TECHNOLOGY Extended-length downhole mud motor designed for more power

Volker Krueger
Baker Hughes Inteq
Celle, Germany

A new positive displacement motor (PDM) designed with an extended power section has several advantages over standard mud motors run alone or in tandem.

Laboratory tests during design analysis and field tests have indicated these motors can outperform both conventional and coupled mud motors, providing higher penetration rates, longer bit runs, and easier steering.

As requirements for improved performance and durability of PDMs have become more demanding, a design team began working on an entirely new motor series (Fig. 1 [41020 bytes]). The requirements for a modern drilling motor came from extensive successes with today's conventional motors. Conventional motors were successful because they had met and extended criteria established for their own design. But the next step in PDMs had to achieve new objectives:

• At least a doubling in power

• Optimized rpm/torque ranges for improved bit performance and life

• High stalling reserve for directional drilling

• High fluid flow rates for extended-reach drilling

• A wide range of steerability beyond the buildup rates commonly realized for medium-radius drilling

• Compatibility with all drilling fluids

• Extended temperature ranges for deep well and geothermal applications

• Durability to survive numerous bit runs

• One-piece fishing capability in case of catastrophic failure

• Acceptable manufacturing and operational costs.

Because of the broad range of applications these motors would face, the requirements could not be met with one motor only. As some of the criteria were conflicting, it would be necessary to have special components for special cases.

Modern mechanical engineering computation methods were applied for the critical and relevant components of the drilling motor assembly. Design methods and laboratory testing of entire motors, especially for the elastomer stator section, required unique melding of modeling and design evaluation techniques.

Motor section

Length and lobe configuration of the new motor had to be selected such that maximum power and torque would be made available to the bit. Depending on torque and rpm requirements, there was the choice of low-speed/high-torque or a medium-speed motor section.

Multilobe configurations were to be optimized for the kinematics of the rotor/stator pair, achieving a high volumetric efficiency and low mechanical losses to reduce sliding wear and minimize internal mechanical stresses.

With longer motor sections, higher operating torque and longer life can be achieved only with a compromise regarding sealing capability. The fit between rotor and stator had to be adjusted such that a sufficiently uniform and linear load distribution along the motor section was realized.

New elastomer compounds were developed to cope with the increasingly harsh operations presented by aggressive fluids and high downhole temperatures. For this motor, a new multipurpose elastomer had to cover most of the applications at elevated temperatures in both water-based and oil-based muds. For special requirements, other suitable elastomers were needed.

The rotor was also to be optimized for torsional strength while reducing rotor mass to the lowest acceptable limit.

BHA deflection analysis

Stress analysis of individual motor components requires an in-depth understanding of load conditions on the entire bottom hole assembly (BHA) while it is drilling a hole. Deflection analysis of the entire BHA was necessary to obtain the basis for computations of stress on individual motor components.

The interaction of the BHA with the borehole is a complex problem. This interaction depends upon borehole course, BHA structure, geometry of the tools, stabilizer and bent components, the tool face orientation or angular position of the motor in the curved borehole, and weight on bit.

To predict loads on individual components of the motor, the drillstring is modeled as finite beam elements. For the detection of wall contacts, special finite contact or gap elements are applied between tool surface and borehole wall. Highly sophisticated iterative solution algorithms are then used to solve the nonlinear problem.

The BHA-deflection modeling program realizes a finite-element analysis of the drillstring in a plain but variable curved borehole. Program development for BHA analysis was based upon the Ansys general-purpose, finite-element software package.7 Several series of finite-element analyses, carried out during all design phases, investigated the deformed state, wall contacts, reaction forces, bending moments and stresses, clearance, and steering properties of the new motor.

The modeled lower end of the BHA consisted of the following:

• A Navi-Drill 43/4-in. M1X motor is modeled with a 6-in. bit. Tool face orientation is opposite the borehole high side (tool face orientation at 180).

• Bearing housing stabilizer is 1/8-in. undersized.

