J. Ed AkinRice University

HoustonN. Roland Dove, Stephen K. SmithVortexx Group Inc.

Bellaire, Tex.Lee M. SmithSecurity DBS

Houston

*New developments in the geometric design of fluted drill-bit nozzles increase penetration rates while extending bit life.*

Drillers can easily orient this fluted nozzle by aligning the arrow in the desired direction, using a common spark-plug wrench. For PDC bits, the arrow is typically oriented parallel to the nearest blade (Fig. 3).

This design retains the noncircular, interior-transition surface of prior nozzles, including a fluted channel and sharp interior edges. However, the nozzles now terminate in a circular exit area that is offset to the edge of the nozzle (Fig. 1 [59,793 bytes]).

The fluid outflow from the new fluted nozzle shows that:

- Pressure varies with location over the outlet area.
- Shear stresses vary with location over the outlet.
- The velocity vector varies in both its magnitude and direction over the outlet.
- The outlet flow has angular momentum with respect to the inlet's one-dimensional (1D) flow axis.

- A constant outlet pressure
- Constant parallel velocity vectors
- No angular momentum
- No consideration of the shear stresses.

### Initial design

Initial studies concerning asymmetric nozzles described several novel hydraulics aspects of three-dimensional (3D) flow using fluted nozzles developed by Vortexx Group Inc. (OGJ, July 8, 1996, p. 42).These nozzles produced regions of both positive and negative pressure on a surface as the fluid flow through the nozzle impinged on the surface. This behavior was quite different from the standard circular axisymmetric nozzle, which produced only regions of positive impingement pressure.

These studies resulted in some promising laboratory and field-drilling comparisons for both polycrystalline diamond compact (PDC) and roller cone rock bits (RCB), with and without the fluted nozzles.

The main 3D hydraulic feature of the fluted jets noted at that time was the way the asymmetric-interior, transitional geometry of the jets caused a suction, or less than hydrostatic pressure, to be developed on selected regions of the impingement surface.

This "negative-pressure" aspect of the fluted jets was explained and demonstrated with experimental tank tests in water. It was also noted that computational fluid dynamics studies verified these new hydraulic phenomena, forming the basis for the first patent issued on this technology.

It was initially speculated that the negative impingement pressure was the main reason for improved bit performance as standard jets were replaced with the fluted jets for both PDC and RCB applications.

It was noted, however, that experimental measurements showed the local entrainment of recirculating fluids increased by a factor of four, which in turn, may help cool the drill bit while assisting in cuttings removal.

Since the time of these developments, additional studies have proved that fluted nozzles provide additional hydraulic benefits as a result of 3D flow patterns.

### Proof of concept

The negative-pressure fluted nozzles can be constructed from more than one geometrical design including heart-shaped outlets.A number of proof-of-concept field comparisons were carried out at eight different well sites in central Texas, using ROP comparisons from a number of reliable offset well logs (OGJ, July 8, 1996, p. 46). In that study, PDC bits with fluted nozzles were run on four different manufacturer's bit platforms and compared with the results for the same bits fitted with standard jets.

A total of 61 runs with standard jets were compared to 27 runs with the fluted jets. The increase in ROP at the eight sites ranged from a high of 44% to a low of 11%, with a weighted average of 28% (Fig. 2 [46,057 bytes]). Higher maximum increases were recorded for a small number of RCB runs in Canada.^{1}

Some bit designs, however, did not clearly obtain an ROP increase. This could have been caused by the original hydraulic design or by the orientation of the valentine-shaped asymmetric nozzle outlet as placed relative to the PDC blade or roller cone locations.

After the completion of this proof-of-concept phase, the design went into regular production and was used in locations all over the world. Careful gathering of offset data was discontinued once the fluted nozzles became a commonly used product.

From field reports, however, it was noted that the bi-lobed shape of the outlet in the original design occasionally made it awkward for field personnel to envision the best orientation of the fluted nozzles (Fig. 3).

Thus, after about a year of regular use, engineers began studying three new approaches towards redesigning the fluted nozzle:

- Evaluate alternative fluted-interior geometries needed to improve hydraulics and to simplify nozzle orientations in the field.
- Model additional computational fluid dynamics and analytic fluid mechanics studies concerning asymmetric nozzle flows.
- Continue work with manufacturers in the study of the general hydraulics behavior as related to bit design.

