Frictional pressure drop, estimation

The PIF estimate is only a qualitative check on the potential benefit of a horizontal well. There is actually a diminishing return of production rate on the length of well drilled, due to increasing friction pressure drops with increasing well length, shown schematically in Figure 9.6. 

Combining both expressions gives a simple relation for estimating the frictional pressure drop in straight run pipe. 

Power input per unit mass of the system is equal to the rate of energy dissipation per unit mass of the liquid and it is estimated by considering the permanent pressure head loss across the orifice. The rate of energy dissipation due to eddy losses is the product of the head loss and the volumetric flow rate. Frictional pressure drop at downstream of the orifice can be calculated as,... 

Pressure drop for condensers. For condensers, the frictional pressure drop can be estimated using the relation... 

The same procedure may be applied in principle to design of forced-recirculation reboilers with mell-side vapor generation. Little is known about two-phase flow on the shell side, but a reasonable estimate of the friction pressure drop can be made from the data of Diehl and Unruh [Pet Refiner, 36(10), 147 (1957) 37(10), 124 (1958)]. No void-fraction data are available to permit accurate estimation of the hydrostatic or acceleration terms. These may be roughly estimated by assuming homogeneous flow. 

A large body of literature is available on estimating friction loss for laminar and turbulent flow of Newtonian and non-Newtonian fluids in smooth pipes. For laminar flow past solid boundaries, surface roughness has no effect (at least for certain degrees of roughness) on the friction pressure drop of either Newtonian or non-Newtonian fluids. In turbulent flow, however, die nature... 

The total-frictional pressure drop in the system is the sum of the pressure drops caused by the piping and fittings, control valve, interchanger, and air cooler. Estimates of these loses are listed in Table 5.15. Therefore, the total frictional pressure drop in the system,... 

The frictional pressure drop normally constitutes the largest fraction of the total pressure drop. However, only empirical methods are available for its calculation. It includes not only the momentum transfer between the fluid and the wall, but also the momentum transfer between the individual phases. These two processes cannot be measured separately and can only be estimated for simple flows. Thus, only imprecise ideas of the influence of momentum transfer between the phases exist. 

The frictional pressure drop may be estimated by subtracting the hydrostatic component (calculated from the holdup) from the total pressure gradient, as shown in Figure 4.19. It will be seen that under certain conditions, particularly at low liquid flow rates, the frictional component appears to approach zero. For the flow of air-water mixtures, negative friction losses are well docmnented in the literature. This anomaly arises because not all of the liquid present in the pipe contributes to the hydrostatic pressure, because some liquid may form a film at the pipe wall. This liquid is sometimes flowing downwards and most of its weight is supported by an upward shear force at the wall. The drag exerted by the gas on the hquid complements the frictional force at the pipe wall. 

Estimation of Individual Heat Transfer Coefficients and Frictional Pressure Drop... 

When the flow is through the annulus of a double-pipe heat exchanger, Eqs. (13.15) and (13.19) can be used to estimate the frictional pressure drop, provided that the inside diameter, D of the tube or pipe is replaced by the hydraulic diameter, D , which is defined as 4 times the channel cross-sectional area divided by the wetted perimeter. For an annulus, Du = >2 - ),. 

Thus, the steps in estimating the pressure drop using Equation 7.36 are (i) estimation of the frictional pressure drop of each individual phase, (ii) calculation of the Lockhart-Martinelli parameter ( P), and (iii) estimation of the friction multiplier for liquid, and... 

Normally, the blowdown of the valve is set at 7 to 10% of the set pressure (except in the pilot-operated valve, in which it can be set as low as 3%), and based on the normal setting of blowdown, the mechanical design code restricts the inlet line nonrecoverable pressure drop to a maximum of 3%. The estimated pressure drop is only the frictional pressure drop and excludes any drop or gain due to change in velocity head. This means the velocity head chmge due to the reducer installed at the PRV inlet should be ignored in estimating the pressure drop. 

On occasion one will find that heat-transfer-rate data are available for a system in which mass-transfer-rate data are not readily available. The Chilton-Colburn analogy provides a procedure for developing estimates of the mass-transfer rates based on heat-transfer data. Extrapolation of experimental or Jh data obtained with gases to predict hquid systems (and vice versa) should be approached with caution, however. When pressure-drop or friction-factor data are available, one may be able to place an upper bound on the rates of heat and mass transfer, according to Eq. (5-308). 

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