Friction Losses in Valves and Fittings for Viscoplastic Fluids

Data on pressure drop were obtained in stainless steel, sanitary fittings and valves during laminar and turbulent flow of aqueous suspensions of sucrose and bentonite. The rheological properties of these suspensions were determined and the Bingham model provided the best fitting with the experimental data. Friction losses were measured in fully‐ and partially‐open butterfly and plug valves, bends and union. Values of loss coefficients (k_f) were calculated and correlated as functions of the classical Reynolds number and the Reynolds number proposed by Govier and Aziz (1972) for viscoplastic fluids. The two‐k method and a new proposed model presented the best adjustments for the Govier and Aziz Reynolds number, and Hedstrom and classical Reynolds numbers, respectively.     

Frictional Pressure Drop of Air Non‐Newtonian Liquid Flow through Helical Coils in Horizontal Orientation

Investigations have been carried out to evaluate the two‐phase frictional pressure drop for air non‐Newtonian liquid flow through helical coils in horizontal orientation. The experiments performed using 36 different helical coils and 4 different concentrations of sodium salt of carboxymethyl—cellulose (SCMC) as non‐Newtonian liquids. The effects of air and liquid flow rate, coil diameter, helix angle and liquid properties‐ on two‐phase frictional pressure drop have been discussed. An attempt has been made to fit the experimental two‐phase frictional pressure drop data by the Lockhart and Martinelli, Chem. Eng. Prog. 45 , 39–48 (1949) correlation and the modified Lockhart‐Martinelli correlation as presented by different authors. In another approach, friction factor method was adopted to correlate the experimental data by dimensional analysis. The correlation developed predicts the two‐phase frictional pressure drop with acceptable statistical accuracy.     

Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013     

Characterisation of the mixing of non‐newtonian fluids with a scaba 6SRGT impeller through ert and CFD

An attempt has been made to study the mixing of yield‐pseudoplastic fluids with a Scaba 6SRGT impeller using electrical resistance tomography (ERT) and computational fluid dynamics (CFD). The ERT system with four sensor planes, each containing 16 equispaced stainless steel electrodes, was used to measure the mixing time. The multiple reference frames (MRF) technique and the modified Herschel–Bulkley model were applied to simulate the impeller rotation and the rheological behaviour of the non‐Newtonian fluids, respectively. To validate the model, the CFD results for the power consumption were compared to the experimental data. The validated model was then employed to obtain further information regarding the averaged impeller shear rate, impeller circulation, and pumping capacities. The CFD and ERT data were utilised to investigate the effect of the impeller power, fluid rheology, and impeller size on the mixing time. The mixing time results obtained in this study were in good agreement with those reported in the literature. © 2011 Canadian Society for Chemical Engineering     

Pressure Drop Models for Gas/Non‐Newtonian Power‐Law Fluids Flow in Horizontal Pipes

Models commonly used in literature are evaluated versus 696 data points to predict the pressure drop of gas/non‐Newtonian power‐law fluids flow in horizontal pipes. Suitable models are recommended. A new correlation is developed by ignoring the pressure drop across the gas slug and adopting the liquid slug holdup of gas/non‐Newtonian fluid flow into the homogeneous model. The theoretical curves can capture the test data trends and the overall agreement of predicted values with experimental data is sufficient to be practically applied in industry.     

Rheological evolution of a particular sol‐gel system

Rheological measurements and results discussed in this paper made on gelling mass containing thetraethoxysilane (TEOS or Si(OC₂H₅)₄) and calcium nitrate as sol‐gel precursors is important because of the interest of sol‐gel processes as a possible preparation route of glasses and amorphous body structures (sol‐gel route). The rheological measurements in our study, have been made to investigate the sol‐gel transition of Si(OC₂H₅)₄ by measuring the viscosity evolution at time intervals and temperature values established. The temperature dependence of the viscosity was used to determine the activation energies of the flow.     

Estimation of mixing volumes in buoyant miscible displacement flows along near‐horizontal pipes

We present a methodological framework for estimating the degree of mixing between successive miscible fluids pumped along a near‐horizontal pipe. Either or both of the fluids can be non‐Newtonian, of Herschel–Bulkley type. Overall it is considered that the objective is to minimise mixing. In laminar regimes our estimates are based on front velocity of the leading displacement front. In turbulent regimes the spreading mechanism is dispersion. In addition to the estimates of mixing volumes/lengths, we also predict a minimal flow rate necessary in order to achieve a successful displacement of the residual fluid. © 2013 Canadian Society for Chemical Engineering     

Volumetric mass transfer coefficients in an internal loop airlift reactor with low‐density particles

The influence of organic additives (propanol, benzoic acid, isoamyl alcohol and carboxymethylcellulose) on the volumetric mass transfer coefficient, k_La, in an internal loop airlift reactor with low‐density particles (nylon‐6 and polystyrene) was investigated. The k_La values increased with increase in superficial gas velocity, U_sg, and decreased with increase in solid loading. A draft tube to reactor diameter ratio, D_R/D, of 0.4 gave maximum k_La values. The addition of benzoic acid and propanol increased the k_La values owing to their coalescence inhibiting characteristics. The addition of isoamyl alcohol decreased k_La, owing to the formation of rigid bubbles and recirculation of small bubbles having a low oxygen content. The k_La values decreased with increase in the concentration of the non‐Newtonian fluid carboxymethylcellulose (CMC). The proposed correlations predicted the experimental data well. Copyright © 2006 Society of Chemical Industry     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