• The adjustable kick off (AKO) is set to a 2.0 angle.

• Nonmagnetic compressive service drill pipe is 43/4 in. 3 31/2 in. 3 21/16 in.

• Standard American Petroleum Institute (API) drill pipe is 31/2 in., 13.30 lb/ft.

Computations with tool face orientation at 180 were used to determine the steerability limits of the motor with respect to the minimum radiuses in which these BHAs are allowed to be rotated.

The bending moments and forces computed also serve as input for the more detailed analysis of components and subsystems.

In developing designs for the family of new motors, similar BHA deflection analyses were conducted for each size motor in the series.

Outer tubular connections

The outer thread connections of a steerable motor experience high stress from preload and operating loads, especially bending. To achieve higher buildup rates and increase the reliability of these critical connections, they were substantially strengthened with regard to torque and bending.

Besides the optimization of design and materials, the appropriate makeup torque plays a big role: the preload of the connection must be high enough to avoid shoulder separation and loosening while avoiding plastic deformations from excessive preloads. This optimization requires reliable analysis of thread connections.

Unfortunately, the API thread calculation method (API RP 7G) is limited to torque and tension, and no method is provided explicitly to calculate the bending capacity. Thus, analytical formulae were developed which are suitable for a rough calculation. In addition, a more accurate and sophisticated analysis was conducted with a finite-element program based on the commercial Ansys program.

Figs. 2 [37876 bytes] and 3 [30026 bytes] show examples of this thread analysis. The 3D model is required for the accurate simulation of contact conditions under bending loading. Two-dimensional models, which need much less computing time, are sufficient in the case of axis-symmetric loading such as torque and tension. The model uses a nonlinear elastic-plastic material law to analyze the effects of overloading.

Fig. 4 [34193 bytes] shows the positive results of this evaluation on makeup torque and allowable bending moment for outer thread connections of the new motor series.

This analysis resulted in designs for connections of the adjustable kick off, bearing housing, and stator, whose bending strength was increased by more than 150% as compared with the design of conventional motors.

Drive sub

The drive sub transmits the motor torque to the bit and carries axial loads, but because of side forces to the bit it also is subjected to bending. Fatigue cracks and even drive sub breakages may occur at drive sub areas with high stress concentration, such as the threads, shoulders, and sharp transitions. These "notches" are the main cause of breakage and limited endurance.

For the drive sub of the new motor, considerable effort was spent to maximize the durability and the fatigue strength. This goal was achieved by eliminating notches where possible and optimizing notches which could not be avoided. Through the application of high-strength material and the additional surface treatment of critical areas, compressive stresses were created to combat fatigue failures.

Least stress concentration

Fig. 5 [48557 bytes] shows an example of the stresses at a critical drive sub shoulder for the load case torque. For the optimized design, the maximum stress could be reduced by 24-50% as compared with previous designs. This reduction was accomplished by a smooth rounding with a compound curve that nearly eliminates the harmful stress risers.

With the drive sub diameter slightly increased, improved material applied, and the thrust bearings optimized, the acceptable operational load was significantly improved.

This motor uses a mud-lubricated bearing assembly because of its predictable wear behavior.

Flexible shaft

To determine the stresses on a flexible transmission shaft, a nonlinear, 3D deflection analysis was conducted. The basic loads on the flexible shaft are torque, axial load from the hydraulic thrust of the rotor, and bending.

Bending loads spring from the eccentric motion of the rotor inside the stator and tilting of the bearing assembly relative to the motor section. The use of a flexible shaft to replace conventional joint-shaft designs was challenging for a high-powered motor. Several factors were taken into account:

• Rotor eccentricity and momentary eccentric position of the rotor

• Relative position of the adjustable kick off and bend angle applied

• Cross section, material, length, and shape of the flex shaft

• Geometry of the adjacent drive sub and rotor elements

• Deformed state of the drive sub inside the bearing assembly

• Line support of the rotor inside the hyperelastic stator elastomer

• Axial force of the rotor due to motor thrust.

