STATOR LIFE OF A POSITIVE DISPLACEMENTDOWN-HOLE DRILLING MOTOR Majid S. Delpassand R&M Energy Systems A Unit of Robbins & Myers, Inc. Conroe, Texas F G’ H N ∆P ABSTRACT The power section of a positive displacement drill motor (PDM) consists of a steel rotor and a tube with a molded elastomeric lining (stator). Power section failures are typically due to the failure of the stator elastomer. Stator life depends on many factors such as design, materials of construction, and down hole operating conditions. This paper focuses on the stator failure mechanisms and factors affecting stator life. An analytical method for predicting the effect of various design and operating parameters on the strain state and heat build-up within elastomers is discussed. Q S∆P T Vc W ε tan δ The effect of parameters such as rotor/stator design, down hole temperature, drilling fluid, stator elastomer properties, motor speed, and motor differential pressure on the stator life is discussed. Non-linear finite element analysis is used to perform thermal and structural analysis on the stator elastomer. Data from laboratory accelerated life tests on power section stators is presented to demonstrate the effect of operating conditions on stator life. loading frequency [Hz] elastic modulus [psi] hysteresis heat [BTU/hr-ft3] number of rotor lobes differential pressure across the power section [dpsi] flow rate [gpm] slip or blow-by of fluid past seal lines. A function of differential pressure across adjacent cavities. [number between 0 and 1] torque [ft-lb] cavity volume; stator pitch x pumping area [in3] rotor speed [rpm] strain [in/in] ratio of viscous to elastic modulus BACKGROUND Mud Motor Power Section The power section of a positive displacement drill motor (PDM) converts the hydraulic energy of high pressure drilling fluid to mechanical energy in the form of torque output for the drill bit. A power section consists of a helical-shaped rotor and stator. The rotor is typically made of steel and is either chrome plated or coated for wear resistance. The NOMENCLATURE 1 stator is a heat-treated steel tube lined with a helical-shaped elastomeric insert. Figure 1 is a cross-sectional view of a typical power section. two positions of a power section rotor within its corresponding stator. LOBE CAVITIES Figure 1. Cross-Sectional View of a 4:5 Lobe Power Section. Figure 3. Rotor with Lobe “A” Fully Inserted in Stator Lobe. Figure 4. Rotor Position Rotated Approximately 20 Degrees from Position in Figure 3. As shown in Figure 2, the rotors have one less lobe than the stators and when the two are assembled, a series of cavities is formed along the helical curve of the power section. Each of the cavities is sealed from adjacent cavities by seal lines. Seal lines are formed along the contact line between the rotor and stator and are critical to power section performance as will be discussed later. ROTORS STATORS Figure 2. During drilling operations, high pressure fluid is pumped into the top end of the power section where it fills the first set of open cavities. The pressure differential across two adjacent cavities forces the rotor to turn and as this occurs, adjacent cavities are opened allowing the fluid to flow progressively down the length of the power section. Opening and closing of the cavities occur in a continuous, pulsationless manner causing the rotor to rotate at a speed that is proportional to drilling fluid flow rate (Equation 1). This action converts fluid hydraulic energy into mechanical energy. As shown in Equation 2, the torque of a power section is proportional to cavity volume and differential pressure across the power section. Various Lobe Configurations. The centerline of the rotor is offset from the center of the stator by a fixed value known as the “eccentricity” of the power section. When the rotor turns inside the stator, its center moves in a circular motion about the center of the stator. Rotation of the rotor about its own axis occurs simultaneously but it is opposite to the rotation of the rotor center about the stator center. Figures 3 and 4 illustrate 2 W = [231*Q/ (N * Vc)]*S∆P (1) T = (N*Vc*∆P)/24π (2) The pressure rating is the differential pressure at which a power section should operate to achieve optimum stator life. However, it is not uncommon during aggressive drilling to run power sections well above the maximum pressure rating. In many cases users will target operation at differential pressures just below stalling conditions. This practice does result in significant reduction of stator life. Cavity volume is purely a function of power section design. As shown above, it is defined as pumping (cavity cross sectional) area multiplied by stator pitch. Moineau