Pressure Drop Prediction

For these reasons and other complex influences (e.g., large-diameter pipelines, particle-wall friction, particle shape, bends, etc.), it has been accepted that if high accuracy is needed, then some form of empiricism must be adopted. The preferred test-design procedure is listed below. 

Note that the exponents xl,. ..,x4 and y 1,. 4 are valid only for the test material and bend geometry, respectively. 

To demonstrate the scale-up accuracy of the above design equations, thirty-eight experiments were carried out (Pan and Wypych, 1992a) with a particular fly ash over a very wide range of conveying conditions (i.e., from dilute- to fluidized dense-phase) on the test rig Pipeline I shown in Fig. 14. 

In each experiment, it was believed that all the transducers along the pipeline (Tb-Te) were installed beyond any bend effects. Based on the data obtained from these experiments, the exponents in Eqs. (9) and (12) were determined by minimizing the sum of the squared errors of pressure at points Te2, Tel, Tc2, Tc3 and Tc4, starting from point Tel. The determined values of exponent are listed in Table 1. 

Additional experiments then were carried out on Pipelines II and HI, which are shown in Figs 15 and 16 respectively and detailed in Table 2. 

---

The concurrent flow of liquid and gas in pipe lines has received considerable study [33], [35], [37], [41], However, pressure drop prediction is not extremely reliable except for several gas pipe line conditions. The general determinadons of pressure drop for plant process lines can only he approximated. 

A new approach was developed by Lee and Mudawar (2005a) to improve the accuracy of pressure drop prediction in two-phase micro-channels. Since the bubbly and churn flow patterns are rarely detected in high-flux micro-channel flow, the separated flow model was deemed more appropriate than the homogeneous. 

Since the pressure drop in two-phase flow is closely related to the flow pattern, most investigations have been concerned with local pressure drop in well-characterized two-phase flow patterns. In reality, the desired pressure drop prediction is usually over the entire flow channel length and covers various flow patterns when diabatic condition exist. Thus, a summation of local Ap values is necessary, assuming the phases are in thermodynamic equilibrium. The addition of heat in the case of single-component flow causes a phase change along the channel consequently, the vapor void increases and the phase (also velocity) distribution as well as the momentum of the flow vary accordingly. 

Fig. 13 shows typical results in a plot of pressure drop per unit length against the gas flow factor Fs (= vp°5). Four types of REUs were identified and simulated, and correlations were developed. The pressure drop arising from criss-crossing elements was the largest contribution to pressure drop of the four. The total pressure drop predicted from the individual contributions was in excellent agreement with literature data. 

The next step in the procedure is to determine the sonic pressure ratio. This is found from Equation 4-64. If the actual ratio is greater than the ratio from Equation 4-64, then the flow is sonic or choked and the pressure drop predicted by Equation 4-64 is used to continue the calculation. If less than the ratio from Equation 4-64, then the flow is not sonic and the actual pressure drop ratio is used. 

This correlation (C3) is intended to apply for turbulent-turbulent horizontal flow in pipes, and was developed to give better pressure-drop prediction for higher pressures and larger-diameter pipes. On an entirely empirical basis, the quantity APtp/aPl is given as a function of liquid volume-fraction of the feed, with a quantity >Pq pl/ l po as a parameter. For this correlation aP l is evaluated as the pressure-drop based on the total mass-flow using the liquid-phase properties. The parameter po ph/ Lpo is defined as... 

The accuracy of pressure-drop predictions based on Fig. 4 depends... 

Pressure drop prediction under different inlet velocity... 

B. Mi, P.W. Wypych, Pressure drop prediction in low-velocity pneumatic conveying, Powder Technol. 81 (1994) 125-137. 

For sieve trays, most designars (3-5,18,81) have been recommending Fair s pressure drop correlation (18,31). A recent correlation by Bennett et al. (81) was recommended (18,81) for accurate pressure drop prediction. For valve trays, a slight modification of Fair s sieve tray correlation (80) is described. 

A weak link in the correlation is the packing pressure drop prediction. Inaccurate pressure drop prediction procedures will lead to inaccurate flood-point predictions using this correlation. For best results, the author recommends applying Eq. (8.1) together with pressure drop predictions by interpolation (Sec. 8.2.9). 

Chapter 10 presents a compendium of GPDC data interpolation charts for flood, MOC, and pressure drop prediction, both for random and structured packings. When flood data are absent, pressure drop data can be used for approximating the flood point using Eq. (8.1). 

Interpolation of actual experimental data circumvents the systematic correlation limitations, gives reliable and accurate pressure drop prediction, is difficult to computerize, and requires that suitable interpolation charts are available. This saction deals with predicting pressure drop by correlation. Section 8,2.9 describes interpolating experimental pressure drop data. 

---