Flow of viscoelastic polymer solutions in mixed beds of particles

Abstract

he flow of non-Newtonian fluids through model packed T beds represents an idealisation of many industrially important processes. Typical examples include the enhanced oil recovery via polymer flooding, the filtration of polymer melts and solutions using sandpack filters, and the flow in fixed and fluidised bed catalytic reactors, etc. Notwithstanding the significance of the detailed kinematics of flow, there is no question that the main interest in all these applications lies in the prediction of the frictional pressure drop across the bed of particles for a given flow rate. Consequently, considerable research effort has been expended in developing reliable methods for the prediction of pressure loss for a liquid of known rheology through a bed of known structure, namely, particle size and shape, porosity and tortuosity. Satisfactory estimation methods are now available for the flow of purely viscous, time-independent fluids through beds of single-size spherical, non-spherical, and of mixed-size paricles. Reviews are available in the literature which summarise the current status of this field (Kemblowski et al., 1987; Chhabra, 1993a,b). Most of the work has focussed on beds of uniform size spheres. There have been only a few studies dealing with the effect of particle shape on pressure losses in packed beds. Based on the limited amount of data, Gaitonde and Middleman (1967) suggested the use of the volume-average diameter as a characteristic particle size for beds of mixed size spheres, whereas a more recent work @a0 and Chhabra, 1993) points towards the mean of hydraulic radii to be a more appropriate characteristic size. Similarly, scant results available for beds of non-spherical particles (Chhabra and Srinivas, 1991;Sharma and Chhabra, 1992) seem to correlate well in terms of an equal volume sphere diameter multiplied by its sphericity. More recent work (Sabiri and Comiti, 1995) suggests, however, that this

Flow of Newtonian and Non-Newtonian Fluids Through Packed Beds: An Experimental Study

“…is high. However, model due to Tiu et al (1997) predicts the present data with least M.R.Q.E. This model takes into account the effect of fluid elasticity in terms of fluid Wessinberg number (We).…”

“…Rao and Chhabra (1993) used definition of Reynolds number proposed by Kemblowski and Michneiwicz (1979) for correlating the pressure loss data in packed bed and modified it by accounting for the wall effects. Tiu et al (1997) gave a distinct correlation between the excess pressure drop observed with viscoelastic fluids and the Wessinberg number. The flow of low concentration Non-Newtonian viscoinelastic fluids like CMC through packed bed may exhibit drag reduction (Jones and Maddock 1966).…”

“…The observed bed friction data on PAA was compared with the predicted values using models proposed by Ergun (1949), Christopher and Middleman (1965), Kumar and Upadhyay (1981), Rao and Chhabra (1993), Al Fariss (1990), Hayes et al (1996), Tiu et al (1997), and M.R.Q.E for each model are given in Table 5. It is observed from Table 5 that for these models, the value of M.R.Q.E.…”

“…This model takes into account the effect of fluid elasticity in terms of fluid Wessinberg number (We). The model proposed by Tiu et al (1997) is expressed as:…”

“…The parameters, K 1 and m, were obtained using non-linear regression technique and are given in Table 2. The fluid characteristic time, λ, was obtained using the approach of Tiu et al (1997), where λ = N 1 2τγ . For flow through packed beds, shear rate, τ , is defined as:…”