theory defines the maximum pumping area that can be obtained within a given stator tube diameter. Power section speed is inversely proportional to stator pitch length. Figure 5 illustrates the effect of pitch length on rotor speed at a given fluid flow rate. 1 Slip is caused when high pressure fluid blows by rotor and stator seal lines. Slip results in power section speed reduction and is defined as the percent reduction in rotor speed below maximum theoretical for a given flowrate. The following table summarizes the impact of different design and operating parameters on power section slip. 4:5 LOBE NORMALIZED ROTOR SPEED 0.8 0.6 Table I. Parameters Affecting Slip. 0.4 Parameter Pressure differential increase Compression fit increase Rubber modulus increase Flow rate increase Rotor/Stator wear Stator expansion due to temperature or chemical swell 0.2 0 1 2 3 4 5 NORMALIZED STATOR PITCH Figure 5. Reduction in Rotor Speed with Increasing Stator Pitch. Pressure Rating and Slip The recommended differential pressure of a power section is the summation of the pressure ratings for each individual stage. Although the definition of a stage is somewhat arbitrary, it is typically defined as one pitch length of the stator. The pressure differential rating for an individual stage generally ranges from 100 to 300 dpsi and depends on number of lobes, pitch length, compression fit, and elastomer physical properties. For a power section, at otherwise identical conditions, higher pressure per stage usually means lower stator life. This will be discussed later. Effect on Slip Increase Decrease Decrease No change Increase Decrease During drilling, differential pressure and slip increase as the load on the bit increases. This causes the rotor speed to slow down until at some point above maximum rated pressure, the power section stalls. Once the motor is stalled, all drilling fluid blows by the seal lines. The differential pressure at which stall is reached can be increased by increasing compression fit between the rotor and stator. Figure 6 shows the impact of a large fit variation on power section speed and torque output. If the rotor-stator fit becomes too tight, stator life will be significantly reduced. Optimal fit provides a slip efficiency that is a compromise of stall margin at maximum rated pressure and stator life. 3 1 0.9 0.8 0.7 0.7 0.6 0.6 0.5 0.5 0.4 0.4 0.3 0.3 TORQUE 0.2 0.1 TIGHT 0.2 LOOSE 0.1 0 TORQUE (FT-LB) SPEED 0.8 NORMALIZED TORQUE NORMALIZED ROTOR SPEED 1 0.9 450 400 350 300 250 200 150 100 50 0 0.2 0.4 0.6 0.8 INCREASING FLOWRATE 0 0 0 EFFECTIVE ∆P OFF-BOTTOM PRESSURE LOSSES 1 100 200 300 400 500 DIFFERENTIAL PRESSURE (PSI) NORMALIZED DIFFERENTIAL PRESSURE Figure 6. Figure 8. Effect of Fit on Power Section Performance. Figure 8 shows that torque output of a power section increases essentially linearly with increasing differential pressure across a power section. The pressure losses shown are the combined effects of flow losses in the entrance region of the power section and of frictional losses between the rotor and stator. The losses are quantified as the differential pressure required to start the rotor turning and are dependent on drilling fluid flowrate. In the example above, the losses range from 50 psi at the lowest flowrate to 120 psi at the highest flowrate. The differential pressure needed for startup does not contribute to torque generation by the power section. For example, if a power section is operated at 400 psi differential pressure and the start-up differential pressure is 100 psi, the differential pressure that is effectively generating power is 300 psi. Figures 7 and 8 are performance charts for a typical power section. As the load on bit is increased, the differential pressure across the power section and torque output increase while the rotor speed decreases. The full load curve represents the maximum recommended differential pressure at which the power section should be operated. Note that the pressure rating decreases as flow rate and rotor speed increase. The reason for derating a power section is to achieve longer life. This will be explained in more detail later. ROTOR SPEED (RPM) 250 200 MAX ∆P LINE INCREASING FLOWRATE 150 100 50 FAILURE MECHANISMS One of the most challenging aspects of utilizing power sections for drilling operations is understanding and predicting failure. Power section failures are primarily due to destruction of the stator elastomer. Rotor failures due to wear or chemical attack are rare compared to stator failures and are not discussed in this paper. Elastomer failures may be classified as those which result in a reduction in performance and those which are catastrophic. In 0 0 100 200 300 400 500 DIFFERENTIAL PRESSURE (PSI) Figure 7. Typical Power Section Performance. Typical Power Section Performance. 