### Field orientation

An important consideration in utilizing a nonaxisymmetric nozzle is that its primary direction of flow must be optimally oriented relative to the bit blades or cones. Improper orientation can negate the benefits of the fluted nozzle.To overcome early confusion about field orientation, each fluted nozzle is now manufactured with an arrow etched on its top surface, indicating the flow direction. In addition, the bit manufacturer usually provides a top view of the bit showing the suggested orientation for each nozzle.

While most bits have the fluted nozzles installed and oriented in the factory, it is not unusual to have them installed in the field. This allows for on site considerations including the use of various orifice sizes to enhance cross flows. One method currently used by Security DBS, and developed in conjunction with Rogers Tool Works, allows the nozzle to be orientated in 15° increments.

This is a two-piece system (patent pending) comprised of a carbide nozzle body and compression fit retainer. The nozzle retainer portion is a threaded steel device with 24 flats milled on the interior diameter, matching up with the 8 flats on the carbide nozzle body. There is a longitudinal slit in the retainer body that allows a spanner wrench to be used to click the retainer around the carbide body.

### Insights

The important flow differences between the updated fluted and standard nozzles are shown in Fig. 4 [61,458 bytes]. While the flow through the fluted jets is fully 3D, it is possible to gain some insight into the flow differences when averaging the velocity over the interior cross-sectional area and then comparing those averages to the classic 1D circular jets for the same flow rate, inlet area, and outlet area.Of course, they must have the same inlet and outlet average velocities as confirmed by the nondimensional velocity-vs.-position graph in Fig. 5 [64,387 bytes], where z/L denotes the nondimensional length along the nozzle. From this figure, it can be seen that the average velocities and velocity gradients of the two designs differ, especially at the outlet.

To emphasize the differences, the corresponding nondimensional velocity gradients vs. position is shown in Fig. 6 [51,023 bytes]. This figure shows that the fluted jet is designed in part to maximize the velocity gradient at the outlet.

The shear stresses are defined by the velocity gradient. Thus, this creates high shear stresses at the outlet flow area of the fluted nozzles. The increased shear stresses are important for 3D calculations of hydraulic power, but drop out of a 1D flow approximation.

Another fluid-mechanics consideration is that turbulent energy and turbulent momentum equations both involve the product of the velocity and gradient. This product is zero at the standard nozzle outlet but is quite large for the fluted design. Thus, the fluid exiting the fluted design has more turbulent energy and turbulent momentum.

### Enhanced performance

The new design has been in widespread use around the world for more than a year. To aid in assessing the improved ROP performance of this design, an extensive search of site records was carried out to locate off-set runs for PDC bits with the same IADC code, equivalent formation runs, and runs made with and without the new fluted jets.Fig. 7 [54,197 bytes] shows the comparison for 81/2-in. PDC bits where five standard jet runs and one fluted jet run were made through the Belagim formation in Egypt. Penetration rates of 12.1 m/hr were achieved while the average for the standard nozzles made 4.9 m/hr.

For the Rabbi field in Gabon, there were two primary formation segments that were also drilled with 81/2-in. PDC bits. In the limestone, a 19.3-m/hr fluted-nozzle run was compared to three standard runs that averaged 9.7 m/hr (Fig. 8 [58,745 bytes]).

This represented a 99% increase in ROP, but dropped to about 44% for the salt/shale formation where two fluted runs averaged 21.27 m/hr as compared to eight standard jet runs that averaged 14.73 m/hr.

For a pair of 81/2-in. PDC bit runs in the Mungarong shale formation of the Gorgon 6 field, the standard jet run made 37.9 m/hr while the fluted jet run made 66.3 m/hr.

Runs with 121/4-in. PDC bits were compared in the Asab field in Abu-Dhabi. For rotating operations, two fluted jet runs averaged 19.23 m/hr while six standard jet runs recorded a weighted average of 12.43 m/hr.

Also in drilling-motor operations in a field where nine standard jet runs averaged 17.05 m/hr, one fluted jet run made 23.27 m/hr.

