Evaluation of Jet-Bit Pressure Losses
- Tommy M. Warren (Amoco Production Co.)
- Document ID
- Society of Petroleum Engineers
- SPE Drilling Engineering
- Publication Date
- December 1989
- Document Type
- Journal Paper
- 335 - 340
- 1989. Society of Petroleum Engineers
- 1.6 Drilling Operations, 5.2.2 Fluid Modeling, Equations of State, 4.2 Pipelines, Flowlines and Risers, 4.3.4 Scale, 4.1.5 Processing Equipment, 1.5 Drill Bits, 1.6.1 Drilling Operation Management, 4.1.2 Separation and Treating, 1.5.4 Bit hydraulics, 1.11.2 Drilling Fluid Selection and Formulation (Chemistry, Properties)
- 0 in the last 30 days
- 519 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
An experimental and theoretical study was conducted to resolve discrepancies between observed and calculated pressure losses for fluids flowing through the nozzles of jet bits. The use of a nozzle discharge coefficient of 0.95, which is commonly used for roller-cone bits, results in the calculated pressure drop being up to 30% more than actually occurs, with the average error being 14.7% for 770 data points measured with nine different fluids. A relationship is presented to calculate the discharge coefficient as a function of borehole pressure, nozzle size, and mud density, which reduces the mean absolute error to 3 % for these data points. Simply increasing the discharge coefficient to a constant value of 1.02 results in reducing the error to 4.1 % without using the more complicated relationship.
The pressure loss through the nozzles of a jet bit is a very significant part of the total circulating pressure on a rig. Kendall and Goins1 indicated that a bit pressure drop of 59 to 66 % of the total pump pressure is needed for the most effective use of the pump horsepower for cleaning the bit (assuming that this pressure drop results in a flow rate sufficient to exceed the minimum annular velocity). These percentages are based on maximizing the impact force and the bit hydraulic horsepower. It is not unusual for the bit pressure loss to be greater than 60% of the total pump pressure at shallow depths, but the percentage typically decreases as well depth increases.
Bit pressure losses are usually calculated with Eq. 1:
The nozzle discharge coefficient, Kd, in this equation is normally assumed to be 0.95, and thus the pressure loss is simply a function of mud density, ?, flow rate, q, and nozzle diameter, dn. Refs. 2 through 6 indicated that the discharge coefficient may be dependent upon the nozzle geometry, fluid density, jet velocity, cavitation number, and fluid composition.
Roller-cone bit pressures were observed to be lower than those calculated with Eq. 1 for drilling tests conducted at Amoco over several years. In 1983, Ramsey et al.2,7 presented the results of a similar observation that indicated that the bit pressure losses were 10 to 25 % lower than expected. They concluded that the smaller total bit pressure loss was caused by "pressure recovery" and that the pressure-recovery phenomenon could affect the calculation of the equivalent circulating density (ECD). Cook et al.8 reported field measurements of the bit pressure drop that were lower than those calculated and suggested that the inaccuracy could be caused by a lower-than-expected pump efficiency. Because of the abundant evidence that the conventional method for calculating bit pressure losses is inaccurate, a study was conducted to provide a more accurate method of calculating them.
Background of Bit Pressure-Loss Equation
Eq. 1 is derived by applying Bernoulli's equation between a point upstream of a nozzle and a point at the nozzle throat. A discharge coefficient, typically 0.95, is added to the equation primarily to account for the nonideal behavior of the fluid.
Most literature that includes a reference to the discharge coefficient for bits refers to Eckel and Bielstein3,4 and implies that they recommend the use of a value of 0.95. Eckel and Bielstein present the results of an experimental study aimed at designing a more efficient nozzle for rock bits at a time (1953) when "jets" were first being used to replace open-flow ports. They tested a variety of nozzle entrance and exit geometries and identified a particular entrance geometry that consistently gave discharge coefficients greater than 0.98. In some cases the discharge coefficient was greater than 1.0. Their work made a significant contribution to the advancement of bit hydraulic designs, but is of little help in determining the best value to use for the discharge coefficient with today's nozzle designs. In fact, the recommendation to use a discharge coefficient of 0.95 is not found in Ref. 3 or 4.
Bit Pressure Recovery
Fig. 1 is a schematic of the flow through and around a bit. The bit pressure drop is defined as the pressure in the bore at the top of the bit, pb, minus the pressure in the annulus at the top of the bit, pa. It is not apparent from an examination of Fig. 1 that the pressure loss can be represented totally by the change in pressure from the bit bore to the nozzle throat, as assumed in the previous discussion of the pressure-loss equation. There may be additional pressure changes associated with viscous frictional losses around the bit, losses associated with the 180° change in flow direction under the bit, and pressure increases caused by fluid velocity decreases downstream of the nozzle.
The pressure loss around the bit can be determined only by experimental measurement because no reliable analytical methods are available to calculate the pressure drop from pa to pb. Eq. 1 predicts only the pressure drop that results from accelerating the fluid through the nozzle throat. This prediction can be improved somewhat by including an abrupt expansion downstream of the nozzle. This method is only slightly better than the previous method, but it provides for an estimate of the maximum possible value of "pressure recovery."
Bernoulli's equation can be applied from Point 1 to Point 2 in Fig. 1.
|File Size||474 KB||Number of Pages||6|