4 many cases continued operation under conditions of reduced performance will lead to catastrophic failure. Each type of failure may be caused by a variety of reasons. In the following sections, key stator failure mechanisms and the factors that influence them are categorized. number of power section lobes increases, fatigue life decreases because the loading frequency increases. One method for compensating for this is to reduce rotor speed. At high loading frequencies, the strain and strain rates on the elastomer will be sufficient to promote the initiation and propagation of microscopic cracks in the stator lobes. This phenomenon, known as fatigue crack growth, occurs under high strain and strain rate depending on the elastomer tear strength and strain energy release rate. If the elastomer is subjected to strain below the critical level, the onset of fatigue crack growth may not occur even at very high frequencies. However, at strains above the critical level, cracks will initiate in the high strain region, usually in the bottom of the stator lobes, and the crack growth rate will depend on the cyclic rate of loading. Figure 10 illustrates failure of a stator operated above the critical strain level for a given loading frequency. Mechanical and Fatigue Mechanical failure of the stator elastomer occurs when the elastomer is overloaded beyond its stress and strain limits. Any number of the following factors may contribute to premature stator mechanical failures: 1) excessive pressure during aggressive drilling operations; 2) repeated stalling; or 3) high compression fit between rotor and stator. Each of these factors results in overstrain of the stator lobes beyond their mechanical limits. Figure 9 is an illustration of a stator that failed under high mechanical loading. In some cases, power section stators can fail due to fatigue at mechanical loading conditions well below the rubber tear strength. FATIGUE CRACKS AT BOTTOM OF LOBES Figure 10. Figure 9. Chunked Stator Due to Overpressure. Thermal and Hysteresis Failures Thermal failures occur when stator elastomer temperature exceeds its rated temperature for a prolonged duration. Stator elastomer physical properties usually weaken as temperature increases. The weakening of the elastomer properties results in shortened stator life. High elastomer temperatures Fatigue failures are the result of high cyclic loading on the stator elastomer due to rotor speed. Equation 3 defines the loading frequency for a power section stator. F = (RPM/60)* N Failed Stator Due to Fatigue Crack Growth. (3) The cyclic loading simply defines the number of times a stator lobe is flexed in a unit of time. As the 5 may be due to down-hole temperature, hysteresis heat, or the combination of both. Exposure to the down-hole temperature will cause the stator elastomer to expand which tightens compression fit. Degradation of elastomer physical properties will occur if the down-hole temperature is above the temperature rating of the elastomer. Hysteresis heat generation is due to repeated flexing of the stator lobes by the rotor and the pressurized fluid. Because elastomers are visco-elastic materials, a portion of the flexing energy is converted into thermal energy. Equation 4 from Reference 1 can be used to estimate hysteresis heat generation within elastomers. H = 2100* G’ * tan δ *ε2 * F (4) The location of peak hysteresis heat build-up is near the center of the stator lobes. The strain in this region combined with the low thermal conductivity of elastomers result in this heat build-up. Figure 11 shows the temperature distribution within a typical stator due to hysteresis heat build-up. Note the 30 degree F temperature build-up due to hysteresis. The heat build-up increases as power section speed, pressure differential, or compression fit is increased. The maximum temperature within the stator may exceed the elastomer’s temperature rating, even if the down-hole temperature is well within the operating limits of the stator. Therefore, at elevated down-hole temperatures, power section life may be prolonged if the power sections are operated at slow speed or low differential pressure. Figure 11. Hysteresis Heat Build-up Within Stator Elastomer. In all the cases described above, the result of elastomer temperature exceeding its temperature rating is: 1) the reduction of elastomer physical properties; and 2) the expansion of the elastomer which tightens rotor/stator compression fit. The combined thermal and mechanical effects significantly reduce stator life. Using an oversize stator is one method for compensating