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7.1 Introduction
This chapter deals with practical methods of calculating pressure losses in the various parts of the circulating system and the selection of nozzle sizes. Several models exist for the calculation of pressure losses in pipes and annulus. Each model is based on a set of assumptions which cannot be completely fulfilled in any drilling situation. The Bingham plastic, Power law and Herschel-Buckley models are the most widely used in the oil industry.
7.2 Pressure Losses
Figure 7.1 below gives a schematic of the circulating system. We have divided the circulating system into four sections:
1. Surface connections.
2. Pipes including drill-pipe, heavy walled drill-pipe and drill collars.
3. Annular areas around drill-pipes, drill-collars, etc.
4. Drill Bit.
Figure 7.1
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Drilling Bits Hydraulics Chapter # 7
50 Our objective is to calculate the pressure (energy) losses in every part of the circulating system and then find the total system losses. This will then determine the pumping requirements from the rig pumps and in turn the horse power requirements.
7.2.1 Surface Connection Losses (P1)
The pressure losses in surface connections (P1) are those taking place in standpipe, rotary hose, swivel and Kelly. The task of estimating surface pressure losses is complicated by the fact that such losses are dependent on the dimensions and geometries of surface connections. These dimensions can vary with time, owing to continuous wear of surfaces by the drilling fluids. The following equation gives pressure losses in surface connections:
P1E0.8Q PV1.8 0.2 7.1 Where
ñ= mud weight (lbm/gal) Q = volume rate (gpm)
E = a constant depending on type of surface equipment used PV = plastic viscosity (cp)
In practice, there are only four types of surface equipment; each type is characterized by the dimensions of standpipe, Kelly, rotary hose and swivel. Table below summaries the four types of surface equipment.
Table: Types of surface equipment
The values of the constant E in Equation (7.1) are given in Table Table: Values of constant E
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7.2.2 Pipe and Annular Pressure Losses
The pipe losses take place inside the drillpipe and drill collars and are described in Figure 7.1 as P2 andP3, respectively. Annular losses take place around the drill collar and drillpipe and are given the names P4 and P5 as shown in the figure 7.1. The magnitudes of P2 , P3 ,P4 ,and P5 depend on:
Dimensions of drillpipe (or drill collars), e.g. inside and outside diameter and length;
Mud rheological properties, which include mud weight, plastic viscosity and yield point; and
Type of flow, which can be laminar, or turbulent.
It should be noted that the actual behavior of drilling fluids downhole is not accurately known and fluid properties measured at the surface usually assume different values at the elevated temperature and pressure downhole.
7.2.3 Pressure Drop across Bit
Drill bits are provide with nozzles to provide a jetting action, mainly required for cleaning and cooling, but can also help with rock breakage in soft formations. The largest nozzle is one inch in size, often termed open, but more often the nozzles used are a fraction of an inch. Hence, the pressure requirements to pass, say 1000gpm, through such small nozzles will be large.
For a given length of drill string (drillpipe and drill collars) and given mud properties, pressure losses P1, P2, P3, P4, and P5 will remain constant. However, the pressure loss across the bit is greatly influenced by the sizes of nozzles used, and volume flow rate.
For a given flow rate the smaller the nozzles, the greater the pressure drop and, in, turn the greater the nozzle velocity. For a given maximum pump pressure, the pressure drop across the bit is obtained by subtracting Pc (= P1+ P2 +P3 +P4+P5) from the pump pressure.
7.3 Fundamentals of Hydraulics
The following are definitions of terms required to understand the various hydraulics equations. The symbols and units are given with the definitions.
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7.3.1 Shear rate (sec -1):
This is a term most applicable to laminar flow. It refers to the change in fluid velocity divided by the width of the channel through which the fluid is flowing in laminar flow.
7.3.2 Shear stress, t (lb/100 ft):
The force per unit area required to move a fluid at a given shear rate.
7.3.3 Viscosity, µ (centipoises (cp):
This is the ratio of shear stress to shear rate.
7.3.4 Plastic viscosity, PV (cp):
Plastic viscosity represents the contribution to total fluid viscosity of a fluid under dynamic flowing conditions. Plastic viscosity is dependent on the size, shape, and number of particles in a moving fluid. PV is calculated using shear stresses measured at 600and 300 rpm on the Fann 35 viscometer.
7.3.5 Effective viscosity, µ (cp):
This term takes account of the geometry through which the fluid is flowing and is therefore a more descriptive term of the flowing viscosity.
7.3.6 Yield stress (lb/100 ft):
This is the calculated force required to initiate flow and is obtained when the rheogram (a plot of shear stress vs shear rate) is extrapolated to the y-axis at Y = 0 sec-1. In practice the yield point is calculated using Equation (7.3).
7.3.7 Gel strength (lb/100 ft):
All drilling fluids build a structure when at rest. The gel strength is time-dependent measurement of the fluid shear stress when under static conditions. Gel strengths are commonly measured after 10 seconds, 10 minutes, and 30 minutes intervals.
7.3.8 Reynolds number, Re:
This is a dimensionless number which determines whether a flowing fluid is in laminar or turbulent flow. A Reynolds number greater than 2,100 marks the onset of turbulent flow in most drilling fluids. For laminar flow (Re < 2,100) and for turbulent flow (Re > 2,100).
Drilling Bits Hydraulics Chapter # 7
53 Figure7. 2