Frank V. De Lucia
Security Downhole Motor Services
Houston

A system analysis of the bit, positive-displacement motor, and hydraulics helps improve the efficiency of downhole-motor guidance systems, even for routine drilling applications.

The bit and motor system must operate with ideal hydraulics for efficient drilling.

The poor state of the drilling industry has forced drillers to examine drilling performance more critically, not only in terms of cost per foot, but also with the costs amortized over the life of the well. Thus, drilling contractors and operators should place more emphasis on optimizing downhole-motor performance as part of ordinary drilling plans.

For many years, the drilling industry has used a trial-and-error method to determine which type of bit drills best with which particular downhole motor. To increase penetration rates and improve drilling efficiency, however, drillers must understand how the mechanical and hydraulic design variables of a bit affect downhole-motor performance.

BIT DESIGN

A model was developed to evaluate field data and investigate bit design alternatives. It describes the action of a bit in terms of equivalent blades, in which each blade makes a series of cuts in a stair-step fashion as the bit makes one revolution.

Fig. 1 is a schematic of the model with the following assumptions:

The bit has a flat bottom.
The number of cutters (F) may vary.
The cutter diameter is round (D).
The width of cut (C) is perpendicular to the center line of the hole.
The blade length (B) is from the center line of the hole to the gauge point.

The cross section of the bit shows enough cutters set along the cutting face to form an equivalent blade (CB).

Each equivalent blade makes a uniform depth of cut (P) from the center line of the hole to the gauge section (Equations 1 and 2).

Fig. 2 shows an expanded view of the gauge section of the hole with the position of each equivalent blade at various times during one revolution. The bit advancement (BA) per revolution is equal to the depth of cut times the number of equivalent blades (Equation 3).

After traveling at a given depth of cut, the cutters reach the section removed by the proceeding equivalent blade and then repeat the process with the bit advancing into the formation. From a practical perspective, the actual bit advancement of the cutters follows a spiral pattern.

Fig. 1 also shows the cutters as they would appear during drilling. The depth of cut can only penetrate the formation if the load applied (W) to each cutter divided by the projected surface area (SA) in contact with the formation exceeds the formation resistance (FR). The formation resistance is given by Equation 4.

To determine the total weight on bit (WOB) applied to the cutters, both the mechanical weight on bit and hydraulic lift must be considered. The bit mechanical and hydraulic characteristics are a function of its design.

HYDRAULIC LIFT

The hydraulic lift component is the sum of the net hydraulic forces acting on the bit face, which in turn, is the sum of the pressure differential or fluid velocity at each point and the exposed area on which it acts.

A true comparison of the drilling performance of two bits must take into account the hydraulic lift. Fig. 3 is a comparison of the hydraulic lift for two different bit designs.

The hydraulic lift of Bit R-1 is three times greater than that for Bit C-1, illustrating the importance of this characteristic. The hydraulic lift of each bit increases exponentially with flow rate. The mechanical WOB required to drill at a given rate of penetration (ROP) is nearly identical for the mechanically similar bits.

If a drilling engineer did not know the hydraulic lift for both bits, he could misinterpret their performances. If the effective hydraulic lift areas are known, however, the variations in hydraulic lift can be accounted for and predicted.

Equations 1-4 can be expressed for any bit diameter, and the true ROP can be calculated from Equation 5. These five equations lead to the following three observations on improving ROP:

If bits with the same number of cutters are compared, the bit with the smallest cutter (D) will drill fastest. Because each cutter has the same area of contact with the formation, this contact occurs at a greater depth of cut for the smallest cutter. As the depth of cut increases, the ROP increases.
If bits with the same size cutters are compared, the bit with the fewest cutters will drill the fastest. Each cutter makes a wider and deeper cut. With a larger equivalent blade (CB) and depth of cut, the ROP should increase.
If bits with an equal number of cutters are compared, the bit with the largest cutters will drill the fastest. The larger cutters will increase the number of equivalent blades, increasing ROP.

Obviously, there are practical limits to which these points can be pursued without adversely affecting bit life.

TOTAL FLOW AREA

After the bit type has been selected based on ROP relationships and on the formation resistance, an appropriate total flow area (TFA) must be selected.

Two theories are commonly used to describe the role of hydraulics in maximizing the ROP: Hydraulic horsepower per square inch is expended at the bit, and the fluid velocity is optimized under the bit.

Both theories are based on the premise that rock cuttings are not completely removed from the hole bottom as they are created by the scraping action of the bit. The cuttings must be lifted from the bottom of the hole by drilling fluids to reduce the amount of regrinding, thus allowing the bit to drill new formation with each revolution.

It is therefore important to flush the cuttings away from the face of the bit by maximizing the fluid-flow rate (Q) through the bit (Equation 6). A good recommended fluid-flow volume (FO) is in the range of 4.5-7.0 gpm/sq in. of hole area, based on the hardness of the formation.

Another goal is to optimize the bit pressure drop (PB), or the hydraulic horsepower (HHP) per square inch of hole area to generate as much turbulence as possible at the bit face.

In Equations 7 and 8, the maximum fluid flow should be used in combination with the largest acceptable bit pressure drop to achieve an acceptable total flow area (TFA) or nozzle size.

Another method of determining the ability of the hydraulic system to clean the bit and cool the cutters is to study the fluid velocity under the bit. Normally, an average fluid velocity is chosen because of the velocity variation over the face of the bit. To obtain an acceptable TFA, in Equations 6 and 9 the maximum fluid flow rate should be used in combination with the largest acceptable average fluid velocity (V).

Fluid velocities under the bit range from 150 to 300 fps in normal drilling operations. In soft formations, large velocities are essential for formation removal and cutter cooling. As drilling becomes more difficult, the fluid velocities decrease.