for increased fit due to elastomer expansion. Chemicals and Aromatics Drilling fluids are composed of many different chemicals and are uniquely designed to improve drilling penetration rate, prevent formation damage, allow easy clean-up, and facilitate other drilling requirements. Some of the chemicals, synthetic oils, or aromatics used in drilling fluids weaken the rubber molecular chain resulting in reduction in rubber physical properties and shrinkage or swell. Weakening of the rubber combined with a change in compression fit due to shrinkage or swell will accelerate stator failure. Figure 12 shows an 6 example of change in elastomer properties when exposed to a common drilling fluid at 4000 psi and 300 degrees F. Discussions related to the elastomer compatibility with various drilling fluids is outside the scope of this paper. is “too loose” or “too tight.” Figure 13 shows the normalized data obtained in the lab. NORMALIZED STATOR LIFE 1 % LOSS IN PHYSICAL PROPERTIES 4000 psi at 300 Deg F 60 50 40 30 20 10 0 Nitrile 0.6 0.4 0.2 HNBR 0 0 0.5 1 1.5 2 NORMALIZED OPTIMUM COMPRESSION FIT Drilling Fluid 1 Figure 12. 0.8 Drilling Fluid 2 Figure 13. Effect of Drilling Fluid on Elastomer Properties. Stator Life is Reduced if Compression Fit is “Too Loose” or “Too Tight.” In cases where the interference is lower than optimal, power section efficiency drops due to slippage of high pressure fluid between cavities and stator life decreases due to increased susceptibility to stalls and stator wear. STATOR LIFE OPTIMIZATION Stator life is critical to all drilling operations. In order to achieve optimum life, stators must be designed and operated with knowledge of the factors that influence life. The following section describes these factors and how each is accounted for in design practices to optimize power section life. The power section design process involves selecting a compression fit that will provide optimal stator life at a specific down-hole temperature. Fit selection is made based on test data, field data, and experience. Design parameters such as lobe configuration, stator pitch, and elastomer type are also considered in the fit selection process. Rotor/Stator Interference Fit Interference (compression) fit is probably the most critical factor that determines stator life. Optimum fit provides a balance between frictional losses, power section efficiency, and stator life. If the interference is higher than optimal, power section efficiency increases because of reduced fluid slip between cavities (see Figure 6). At high interference, frictional losses and rubber strain increase dramatically, and stator life is degraded due to high strain conditions. Laboratory tests show that stator life is significantly reduced if compression fit After the power section design process has been completed and rotors and stators have been manufactured, proper rotor/stator fit must be selected depending on the drilling conditions. Power section manufacturers offer various rotor and stator sizes to accommodate fit selection for different applications. For example, a standard rotor and stator may be used at a circulating temperature of 150 degrees F while a standard rotor and an oversize (OS) stator is used to achieve the same performance and stator life at 250 degrees F. 7 Oversize stators are also utilized when using drilling fluids that are known to cause elastomer swell. plasticizers. Rubber compound formulations are proprietary to power section manufacturers and are designed to address different applications. Accurate measurements of rotor and stator sizes are important in power section fit selection. Variations in stator sizes of as little as 0.005-0.010 inches can result in significant changes in performance and stator life. Accurate measurement of stator profile size and shape is extremely difficult because: 1) there are size changes with variations in ambient temperature and humidity; 2) the internal geometry of the stator is complex; 3) the elastomer flexes during measurement; and 4) measurement techniques vary. Most manufacturers of power sections provide rotor and stator dimensions so that the operators can match the rotor and stator to achieve the desired fit for the particular application. The majority of stator elastomer properties are determined by the base polymer used in the compound. All nitrile polymers are prepared with varying ratios of ACN. The amount of oil and solvent resistance is based on the ACN content of the polymer. Compounds with 25 to 35 percent ACN content are “medium”, and compounds with 35 to 50 percent ACN are known as “high” ACN compounds. Hydrogenated nitriles (HNBR) are produced by introducing hydrogen to dissolved nitrile