The complex boundary conditions and geometric parameters and the second order theory deflection could be handled only by a finite-element analysis. Three key positions of the eccentricity of the rotor relative to the adjustable kick off (equal, opposite, and orthogonal) were processed. Also, the specific elastomer stiffness, radial clearance of the bearing assembly, and deflection of the rotor and drive sub were taken into account.

Considering, in addition, the deflection of the entire motor lying inside a curved borehole, a worst-case scenario of the bending loading could be obtained. With this model, the deformed state, the bending loading, and the stresses of rotor, flex shaft and drive sub were computed.

Rotor section modulus

Regarding torsion, the valleys of a multilobe rotor have to be considered as notches or stress risers. For an optimum design which requires also the lowest possible mass of a rotor, it is essential precisely to determine the stresses in the valleys or the stress raising effect they cause.

The area moment of inertia of various cross sections can be computed analytically by a computer-aided design (CAD) system, while the determination of the torsional section modulus of bars with arbitrary cross sections is not a trivial problem. Analytical solutions are available only for simple cross sections (that is, circular, rectangular, or elliptical profiles).

A parametric 3D finite-element model was designed to master this problem: the model is based on original NC profile data. Numerical results were verified carefully with analytical solutions for simple cross sections. With the help of the 3D finite-element analysis, it is possible precisely to compute the torsional loading capacity for many kinds of rotor profiles. It is also possible to examine the influences of profile contour, the number of lobes and rotor lead, and profile warping.

Fig. 6 [39443 bytes] shows a stress plot of a five-lobed rotor profile. The maximum torsional stress arises inside the lobe valley at the inner envelope circle. The stress gradient inside the cross section is about 300%. With these data, it was possible to optimize the motor layout regarding minimum rotor mass and to avoid torsional overloading at challenging operating limits.

Stator elastomer profile

The inherent properties of the stator elastomer material are hyperelastic and nonlinear. They depend upon the load level, the load cycles, and the operating temperature. Special approximations and iterative solution algorithms are needed for simulating the behavior of an elastomer.

Finite-element methods were applied to analyze the design of the stator profile and to identify the areas inside the profile having critical heat concentrations, as they would be the nuclei for elastomer deterioration. For the computation, the 2D parametric finite-element model simulated the interaction between the rotor and the elastomer inside the stator tube.

To evaluate different profiles and different loading conditions, elastomer strain was measured for the static equilibrium state of rotor and stator under simulated operating conditions. Load conditions considered included the following:

• Hydraulic loading per chamber as a combination of hydrostatic pressure and pressure loss per stage

• Temperature strain from a uniformly increased temperature

• Unbalanced force of the rotor mass and the mud inside the rotor bore

• Coulomb friction forces at the rotor/elastomer contact areas.

A wide range of computations covering all possible rotor positions was carried out to detect the worst case. Fig. 6 [39443 bytes] illustrates how well highly strained regions at the surface and inside the elastomer were identified. Comparison of these computer simulations for different profile layouts led to an optimum contour regarding least strain and expected best performance for the new motor series.

Elastomer development

In a continuous development effort, substantial progress was made with respect to elastomers for high temperature service and with improved chemical resistance. Although the elastomer is the essential part of the stator, the bonding system to permanently attach the elastomer to the steel tube is a key element as well, especially with increased service temperatures.

The bonding process, the elastomer composition, and elastomer processing all contribute to reliable performance of the motor.

Elastomer compositions undergo vulcameter, rheometer, and chemical analyses. Molded and fully vulcanized sample testing determines physical and chemical properties (resistance to chemicals, tensile strength, hardness, abrasion resistance, and swelling in fluids). Dynamic testing determines heat buildup during loading-preferably in the presence of fluids and under simulated operating conditions.

Full-size motors are tested in autoclaves under high temperature while operated in the pump mode.

