rate of penetration. At 25 klbf this pendulum still has more than half the side-force drop it had at 5 klbf (1.14 against 1.90°/100 ft). Check the trade with the model before cutting weight on the rig.

Keep the rotary speed off the critical speeds. The pendulum's 66 ft span has its first critical at 66 rpm, and the collar column above the top stabilizer, which the engine cuts to its 85 ft sag-contact length, at 39 rpm. Both layouts are clear of these lateral criticals at 120 rpm; run through the 59–72 rpm band quickly when starting rotation. The packed layout's shorter spans sit at 207 rpm and above.

Check the rest of the string as usual. At 25 klbf the neutral point is 205 ft above the bit, in the collars and below the jar. The engine's weight-on-bit limit is 37.4 klbf, set by sinusoidal buckling of the 5″ HWDP with a 1.3 safety factor. The 8″ × 2-13/16″ collars with 6⅝″ REG connections have a bending strength ratio of 2.60, inside the 2.25–2.75 band for that size. For how these loads feed the string's torque and drag, see the torque and drag article.

A checklist for the rig team

• Read the formation's tendency from the surveys before changing the BHA.
• Run the model on both layouts at the hole's actual inclination and weight on bit.
• Look at both bounds, the side force and the tilt.
• Place the pendulum's first stabilizer just short of where the collar touches the low side at your weight on bit.
• Gauge every stabilizer before it goes in the hole; a worn blade changes the answer.
• Choose a bit whose gauge suits the layout's steering mechanism.
• Keep the rotary speed out of the lateral critical bands, and pass through them quickly.
• Survey often enough to see the trend within a stand or two of a change.

How DrillIQ handles it

In DrillIQ the BHA Design module builds each assembly from a tool catalogue and checks it: buoyed weight, neutral point, buckling and the weight-on-bit limit, bending stress, and every connection's bending strength ratio and fatigue life. Its beam-column model gives the bit side force and tilt, every wall contact, and the side-force, tilt and rotating equilibrium rates, and draws the contacts on the in-hole view. The stabilizer sweep moves a stabilizer along the string and shows the rate at each position, and the vibration screen lists each span's critical speeds against the speed it turns at. Everything above was worked out with the same engines.

Book a demo → See all capabilities

References

1. Lubinski, A. and Woods, H.B. Factors Affecting the Angle of Inclination and Dog-Legging in Rotary Bore Holes. API Drilling and Production Practice, 1953.
2. Millheim, K.K., Jordan, S. and Ritter, C.J. Bottom-Hole Assembly Analysis Using the Finite-Element Method. Journal of Petroleum Technology 30(2), 1978 (SPE 6057).
3. Bourgoyne, A.T., Millheim, K.K., Chenevert, M.E. and Young, F.S. Applied Drilling Engineering. SPE Textbook Series Vol. 2, 1986.
4. American Petroleum Institute. Recommended Practice 7G: Drill Stem Design and Operating Limits.

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