elastomers to improve its physical properties. The HNBR properties that are most relevant to power section stators are high tensile strength, high modulus retention at elevated temperatures, high hot tear resistance, improved oil and solvent resistance over NBRs, and heat resistance. The hydrogenation level of an HNBR varies from 80 to 99 percent. HNBRs with 90 percent or higher hydrogenation are sometimes referred to as Highly Saturated Nitriles or HSN. Operating Conditions Running a power section at or below maximum recommended pressure is the primary operational consideration that must be made to maximize stator life. Excessive differential pressure during drilling causes extreme deformation of the stator lobes resulting in premature mechanical failures. Consideration must also be made during drilling operations for rotor speed. As shown in Figure 7, the differential pressure rating for a power section decreases as rotor speed (flow rate) increases. The reason power section pressure differential is derated with increasing rotor speed is to offset the effect of increased rubber strain rates. If the maximum pressure rating is not derated at high rotor speed, stator life will be reduced. A stator rubber compound is designed for different drilling applications. Typically, HSNs are used for high temperature applications and high ACN compounds are used for applications with more aromatic oil-based drilling fluids. Compound design will determine rubber properties such as tensile strength, hysteresis heat build-up, fatigue life, and modulus retention all of which are critical to a power section’s operation and life. Elastomers Power section stators are commonly made with nitriles (NBR) because of their excellent physical properties and oil resistance. Nitrile rubbers (NBR) are manufactured by copolymerization of butadiene with acrylonitrile (ACN). Typical stator rubber compound consists of a nitrile base polymer, reinforcing materials, curatives, accelerators, and ANALYTICAL MODELLING The following section describes a method for predicting stator life under various operational conditions. The results may be used as a guideline to maximize stator life. Analytical technique for stator life prediction 8 To conduct FEA, geometrical and thermal boundary conditions must be simulated. The structural boundary conditions imposed on the stator elastomer are compression fit between the rotor and stator, hydraulic pressure across the stator lobes from the drilling fluid, and elastomer-to-tube bond. Radial forces caused by the eccentric motion of the rotor can be ignored for smaller power sections. A non-linear finite element analysis (FEA) approach can be used to predict the elastomer strain levels of a typical power section with various interference fits, at different operational and down-hole conditions, and for different rotor positions within the stator. The calculated strain state can then be utilized as input for predicting hysteresis heat buildup within the elastomer. Earlier work (Delpassand, 1995) describes the two-part analysis used to calculate heat build-up within stator elastomers. Operating Conditions Iterations The thermal boundary conditions on the stator are forced convection between the drilling fluid and the internal surfaces of the stator and the tube outside wall. Hysteresis heat input to the elastomer is calculated using Equation 4. Design Parameters Elastomer Strain and Strain Rate Hysteresis Heat Buildup Results The following section provides an example of the stator life prediction method described above. Table II lists the selected operating conditions for the analysis. Iterations Table II. Example Operating Conditions. Mechanical Strain and Stress PARAMETER Elastomer Ambient Compression Fit [in] Circulating Temp [degrees F] Rotor Speed [rpm] Differential Pressure per Stage [psi] Laboratory Data Empirical Life Prediction Figure 14. Life Prediction Analysis Flow Chart. Next, empirical data may be employed to determine the physical property reduction of an elastomer as temperature increases. Finally, an estimate of stator life can be made based on the stress and strain of the elastomer at the temperature generated within the center of the stator lobes. Typical Nitrile 0.010 150 250 125 Figure 15 illustrates the predicted strain state in the elastomer of a 5-lobe stator at the down-hole operating conditions in Table II and with the rotor in the top dead center (TDC) position. For the purpose of analysis, the rotor position which resulted in the highest strain levels was utilized in heat generation predictions. At the strain levels encountered in the stator elastomer at down-hole conditions, the material properties are non-linear. This is shown in Delpassand (1995). Therefore, use of non-linear elastomer properties as determined through laboratory testing is important in order to achieve accurate results. 