## Flow Characteristics

A comparison is made of the flow characteristics of mud drilling and air drilling in an example deep well. A schematic of this example well is shown in Figure 115. The well is cased from the surface to 7,000 ft with API 8 5/8 inch diameter, 28.00 lb/ft nominal, casing. The well has been drilled out of the casing shoe with a 7 7/8 inch diameter drill bit. The comparison is made for drilling at 10,000 ft. The drill string in the example well is made up of (bottom to top), 7 7/8 inch diameter drill bit, ~ 500 ft of 6 3/4 inch outside diameter by 2 13/16 inch inside diameter drill collars, and ~ 9,500 ft of API 4 1/2 inch diameter, 16.60 lb/ft nominal, EU-S135, NC 50, drill pipe.

Figure 1-15: Comparison example well and drill string.

The mud drilling hydraulics calculations are carried out assuming the drilling mud weight is 10 lb/gal (75 lb/ft ), the Bingham mud yield is 10 lb/100 ft2, and the plastic viscosity is 30 centipose. The drill bit is assumed to have three 13/32 inch diameter nozzles and the drilling mud circulation flow rate is 300 gals/minute. Figure 1-16 shows the plots of the pressures in the incompressible drilling mud as a function of depth. In the figure is a plot of the pressure inside the drill string. The pressure is approximately 1,400 psig at injection and 6,000 psig at the bottom of the inside of the drill string just above the bit nozzles. Also in the figure is a plot of the pressure in the annulus. The pressure is approximately 5,440 psig at the bottom of the annulus just below the bit nozzles and 0 psig at the top of the annulus at the surface.

The pressures in Figure 1-16 reflects the hydrostatic weight of the column of drilling mud and the resistance to fluid flow from the inside surfaces of the drill string and the surfaces of the annulus. This resistance to flow results in pressure losses due to friction. The total losses due to friction are the sum of pipe wall, openhole wall, and drill bit orifice resistance to flow. This mud drilling example shows a drilling string design which has a open orifice or large diameter nozzle openings in the drill bit. This is reflected by the approximate 700 psi loss through the drill bit. Smaller diameter nozzles would yield higher pressure losses across the drill bit and higher injection pressures at the surface.

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Figure 1-16: Mud drilling pressures versus depth.

The air drilling calculations are carried out assuming the drilling operation is at sea level. There are two compressors capable of 1,200 scfm each, so the total volumetric flow rate to the drill string is 2,400 scfm. The drill bit is assumed to have three open orifices (~0.80 inches diameter). Figure 1-17 shows the plots of the pressures in the compressible air as a function of depth. In the figure is a plot of the pressure inside the drill string. The pressure is approximately 260 psia at injection and 270 psia at the bottom of the inside of the drill string just above the bit orifices. Also in the figure is a plot of the pressure in the annulus. The pressure is approximately 260 psia at the bottom of the annulus just below the bit orifices and 14.7 psia at the end of the blooey line at the surface (top of the annulus).

As in the mud drilling example, the pressures in Figure 1-17 reflects the hydrostatic weight of the column of compressed air and the resistance to air flow from the inside surfaces of the drill string and the surfaces of the annulus. This resistance to flow results in pressure losses due to friction. In this example the fluid is compressible. Considering the flow inside the drill string, the hydrostatic weight of the column dominates the flow (relative to friction losses) and this results in the injection pressure at the surface being less than the pressure at the bottom of the drill string (inside the drill string above the bit open orifices).

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Figure 1-17: Air drilling pressures versus depth.

Figure 1-18 shows the plots of the temperature in the incompressible drilling mud as a function of depth. The geothermal gradient for this example is 0.01°F/ft. Subsurface earth is nearly an infinite heat source. The drilling mud in a mud drilling circulation system is significantly more dense than compressed air or other gases. Thus, as the drilling mud flows down the drill string and up through the annulus to the surface, heat is transferred from the rock formations through the surfaces of the borehole, through the drilling mud in the annulus, through the steel drill string to the drilling mud inside. It is assumed that the drilling mud is circulated into the top of the drill string at 60°F.

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Figure 1-18: Mud drilling temperature versus depth.

As the drilling mud flows down the inside of the drill string the drilling mud heats up as heat flows from the higher temperature rock formations and drilling mud in the annulus. At the bottom of the well the drilling mud temperature reaches the bottomhole temperature of 160°F. The drilling mud flowing up the annulus (usually laminar flow conditions) is heated by the geothermal heat in the rock formation.

