Prediction frictional pressure drop

Pressure Drop. The prediction of pressure drop in fixed beds of adsorbent particles is important. When the pressure loss is too high, cosdy compression may be increased, adsorbent may be fluidized and subject to attrition, or the excessive force may cmsh the particles. As discussed previously, RPSA rehes on pressure drop for separation. Because of the cychc nature of adsorption processes, pressure drop must be calculated for each of the steps of the cycle. The most commonly used pressure drop equations for fixed beds of adsorbent are those of Ergun (143), Leva (144), and Brownell and co-workers (145). Each of these correlations uses a particle Reynolds number (Re = G///) and friction factor (f) to calculate the pressure drop (AP) per... 

The investigation shows agreement between the standard laminar incompressible flow predictions and the measured results for water. Based on these observations the predictions based on the analytical results of Shah and London (1978) can be used to predict the pressure drop for water in channels with as small as 24.9 pm. This investigation shows also that it is insufficient to assume that the friction factor for laminar compressible flow can be determined by means of the well-known analytical predictions for its incompressible counterpart. In fact, the experimental and numerical results both show that the friction factor increases for compressible flows as Re is increased for a given channel with air. 

The frictional pressure drop for liquid flows through micro-channels with diameter ranging from 15 to 150 pm was explored by Judy et al. (2002). Micro-channels fabricated from fused silica and stainless steel were used in these experiments. The measurements were performed with a wide variety of micro-channel diameters, lengths, and types of working fluid (distilled water, methanol, isopropanol), and showed that there were no deviations between the predictions of conventional theory and the experiment. Sharp and Adrian (2004) studied the fluid flow through micro-channels with the diameter ranging from 50 to 247 pm and Reynolds number from 20 to 2,300. Their measurements agree fairly well with theoretical data. 

Several models have been proposed to evaluate the two-phase mixture viscosity, and the model selected may affect the predicted two-phase frictional pressure drop ... 

Equation 2.5 shows that the value of tw can be determined if the pressure gradient is measured this is how values of the friction factor discussed in Section 2.3 have been found. Alternatively, if tw can be predicted, the pressure drop can be calculated. 

In summary, the calculation of pressure drops by the Lockhart-Marti-nelli method appears to be reasonably useful only for the turbulent-turbulent regions. Although it can be applied to all flow patterns, accuracy of prediction will be poor for other cases. Perhaps it is best considered as a partial correlation which requires modification in individual cases to achieve good accuracy. Certainly there seems to be no clear reason why there should be a simple general relationship between the two-phase frictional pressure-drop and fictitious single-phase drops. As already pointed out, at the same value of X in the same system, it is possible to have two different flow patterns with two-phase pressure-drops which differ by over 100%. The Loekhart-Martinelli correlation is a rather gross smoothing of the actual relationships. 

Winkelmann et al. (54) have studied air-water flows in a corrugated heat exchanger. Flow visualization and two-phase pressure drop measurements have been performed. The flow visualizations have shown that the flow pattern is complex and that a wavy or a film flow occurs in most cases (Figure 29). The two-phase pressure drop depends on the total flow rate and vapor quality, and Chisholm-type correlation is proposed. More work is required to characterize the flow structure in compact heat exchangers and to develop predictive methods for the frictional pressure drop and the mean void fraction. 

Proppant Effects. The introduction of proppant into stimulation fluids further increases the difficulty in the prediction of pressure drop due to friction. The calculation used to determine friction pressures is further complicated by the addition of proppant. Harris et al. (46) developed a useful analytical method to account the effects in rheology by introducing a proppant. 

Comparison Between Different Viscometers. To validate their rheological measurements, several authors have tried to compare the results obtained using coaxial cylinder and pipe viscometers. Their findings are not necessarily in agreement. Bannister (15) was able to predict the frictional pressure drops of a cement slurry in a 1.815-in. ID pipe from pipe viscometer data corrected for wall slip. Mannheimer, who tried to reconcile coaxial cylinder and pipe viscometer data, both of them being corrected for wall slip was successful with one cement slurry formulation, but the approach failed with another one (13). Denis et al. (16) showed good agreement between coaxial cylinder and pipe viscometer data above a critical shear rate—or shear stress—that is pipe diameter dependent. 

For two-phase cocurrent gas-liquid flow, there is the wide variety of possible flow patterns which are governed principally by the physical properties (density, surface tension, viscosity of gas, rheology of liquid), input fluxes of the two phases and the size and the orientation of the pipe. Since the mechanisms responsible for holdup and momentum transfer (or frictional pressure drop) vary from one flow pattern to another, it is essential to have a method of predicting the conditions under which each flow pattern may occm. Before developing suitable methods for the prediction of flow pattern, it is important briefly to define the flow patterns generally encountered in gas-liquid flows. Horizontal and vertical flows will be discussed separately as there are inherent differences in the two cases. 

To predict the pressure drop for this flow regime, an empirical correlation for estimating the friction factor was obtained from experimental data in the range of 0.008 < uq -H l) < 1 ms ... 

Lazarek and Black [67] obtained good predictions of their data by using a value of 30 in the generalized Chisholm/Lockhart-Martinelli correlation for C. Mishima and Hibiki [66] obtained reasonably good predictions for their frictional pressure drop data for air-water flows by correlating the Chrisholm C parameter in the Lockhart-Martinelli correlation as a function of the tube diameter as follows ... 

G. Ribatski, L. Wojtan, J. R. Thome, An analysis of experimental data and prediction methods for two-phase frictional pressure drop and flow boiling heat transfer in microscale chaimds, Exp. Thermal Fluid Sci., 2006, 31,1-19. 

Initially he conducted the experiment on water flow through horizontal pipe (same PVC pipe for both cases) to find the roughness values (Venkatesan et al. [62], He compared the experimental friction factor for coil with the values obtained from smooth coil equation and observed that the experimental friction factor was higher than that of smooth coil. He found that as coil diameter increased the friction factor decreased (Figure 2). He presented a generalized correlation for predicting the frictional pressure drop across the rough helical coils as... 

A large number of experimental data on friction factors of smooth pipe and pipes of varying degrees of equivalent roughness have been obtained and the data correlated. For design purposes to predict the friction factor/and, hence, the frictional pressure drop of round pipe, the friction factor chart in Fig. 2.10-3 can be used. It is a log-log plot of/... 

Equations for flow in a tube. In order to predict the frictional pressure drop Ap in laminar flow in a tube, Eq. (3.5-4) is solved for Ap. 

The frictional pressure drop for vapors condensing inside tubes can be predicted as below ... 

Chilton and Colburn (Ref. 4) have published a method for predicting such pressure drop for solid packings, based on the Fanning equation for friction in pipes. They modify the friction equation to... 

The Martinelli and Nelson correlation predicts the average of our experimentally determined values of < > with an accuracy of 10 to 30 per cent, if simple momentum corrections are made. It should be noted, however, that the deviation is greater for the frictional pressure drop because... 

---