9 temperature within the center of the stator lobes is 30 degrees higher than the circulating temperature. High strain region where fatigue cracks typically form. STRAIN ENERGY (KPSI) Figure 15. The foregoing figures illustrate the effect of design and operating conditions on the heat generation within the elastomer of a stator. Figure 17 shows the strain-energy capability of a typical nitrile as a function of elastomer temperature. Strain energy is defined as the area under the rubber stress-strain curve. Strain State with Rotor in TDC Position. Lighter Sections Show Higher Strain. 500 Nitrile 400 HNBR 300 200 100 0 150 200 250 300 TEMPERATURE (F) Figure 17. Finally, knowledge of elastomer strain energy reduction due to temperature can be correlated to stator life. Table III shows an example of stator life prediction data for a 6.75” diameter 4:5 lobe power section. In the cases selected, FEA was used to predict the rubber strain and temperature build-up at various circulating temperatures, pressures per stage, and rotor speeds. The predicted maximum stator temperature was then used in conjunction with Figure 17 to determine the rubber strain energy. Finally, the results were correlated with stator life test data collected under the first set of conditions in Table III. The analysis does not include the impact of drilling fluid compatibility or any other specific operating conditions. Elastomer deflection due to compression. Figure 16. Elastomer Strain Energy Capability. Elastomer Deflection with Rotor Position 15degrees from TDC. Figure 16 shows the rubber deflection and strain at the above conditions but with the rotor positioned 15 degrees from TDC. Figure 11 illustrates the predicted temperature distribution within the stator elastomer at the selected conditions. In the example given, the 10 Table III. Life Prediction For 6.75” 4:5 Lobe. Circulating Pressure Temperature per Stage (F) (PSI) 150 100 200 200 200 100 250 100 Rotor Speed (RPM) 400 400 600 400 Maximum Normalized Stator Rubber Temp (F) Strain 238 1 344 2.3 332 1.2 338 1.3 Rubber Strain Energy (KPSI) 125 49 52 51 incompatibility, or high temperature. Mechanical failures occur when the stator elastomer is overloaded beyond its stress and strain levels. Excessive pressures, repeated stalls, or too much compression between rotor and stator result in a mechanical failure. Fatigue failures occur when elastomer strains are above critical limits and the stator lobes are subject to high cyclic loading. Cracks due to fatigue are often initiated in the transition between the crests and valleys of the stator lobes and lead to stator failure. Some of the chemicals and oils used in drilling fluids change the physical properties of the stator elastomers. Weakening of the rubber combined with a change in the compression fit due to shrinkage or swell will accelerate stator failure. High temperature is one of the most important parameters leading to a power section stator failure. High elastomer temperatures are due to down-hole conditions, hysteresis heat build-up, or the combination of both. At elevated temperatures, elastomer properties are degraded and all failure modes are accelerated. Stator Life Normalized Estimates (hours) Stator Life 1 500 0.17 87 0.33 167 0.31 154 The figures 18 and 19 illustrate a few of the test results recently obtained in the laboratory. The figures show the effect of rotor speed and differential pressure on heat build-up within the elastomer. ELASTOMER TEMP (F) 120 4:5 LOBE 110 200 psi 100 100 psi 50 psi 90 80 70 0 psi 60 0 200 400 600 800 ROTOR SPEED (RPM) 1000 In order to maximize stator life, compression fit between the rotor and stator must be selected for the down-hole conditions. In addition, power section differential pressure should be reduced as rotor speed is increased to maintain stator life. Finally, the stator elastomer must be carefully selected to insure compatibility with the drilling fluid. Figure 18. Heat Generation Due to Rotor Speed. STATOR TEMP INCREASE (F) 120 100 7:8 LOBE, 450 GPM 80 60 40 20 TEST DATA REFERENCES Delpassand, Majid, 1995, “Mud Motor Stator Temperature Analysis Technique”, ASME Drilling Technology, Book No. H00920. 0 0 100 200 300 400 500 600 700 800 DIFFERENTIAL PRESSURE (PSI) Figure 19. Heat Generation Due to Differential Pressure. CONCLUSIONS Power section stators typically fail due to high mechanical loading, fatigue, drilling fluid 11
Report "Paper - Stator Life of a Positive Displacement Down-hole Drilling Motor - Por Majid s. Delpassand r&m Energy Systems"