While the statistical base for these comparisons is not as strong as that used in the original proof-of-concept tests (Fig. 2), they clearly show that the current design exceeds the 28% average ROP increase found in the original design as compared with standard nozzles.

Of course, these results will clearly vary with lithology and other factors. Thus, it is not practical to predict the performance increase in every case although randomly selected comparisons show that a significant ROP increase can be expected.

### Bit wear

Penetration rates are not the only consideration of importance for nozzle selection. The wear state of the bit is also important, although somewhat subjective. Anecdotal comments and supporting photos suggest that the flows associated with the fluted jets also extend bit life in several formations.The less-than-hydrostatic impingement pressure can clearly contribute to increased penetration rates in some formations. In addition, the large local recirculation flows may remove more cuttings, keep the bit cooler, and reduce balling in order to extend bit life. However, those features alone were not sufficient to explain the increases in ROP found with the initial design.

The initial laboratory drilling tests clearly suggest that there were additional hydraulic aspects of the fluted jet flows that were not yet understood. The redesign studies provided proof that the fluted jets have higher hydraulic impact forces, confirming the suspicion that they significantly increased the hydraulic horse power (hhp) imparted to the exiting fluid.

### Double the power

An important mechanical aspect of drilling hydraulics concerns the level of hhp that a nozzle imparts to its fluid, and thus on to the surface. The definition of the power (P) of a force vector (F) at a given point is the scalar product of the force vector and the velocity vector (V) of the point.The magnitude of the (scalar) power is the product of the force and velocity times the cosine of the angle (ang), between their two directions as shown in Equation 1 (see Equation Box [66,197 bytes]).

Thus, power is zero when the velocity and force vectors are perpendicular (ang = 90°), and when V = 0, occurring for a viscous fluid at a fixed solid wall. Otherwise, a moving force produces power. At a point in a fluid moving with a velocity (V), a differential force (dF) is present and causes a differential power contribution as shown in Equation 2.

The fluid force (dF) comes from the pressure and shear stresses at a point acting over a differential area (dA). To obtain the total power (P) imparted to the fluid flowing through any nozzle, it is necessary to integrate the differential power (dP) over the surface of the nozzle control volume.

For a nozzle control volume, it is only necessary to consider its inlet and outlet areas when calculating the power because the fluid at the nozzle wall has zero velocity (V_{wall} = 0) and produces no power.

Consider a cross-section of the nozzle (of area A_{n}) that is perpendicular to the flow. The volumetric flow rate, Q, is related to the velocity by Q = A_{n} * V_{n}, where V_{n} is the component of the velocity (V) that is perpendicular to the cross-section.

For a steady flow in a standard circular section, the flow is accurately described by the classical 1D theory found in beginning engineering courses and hydraulics references.^{3 4} As noted above and in Fig. 4, the 1D flow has a constant velocity, V = V_{n}, a constant pressure (p), and a constant shear stress (T).

The 1D theory makes it easy to calculate the power because the value of any constant iterated over an area is simply the area times the constant. In the 1D case, the force (dF) in the direction of the fluid flow is simply caused by the constant pressure (dF = p dA).

Thus, the power applied at such a section can be found in Equation 3, which is simply the pressure times the flow rate. It is important to note that in the 1D theory, the shear stress (T) does not appear in the power calculations because it is tangential to the plane of the cross-sectional area and thus perpendicular to the total velocity, V = V_{n}.

In other words, the ang = 90° between V and the shear stress part of dF prevents the shear stress from contributing to the hydraulic power of a standard circular jet. This special case does not occur in the fluted nozzle.

For a standard circular nozzle defined by the 1D theory, the total power imparted to the fluid by the nozzle (P_{std}) is found as the difference in the power at the outlet and inlet sections from Equation 3. This results in the common expression for hydraulic power as shown in Equation 4 where the subscripts 1 and 2 denote the inlet and outlet sections, respectively.

Thus, the net power for a standard jet is simply the pressure drop through the nozzle, (p2 - p1) times the flow rate (Q).^{2 3} For a fluted jet with the same flow rate and pressure drop, a higher hhp (P_{vtx}) is created in part by the inclined velocity vectors combining with the increased shear stresses.