The heated drilling mud flowing in the annulus heats the outside of the drilling string and this in turn heats the drilling mud flowing down the drill string. Because of its good heat storage capabilities, the drilling mud exits the annulus with a temperature greater than the injection temperature but less than the bottomhole temperature. In this example, the temperature of the drilling mud exiting the annulus is approximately 130°F.

Figure 1-19 shows the plots of the temperature in the compressible air drilling fluid as a function of depth. The compressed air drilling fluid is significantly less dense than drilling mud. Thus, compressed air has poor heat storage qualities relative to drilling mud. Also, compressed air flowing in the drilling circulation system is flowing rapidly and therefore the flow is turbulent inside the drill string and in the annulus. Turbulent flow is very efficient in transferring heat from the surface of the borehole to the flowing air in the annulus and in the inside the drill string. Assuming the compressed air entering the top of the drill string is at 60°F the heat rapidly transfers to heat (or cool) the air flow in the well. Under these conditions the compressed air exiting the annulus has approximately the same temperature as the air entering the top of the drill string.

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Figure 1-19: Air drilling temperature versus depth.

Figure 1-19 shows that the temperature of the compressed air at any position in the borehole is approximately the geothermal temperature at that depth. Thus, the temperature of the flowing air at the bottom of the hole is the bottomhole temperature of 160°F. There is some local cooling of the air as it exits the open orifices of the drill bit at the bottom of the hole. This cooling effect is more pronounced if nozzles are used in the drill bit (when using a downhole motor ). This cooling effect is known as the Joule-Thomson effect and can be estimated [8]. However, it is assumed that this effect is small and that the air flow returns very quickly to the bottomhole geothermal temperature.

Figure 1-20 shows the plot of the specific weight of drilling mud for this example calculation. The drilling mud is incompressible and, therefore, the specific weight is 75 lb/ft3 (or 10 lb/gal) at any position in the circulation system. There is some slight expansion of the drilling mud due to the increase in temperature as the drilling mud flows to the bottom of the well. This effect is quite small and is neglected in these engineering calculations.

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Figure 1-20: Mud drilling specific weight versus depth.

Figure 1-21 shows the plot of the specific weight of the compressed air in this example. The compressed air is injected into the top of the drill string at a specific weight of 1.3 lb/ft3 (at a pressure of 260 psia and temperature of 60°F). As the air flows down the drill string the pressure remains approximately the same. At the bottom of the drill string the specific weight is 1.2 lb/ft3 (at a pressure of 270 psia and a temperature of 160°F). The compressed air exits the drill bit orifices into the bottom of the annulus (bottom of the well) with a specific weight of 1.1 lb/ft3 (at a pressure of 260 psia and a temperature of 160°F).

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 \ ^^Exit Injc «¡0 i ■ i ' i j i "i — :\i Speiific Weight (lb/ft Figure 1-21: Air drilling specific weight versus depth. As the compressed air flows to the surface through the annulus it decompresses as it flows to the low atmospheric pressure at the surface. At the surface the air exits the annulus (via the blooey line) with a specific weight of 0.0763 lb/ft3. The surface atmosphere for this example is assumed to be API Mechanical Equipment Standards standard atmospheric conditions (dry air, pressure of 14.696 psia and a temperature of 60°F) [9]. This figure shows a typical friction resistance dominated drill string flow (as opposed to hydrostatic column weight dominated). This type of flow has a drill string injection pressure at the top that is higher than the pressure above the drill bit at the bottom. Friction dominated flow results when the drill bit is run with no nozzles. Figure 1-22 is the concluding plot of these example calculations. This shows the side-by-side comparison of the annulus velocities of the drilling mud and the compressed air as they flow to the surface. It is the power of these return flows up the annulus that keeps the rock cuttings entrained and moving to the surface at a rate that allows the drill bit to be safely advanced. The drilling mud flows in the annulus around the drill collars with an average velocity of about 7.6 ft/sec. The drilling mud slows to an average velocity of about 3.0 ft/sec in the annulus around the drill pipe. For the air drilling case, the compressed air flows in the annulus with an average velocity of about 30 ft/sec around drill collars. The velocity increases up the annulus to about 125 ft/sec at the exit to the annulus. It is instructive to compare the power (per unit volume) of example flows at the positions in the annulus where the power is likely the lowest. For both of these examples the lowest power is just above the drill collars in the annulus around the bottom of the drill pipe. The kinetic energy per unit volume, KE, is [1, 10] where KE is the kinetic energy per unit volume (ft-lb/ft3), p is the specific weight of the fluid (lb-sec2/ft4), V is the average velocity of the fluid (ft/sec). The density of the fluid, p, is

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