Fluid friction pressure losses

Rheological Classification of Drilling Fluids 829. Flow Regimes 830. Principle of Additive Pressures 834. Friction Pressure Loss Calculations 836. Pressure Loss Through Bit Nozzles 839. 

The wellbore, drill string and drilling fluid data from the previous example are used. Casing depth is 4,000 ft. Assuming a drill pipe length of 5,000 ft and a drill collar length of 500 ft, find the friction pressure losses. 

Basically all formations penetrated during drilling are porous and permeable to some degree. Fluids contained in pore spaces are under pressure that is overbalanced by the drilling fluid pressure in the well bore. The bore-hole pressure is equal to the hydrostatic pressure plus the friction pressure loss in the annulus. If for some reason the borehole pressure falls below the formation fluid pressure, the formation fluids can enter the well. Such an event is known as a kick. This name is associated with a rather sudden flowrate increase observed at the surface. 

Euler number Eu A p pV2 frictional pressure loss 2 x velocity head Fluid friction in conduits... 

A typical flow rate of 2 m3/min in the drill pipe (diameter = 0.1 m) gives a fluid velocity of 4.2 m/s, which causes fully turbulent flow in most drilling fluids. The calculation of the pressure drop down the length of the drill pipe is made somewhat complex by the flow being turbulent and the non-Newtonian rheology of the drilling fluid. These calculations are, however, important as about 30% of the total frictional pressure losses occur in the drill pipe. 

Figures 28a and 28b compare the measured and calculated frictional pressure losses for laminar and turbulent flow of the drilling fluid through...

Annulus. From the drill pipe, the drilling fluid is jetted out of the bit nozzles and into the annulus. The jets are designed to remove drilled cuttings away from the drill bit. The pressure drop across the nozzles accounts for about 60% of the total frictional pressures losses during the circulation of the drilling fluid. About 90% of the pressure drop across the nozzles is due to the turbulence at the outlet, with only about 10% due to the flow through the nozzles. 

Marken et al. (110) have given a detailed account of the factors affecting annular pressure losses, including the effects of rotational flow in the annulus. It might be expected that rotational flow in the annulus would decrease the frictional pressure losses as the increased shear rate would lower the viscosity. However, Marken et al. observed an increase in frictional pressure due to the formation of Taylor vortices. McCann et al. (J07) have observed increases in the frictional pressures in slimhole annuli due to annular rotation of the drilling fluid. 

Several studies have been reported to determine friction losses in turbulent flow of slurries. Hannah et al. (29) presented an approach in which they compared expressions for the friction pressure of the slurry and clean fluid. In their analysis, they assumed Blasius (30) turbulent Fanning friction factor versus Reynolds number equation for Newtonian fluids. The following expression for estimating slurry friction pressure knowing the clean fluid friction pressure is proposed. 

A low molecular weight polymer melt, which can be modelled as a power-law fluid with m = 5 kPa-s" and n = 0.25, is pumped through a 13 mm inside diameter tube over a distance of 10 m under laminar flow conditions. Another pipe is needed to pump the same material over a distance of 20 m at the same flow rate and with the same frictional pressure loss. Calculate the required diameter of the new pipe. 

Frictional pressure loss due to the kinetic energy imparted to the fluid... 

Following are some rules and equations for calculating friction pressure losses in pipes and ducts. Consider a Newtonian fluid of density p, flowing at the average velocity u into a smooth... 

We now have to thank Stanton and PanneU, and also Moody for their studies of flow using numerous fluids in pipes of various diameters and surface roughness and for the evolution of a very useful chart (see Fig. 48.6). This chart enables us to calculate the frictional pressure loss in a variety of circular cross-section pipes. The chart plots Re)molds numbers (Re), in terms of two more dimensionless groups a friction factor < ), which represents the resistance to flow per unit area of pipe surface with respect to fluid density and velocity and a roughness factor e/ID, which represents the length or height of surface prelections relative to pipe diameter. 

We also have the Fanning friction factor,/, which equals 2(j) and the Moody friction factor/, which equals 8(, just as we saw earlier when discussing frictional pressure loss in rough and smooth pipe for Newtonian fluids. 

The term pressure drop usually refers to the pressure loss that is not recoverable in the circuit, and it is lost energy that is dissipated into the fluid stream in the form of heat energy. The pressure drop in a flow circuit is associated with various forms of energy dissipation owing to friction, change in flow area, flow turning, and others ... 

There are also many empirical formulas used for calculatiag the friction head loss in piping systems. These must be used carefuUy because many are based on the properties of specific fluids and are not appHcable over a broad range of fluids, temperatures, and pressures. For example, the Ha2en and Wdhams formula widely used for water flow ... 

When a PR valve is relieving at rated capacity, the total frictional pressure drop between a vessel and the inlet of the valve should be less than 3% of the set pressure (kPa). In this calculation, the effect on static pressure of fluid acceleration is ignored rather, only friction loss is considered. 

This is an ultimate case, when the friction factor is no longer a function of the Reynolds number and is a function of roughness the pressure loss is now Ap tv", where w is the fluid velocity in the duct. The surface roughness of typical manufactured ductworks varies between the values of a theoretically fully smooth duct and an artificially roughened one. Accordingly the pressure loss varies between Ap w -w and f =/ (Re, roughness). 

Barth assumed that the pressure loss of a cyclone consists mainly of the pressure loss required to overcome the wall friction of the cyclone and the pressure drop to drive the fluid out of the cyclone outlet pipe. This leads to the following expression for the total loss factor C/ ... 

The mechanical efficiency of a fan is the ratio of the horsepower output to the horsepower input at the fan shaft. The input horsepower to drive the fan consists of the air horsepower, the energy losses in the fan, fluid dynamic losses, shock losses, leakage, disk friction, and bearing losses (all as horsepower), The fan oudet velocity pressure loss has been included in the fluid dynamic losses. 

The theory of pressure losses can be established by developing Bernoulli s theorem for the case of a pipe in which the work done in overcoming frictional losses is derived from the pressure available. For a fluid flowing in a pipe, the pressure loss will depend on various parameters. If... 

While friction increases markedly for sharper curves than this, it also tends to increase up to a certain point for gentler curves. The increases in friction in a bend with a radius of more than 3 pipe diameters result from increased turbulence near the outside edges of the flow. Particles of fluid must travel a longer distance in making the change in direction. When the radius of the bend is less than 2 pipe diameters, the increased pressure loss is due to the abrupt change in the direction of flow, especially for particles near the inside edge of the flow. 

For flow at right angles to the axes of the tubes, the cross-sectional area is continually changing, and the problem may be treated as one involving a series of sudden enlargements and sudden contractions. Thus the friction loss would be expected to be directly proportional to the number of banks of pipes j in the direction of flow and to the kinetic energy of the fluid. The pressure drop - APf may be written as ... 

There are two major sources of pressure loss on the tube-side of a shell and tube exchanger the friction loss in the tubes and the losses due to the sudden contraction and expansion and flow reversals that the fluid experiences in flow through the tube arrangement. 

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