Still, the pressure drop and flow rate, combined with the geometrical shape of the fluted jet, allow the 3D fluted jet power to be obtained by multiplying the classical 1D definition of hydraulic power by a coefficient (C_{v}). This accounts for the 3D nature of its outlet flows as shown in Equation 5 for C_{v} > 1.

Typical values of C_{v} for fluted jets used in drilling applications vary with nozzle size and interior geometry. For the current design shown in Fig. 1, the correction factor has been shown to range from about 1.8 in small sizes (No. 7) to about 2.1 in large sizes (No. 16).^{6}

For fluted nozzles the net power imparted to the fluid is higher because the outlet flow, as shown in Figs. 4-6, is 3D (see Reference 6 for full mathematical details). This causes two velocity components that interact with the shear stress to create additional power not present in the standard nozzle.

The angular momentum at the interior edges causes the new velocity components to become perpendicular to the plane of Fig. 4. In addition, the shear stress magnitude becomes higher because of the high exit velocity gradients shown in Fig. 6.

This means that the shear stresses add significant power to the fluid in the fluted jets, but do not do so in standard jets. Although the inlet power is still given by Equation 3, all of the 3D flow quantities vary significantly across the fluted jet outlet.

This requires an integration of the outlet flow quantities over the outlet area to obtain the outlet power.

While the fluted jet outlet power cannot be computed exactly in closed form because of the turbulent 3D nature of its flow, the result can be calculated by at least two completely independent methods.

The most accurate result for a specific fluted geometry is obtained by calculating the fluid dynamics for the outlet flow quantities,^{5} then numerically integrating those quantities over the outlet area to obtain the outlet power. Those calculations yielded the range in C_{v} cited above.

An independent estimate of C_{v} has been given by Huang where the analogy between turbulent fluid flow and nonlinear electrical power systems was used to bound the coefficient (C_{v}).^{5} In general, Huang shows that the range is 2 < C_{v} < 3 for the same outflow area.

Correcting for the larger area of the fluted, his estimates agree with the computational fluid dynamic results of 1.8 < C_{v} < 2.1.^{6} Therefore, it can be proven that the fluted jets will typically double the hhp imparted to the mud, doubling the hhp/sq in. as computed from the area of the hole.

### Hydraulic impact force

A secondary mechanical aspect of drilling hydraulics concerns the impact force applied perpendicular to a rigid surface on which a jet flow impinges. Recall that the impact force is developed by writing Newton's second law, F = d(m V)/dt, in the Impulse-Momentum Law form, which is the integral of F dt = d(m V).In the above equation, F is the force vector, V the velocity vector, m is point mass, t is time, m V is the momentum vector, F dt is the impulse force vector, and d denotes differentiation.

For a steady fluid flow from a jet, an impact force (I = F) develops an impulse as shown in Equation 6 where the subscripts 1 and 2 now denote reference values before and after the jet impacts the wall, respectively.

The usual assumption is that at impact the fluid stagnates so V_{2} = 0. Rewriting this single particle impulse-momentum model one obtains Equation 7 where the last term in brackets is the mass flow rate.

Thus, a general statement is that the impact-force vector (I) created from a fluid particle has a magnitude that is the product of the mass flow rate and the velocity component before impact-perpendicular to the impingement surface. Of course, its direction is opposite to that of the velocity vector.

The total value of the impact force must be summed, or integrated over all particles in the jet flow. The mass flow rate is the same for both the standard and fluted nozzles and is given by the mud density (P) times its volume flow rate (Q) as shown in Equation 8, where the outlet area of the nozzle is A_{n} and the flow perpendicular to that area is V_{n}. This yields a general impulse force magnitude as shown in Equation 9.

This is the form as presented in Reference 3. For the standard nozzle, unlike the fluted nozzles, the perpendicular exit velocity (V_{n}) is also the total velocity where V_{1} = V_{n} = Q/An. Therefore, for 1D flow, we obtain common result as can be found in Equation 10.^{4}

This is used to create a set of standard nozzle jet impact-force coefficients (C_{s}) that can be tabulated for various nozzle areas and flow rates such that the impact force can be obtained from Equation 11.