In soft drilling, the emphasis is on cuttings removal. In hard drilling, the emphasis is on cutter cooling.

MOTOR PERFORMANCE

Recent development work and analysis of field operations have shown that proper balancing of a downhole-motor drilling system is critical for optimum performance. The system should be able to drill directional, horizontal, and long-interval wells with accuracy and control.

Some of the motor-design features to meet these drilling objectives include a sealed bearing assembly, high torque capability, short power-section length, large operating flow ranges, low pressure drop in the power sections, and a surface geometry to minimize contact pressure.

Fig. 4 shows the characteristic hydraulic curves for a positive-displacement downhole motor (PDM). The theoretical performance characteristic of a PDM is studied at a constant fluid discharge. The mud density (S) or viscosity (PV) has little effect on the performance of a positive-displacement motor.

If the motor is running free off bottom as fluid is pumped through it, the pressure across the motor is constant if the bit torque requirements remain constant.

As the bit touches bottom and weight is added, the fluid circulating pressure increases. This increase in pressure is directly proportional to the additional bit weight, or the drilling torque, and is known as the pressure drop across the motor.

As additional weight is added, the standpipe pressure will increase until the operating pressure drop is reached. The operating torque (TO) is reached at this point. The addition of more weight will increase the standpipe pressure and torque until the maximum design pressure drop is exceeded, and then the motor stalls.

The efficiency curve of a downhole motor has a similar shape. The maximum efficiency may correspond to a downhole-motor pressure drop slightly greater than the nominal operating downhole-motor pressure drop.

With a downhole motor, the drilling torque (T) is directly proportional to the pressure increase of the fluid flowing through it (Equation 10).

Additionally, the speed of rotation (N) is directly proportional to the flow rate (Equation 11). This speed remains essentially constant, however, as the torque requirements increase.

Dynamometer tests show less than a 10% reduction in speed from zero torque up to either maximum torque or the torque just before stall occurs.

The fluid flow through the downhole motor creates a downward axial thrust (WT), which can be calculated with Equation 12. During downhole motor drilling, the weight applied to the bit and formation creates an upward thrust.

The thrust bearing assembly supports the difference between the downward axial thrust and the upward thrust (weight on bit) and transmits this load to the body of the downhole motor. The operation of the motor, with regard to weight on bit, is exactly the same as in rotary drilling.

For optimal bearing life, the two forces should be balanced, theoretically providing a zero bearing load. Properly balancing the downhole motor extends the bearing fife and hence the drilling time on bottom.

The resulting downward axial thrust supported by the thrust bearing assembly produces a loss of power because of friction from the rotating and stationary race spinning on the bearings. Thus, the life of the sealed bearing assembly depends on the load on the bearing' which is determined by the drilling conditions, the bit type, and the bit total flow area.

HYDRAULICS

The success of downhole-motor drilling depends largely upon an analysis of the existing system hydraulics and then use of the bit and motor accordingly.

Fig. 5 shows the general relationships used in tuning a downhole motor system to the available rig power. For a drillstring with a standpipe pressure limit, only one flow rate can deliver maximum hydraulic horsepower (ADH) to the lower end of the drillstring.

In Fig. 5, the maximum standpipe pressure is an upper limit imposed for safety or maintenance requirements, but more importantly, it is also the maximum pressure the driller is willing to use.

As a general rule, the drilling fluid annular velocity (AV) should be as high as practical yet low enough to minimize hole washout. The average annular velocity is given by Equation 13.

The critical velocity (VC) of a fluid circulated up the annulus is the velocity at which flow changes from laminar to turbulent. The critical velocity should be calculated for each drill pipe/hole size combination to determine the maximum circulation rate that can be tolerated without reaching harmful turbulent flow conditions (Equation 14).

Equation 15 gives the average stabilizer velocity (SV) for a given flow rate.

DOWNHOLE PRESSURE

The available downhole pressure (ADP) is the difference between the standpipe pressure limits and the system pressure losses (less bit/downhole motor). The available downhole horsepower should peak in the middle of the "window."

The values of available downhole pressure at several different flow rates should be plugged into Equation 16 to determine the available downhole horsepower.

If the peak is not reached, the window must be moved in the direction of increasing available downhole horsepower until the peak is near the center of the window. Changing the downhole motor system configuration will move the window.

The range of useful flow is depicted by the dashed lines in Fig. 5. It is common to give up 5% of the average available downhole horsepower to remain under the limiting conditions, such as return velocity (Equations 13-15).

Thus, the line covers a flow-rate range that will yield at least 95% of maximum available downhole horsepower to downhole equipment. Based on downhole motor performance data (Fig. 4), the preferred flow rate should be selected and a vertical line drawn on the graph. The intersection with the line labeled ADP will yield a working number.

The available downhole motor pressure is defined by establishing the bit pressure drop. This value is either an optimum pressure drop to be imposed on the bit (Equations 6-9), or it is determined for an existing bit in view of the specific flow rate.

Subtracting the bit pressure drop from the available downhole pressure yields the available motor pressure.

To determine the final power-producing pressure from the downhole-motor data available, one must first determine the empty motor losses for the specific flow rate. This value, often called frictional losses, is the pressure loss in the downhole motor if no power-producing elements are present.

Subtracting the empty downhole motor losses from the available motor pressure yields the final power producing pressure. In Fig. 4, the intersection of the torque line with downhole pressure line indicates this pressure loss.

ACKNOWLEDGMENT

The author wishes to thank Dresser Industries Inc. for permission to publish this article.

Copyright 1993 Oil & Gas Journal. All Rights Reserved.

SYSTEM ANALYSIS IMPROVES DOWNHOLE MOTOR PERFORMANCE

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