With a test stand using small pumps, the elastomer is tested with drilling fluids at maximum temperatures of 300 C. These tests of scale models screen for the most suitable designs. Full-size motors are then tested in a similar but larger autoclave at temperatures up to 250 C. and with realistic torque and speed applied (Fig. 7 [45545 bytes]).

An elastomer found to be significantly improved for high temperature service is highly saturated nitrile. It is a good compromise for applications at elevated temperatures and in a variety of water-based and oil-based drilling fluids. New elastomers have been developed on the basis of fluorocarbon and ethylene-propylene polymers, both of which proved reliable in laboratory testing at temperatures exceeding 200 C. They will find their application when the multipurpose nitrile cannot meet the requirements.

Practical motor optimization

Further optimization of motor geometries is accomplished in a test device, similar to the one in Fig. 7 [45545 bytes], which allows operation of prototype 43/4-in. motors in the pump mode.

Subjects for testing were the following:

• Different motor geometries (profiles)

• Different lobe numbers

• Rotor/stator fit

• Rotor coating

• Rotor surface treatment

• Selected elastomer compounds.

For the evaluation of these different configurations, basic data were compared such as volumetric and mechanical efficiency and maximum torque potential. A comparison of the volumetric and mechanical efficiency of different design options as well as other power characteristics demonstrated the superior performance of the contour design selected for the new motor.

As the last step of motor development, performance of the complete motor assembly was tested on a motor test stand with drilling fluid applied to drive the motor and torque generated by a brake to simulate drilling conditions. The brake can be operated from 30 to 2,600 rpm. Maximum torque generated is 18,000 Nm, and the maximum brake power 400 kw. The maximum pump rate for any type of mud or freshwater is 4,000 l./min.

Computerized control and data acquisition allow a fast and precise determination of prototype and production motor performance. These tests demonstrated that torque and power output of the new motor at nominal operating conditions were more than doubled. This improvement was accomplished partially by improved efficiency, of the positive results of the motor optimization process.

New motor

The basic configuration of the new motor shown in Fig. 1 [41020 bytes], like any drilling motor, has a power section consisting of stator and rotor, a bearing assembly, a transmission shaft, and a concentrically rotating drive shaft inside a bearing assembly.

An adjustable bend between the bearing assembly and the motor section allows continuous adjustment of the buildup rate capability, and a catching device on top of the rotor allows retrieval of the complete motor in case of the unlikely disconnection of outer motor components.

A flexible titanium shaft was designed for the new motor to overcome all of the problems of conventional articulated shafts. Optimization of this unit provides improved bending strength, a higher load-carrying capacity of the thrust bearings, and an increased service life of the journal bearings.

To maximize the bending strength of the adjustable kick-off sub and to further ease rig site handling, a new "half-shell" adjustable kick off allows quick and safe adjustment of the angle while maintaining a high-strength connection. A catching device on the rotor keeps the inner components secured to the top end of the motor, thus allowing fishing and retrieval of the whole assembly even after the worst incidents.

The application of sophisticated engineering and design tools, coupled with thorough prototype testing in versatile test facilities, resulted in a straightforward and timely realization of the design concept. Excellent laboratory results during design analysis and laboratory testing have been fully confirmed in the field.

The new motors outperform both conventional and coupled tandem motors, providing higher penetration rates, longer bit runs, and easier steering. Because of improved component durability, both the meantime between maintenance (MTBM) and the meantime between failure (MRBF) have improved dramatically.

Acknowledgment

The author thanks Frank Radez for his editorial contribution.

Bibliography

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3. Karlsson, H., Brassfield, T., and Krueger, V., "Performance Drilling Optimization," paper 13474, presented at the SPE/IADC Annual Drilling Conference, 1985.

4. Krueger, V., "Novel Navigational System for Directional Drilling," paper presented at the 5th OGEW/DGMK Conference, Innsbruck, Austria, Oct. 22-24, 1984.

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7. ANSYS Software, Swanson Analysis Systems Inc., Houston.

The Author