See Table 8 of Reference 4 for jet impact-force coefficients (C_{s}) for typical values of Q and A_{n}. The impact force from the fluted jets (I_{f}), can be computed in the same way by including an extra correction coefficient (C_{f}) to account for its 3D flow as shown in Equation 12 where C_{f} > 1.

This means that the fluted jet impact force is always larger than that for the standard jet. From Fig. 9 [50,433 bytes], it is easy to see that the fluted-jet correction C_{f} is slightly greater than one (a typical value is 1.1), but one must again employ computational fluid dynamics to obtain a precise value for the correction.

For the fluted nozzles the exiting flow (V_{1}) is 3D, not 1D, varying at every point in the exit area. Since it is 3D, it has two tangential components in the exit area as well as one perpendicular to the exit area.

To have the same flow rate, the fluted jet has the same integral average normal component (V_{n avg}) as the standard 1D jet. That is V_{n avg} = V_{n}.

However, the fluted jet also has an average tangential velocity component (V_{t avg}) that is not present in the standard jet. Thus, we can see that the resultant velocity vector V_{1} used in the impact-force calculation is the vector sum as shown in Equation 13. This has a magnitude which is greater than the magnitude of V_{n} = V_{n avg}, unless the tangential component V_{t} avg is zero, which only occurs in the standard jet.

We can conclude that the fluted jets will slightly increase the hydraulic impact force, say by 10%, even though they can be proven to typically double the hydraulic horsepower imparted to the mud.

### References

- Akin, J.E., Dove, N.R., and Smith, S.K., "New Nozzle Hydraulics Increase ROP for PDC and Rock Bits," SPE/IADC paper 37578, presented at the SPE/IADC Drilling Conference, Amsterdam, Mar. 4-6, 1997.
- Hughes Tool Co., "Hughes Practical Hydraulics," 1976.
- Moore, P.L., Drilling Practices Manual, Hydraulics in Rotary Drilling, Petroleum Publishing Co., Tulsa, 1976, Chapter 10.
- Akin, J.E., Finite Elements for Analysis and Design: Computational Fluid Dynamics, Academic Press, London, 1994, Chapter 18.
- Huang, H.I., "Turbulent 3D Hydraulic Power Electrical Analogy," Modern East-West Co., Beijing, private communication, 1998.
- Akin, J.E., "Increased HSI from Vortexx Nozzles," The Brief, July 1998, pp. 4-7.

### The Authors

J. Ed Akinis a professor of both mechanical engineering and computational and applied mathematics at Rice University in Houston. For more than 25 years, he has worked in computational mechanics and computer-aided design. He serves as a consultant in finite element analysis and computational fluid dynamics. Akin is a fellow of the American Society of Mechanical Engineers and a member of the Society of Petroleum Engineers and the American Society of Civil Engineers. He is a registered professional engineer in Texas and Tennessee. Akin holds a BS in civil engineering and an MS in engineering mechanics from Tennessee Tech University and a PhD in engineering mechanics from Virginia Polytechnic Institute and State University.

N. Roland Doveis a consulting drilling engineer and cofounder of Vortexx Group Inc. in Bellaire, Tex. Currently, he is engaged with BP-Amoco plc in Egypt. His prior experience includes work with major drilling contractors, independent operators, and directional drilling companies. Dove holds a BS in mechanical engineering from Texas Tech University.

Stephen K. Smithis a founder and president of Vortexx Group Inc. in Bellaire, Tex. He has more than 24 years' experience as a consulting drilling engineer on domestic and international projects. Smith's past work includes development of new technology for the directional drilling industry, management of drilling operations for a mid-sized drilling contractor, and projects in Central Asia, Southeast Asia, Former Soviet Union, and South America. He holds a BS in petroleum engineering from the University of Texas.

Lee M. Smithis business development manager for fixed cutter and roller cone drill bits for Security DBS, developing and implementing strategic marketing plans for new product lines. He has more than 17 years' experience, including international assignments in a number of oil field management and engineering positions. Smith has specific experience in MWD, directional drilling, and bit-application technology. He holds a BS in geology from the University of Utah and an MBA from Oklahoma City University. In addition, Smith has performed post-graduate work at Harvard Business School and the University of Houston.

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