Modelling of transport of two proppant‐laden immiscible power‐law fluids through an expanding fracture

Hydraulic fracturing technology is one of the most popular and efficient reservoir stimulation techniques in oil and gas industry since it allows significant increase of the hydrocarbon production rate. A possible advancement of this technology involves consequent pumping of several immiscible fluids laden with solid particles (proppant) into a fracture. This technique has a potential for better control of the proppant placement and, thus, a better control of the fracture shape. The major result of the present work is a mathematical model and a computational code for investigation of a flow of two immiscible slurries inside an expanding fracture. © 2012 Canadian Society for Chemical Engineering     

Natural convection in a vertical porous cavity filled with a non‐newtonian binary fluid

Numerical and analytical study of natural convection in a vertical porous cavity filled with a non‐Newtonian binary fluid is presented. The density variation is taken into account by the Boussinesq approximation. A power‐law model is used to characterize the non‐Newtonian fluid behavior. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the two horizontal ones are assumed impermeable and insulated. Both double‐diffusive convection (a = 0) and Soret‐induced convection (a = 1) are considered. Scale analysis is presented for the two extreme cases of heat‐driven and solute‐driven natural convection. For convection in a thin vertical layer (A ? 1), a semianalytical solution for the stream function, temperature, and solute fields, Nusselt and Sherwood numbers are obtained using a parallel flow approximation in the core region of the cavity and an integral form of the energy and constituent equations. Numerical results of the full governing equations show the effects of the governing parameters, namely the thermal Rayleigh number, R_T, the Lewis number, Le, the buoyancy ratio, φ, the power‐law index, n, and the integer number a. A good agreement between the analytical predictions and the numerical simulations is obtained. © 2012 American Institute of Chemical Engineers AIChE J, 58: 1704–1716, 2012     

Critical gas velocity in a three‐phase internal loop airlift reactor with low‐density particles

In the present investigation the effects of the addition of organic additives (propanol, benzoic acid, iso‐amyl alcohol and carboxymethyl cellulose) on the critical gas velocity, (U_sg)_c, in an internal airlift loop reactor with low‐density particles (Nylon‐6 and polystyrene) were reported. Whereas the (U_sg)_c was reduced by adding the above additives, it increased with solids loading and density of the particles. The draft tube‐to‐reactor diameter ratio (D_E/D) in the range of 0.5–0.6 gave minimum (U_sg)_c values. The proposed dimensionless correlation predicted the experimental data well. Copyright © 2004 Society of Chemical Industry     

Gas Holdup and Solid‐Liquid Mass Transfer in Newtonian and non‐Newtonian Fluids in Bubble Columns

Gas holdup and surface‐liquid mass transfer rate in a bubble column have been experimentally investigated. De‐mineralized water, 0.5 and 1.0% aqueous solutions of carboxy methyl cellulose (CMC), and 60% aqueous propylene glycol have been used as the test liquids. Effects of column diameter, liquid height to column diameter ratio, superficial gas velocity and liquid phase viscosity on gas holdup and mass transfer rate are studied. Generalized correlations for the average gas holdup and wall to liquid heat and mass transfer coefficients are proposed. These are valid for both Newtonian and pseudoplastic non‐Newtonian fluids.     

Effect of scale‐up on wall shear rates in circulating bubble columns

Effective wall shear rates were investigated experimentally in an external loop circulating bubble column made from transparent acrylic resin. The riser (D_R) and downcomer (D_D) diameters were 0.19 m and 0.14 m, respectively. The column working volume (V_R) was 170 dm³, with a scale‐up factor (A_D/A_R) of 0.54, and a dispersion height (H_D) of 2.25 m. Polymer solutions of xanthan gum and carboxymethyl cellulose were used to simulate non‐Newtonian behavior of biological systems. Effective wall shear rates for the non‐Newtonian solutions were found by analogy with Newtonian glycerol solutions, employing downcomer liquid velocity as the measurable and comparable parameter. The experimental shear rate results were found to fit between those of the literature data. A new single correlation taking into account all the relevant data in the literature and the results of this work is proposed. The new correlation is an improvement over the other correlations because it includes two important design constants: scale‐up factor and dispersion height. Copyright © 2005 Society of Chemical Industry     

Power consumption characteristics of an in‐line silverson high shear mixer

In‐line rotor stator mixers differ from in‐tank versions because the flow is often controlled independently of the rotor speed. For in‐tank devices the turbulent power can be adequately described by single impeller type power number. For an in‐line rotor‐stator mixer it is found that the power transmitted by the rotor consists of a power term and a flow term. The constants in this expression are normally obtained from a multilinear regression of a large matrix of experiments. Two simplified methods of obtaining these constants from limited data sets by (1) torque measurement and (2) by heat balance are described herein. These are used to determine the constants for a Silverson 150/250 MS inline mixer with different rotor stator arrangements from the laminar to turbulent regimes. The power and Metzner‐Otto constants determined are shown to be in good agreement to data for a larger matrix of experimental data. © 2011 American Institute of Chemical Engineers AIChE J, 58: 1683–1692, 2012