Heel estimate during pressure-driven drainage of gels from tanks

https://doi.org/10.1016/j.ces.2020.116158Get rights and content

Highlights

  • Residue (heel) in tanks while draining gels can be predicted based on rotational rheometry.

  • Carreau model suffices for CFD calculation of drainage.

  • Vane-cup geometry is best suited to characterize gels rheology.

  • MRI images of contraction flow correlate with heel estimates during drainage.

Abstract

This paper deals with methods to predict residue (heel) in a tank after drainage of polymer gels from the tank. Gels of various rheological properties were considered in which a thixotrope (Xanthan gum) and a thickener (carboxymethyl cellulose) were combined in various ratios so as to change the gel flow curve from strongly to weakly shear thinning. Computational fluid dynamics allows the conversion of rheological data collected on a rotational rheometer into quantitative prediction of the heel. A complementary method to provide insight into the fluid mechanics of tank draining uses contraction flow visualized by magnetic resonance imaging (MRI). The size of the stagnant zone which develops in such flow may also be used as a predictor of the heel during drainage. CFD modeling utilizing a simplified Carreau model, where viscoelasticity was neglected and fitting parameters were extracted from rheometry, was successful in predicting the heel mass in the gel tank.

Introduction

Heel refers to any residue left in a tank after its drainage. In many cases engineers are concerned about it from the point of view of tank cleaning, either when dealing with nuclear waste (see Prokopowicz and Phillips, 2011) or more ubiquitous materials, such as toothpaste (Yang et al, 2019). Process optimization is another common reason to try to minimize the heel or accelerate the drainage. The material can be discharged from the tank either under gravity or by sucking it from the tank under pressure. Generally speaking, engineers usually want the drainage to be done faster and the heel amount to be smaller. However, while there are quite a few publications on drainage rate (see, e.g., Joye and Barrett, 2003, or Toplak et al, 2007), hardly any systematic studies of the heel amount estimates were reported in literature. This paper intends to fill this gap.

The motivation of this paper comes primarily from toothpaste manufacturing, although similar problems are encountered in other industries. A typical “cold process” of toothpaste making, as described, e.g., by Pader (1992), consists of two steps. The first step is making a “liquid mix” which essentially is usually a polymeric gel containing organic gums with water and humectants (typically, glycerin) plus some water-soluble additives. The liquid mix or gel is subsequently transferred to the main mixer to which powders are added and the product becomes a paste. To maintain an efficient and cost-effective process, one wants to minimize the loss of valuable raw materials when discharging the polymeric gel from the tank. The discharge may be entirely gravity driven or, more often, accelerated by the application of negative pressure to the outlet pipe at bottom of the tank. This is where the problem of minimizing heel may become relevant. How to prevent accumulating excessive residue material on the walls of the tank?

This paper is organized as follows. First, we describe experiments on a simplified table-top device emulating gel discharge. Various gels of different rheological properties will be studied and the resulting heel left in the table-top tank estimated. We will show that the amount of the heel can be rather accurately estimated from the rheological parameters of the gel in the framework of a rather simple computational fluid dynamics (CFD) model. Next, we will discuss visualization of the gel transfer flow using magnetic resonance imaging (MRI). Our goal is to establish the most accurate and efficient way to predict the heel.

Section snippets

Materials

The gels were made by dissolving two polymeric materials, Xanthan gum by CP Kelco and carboxy-methyl cellulose (CMC) by Ashland, in a 50/50 mixture of glycerin and deionized water. CMC is a thickener which exhibits rather low yield stress values which is why it is often combined with “thixotropes”, i.e., structure-forming gums, such as Xanthan (Pader,1992). Both gums were first dispersed in glycerin using an overhead mixer after which water was added which resulted in a semitransparent gel. The

Results and discussion

A. Rheological data and model definition

Rheological data, on which subsequent calculations are based, are summarized in Fig. 3, Fig. 4. Both stress- and strain-controlled data were used as explained in Fig. 3 using as an example one of the gels- the one with 3% Xanthan and 1% CMC. In Fig. 3(a) results of the creep tests performed on this gel are shown. Viscosity is estimated as the reciprocal slope of the creep compliance curve based on the last 10% of its stress segment, as shown on this plot.

Conclusions

In this study, CFD modeling utilizing the Carreau model with fitting parameters extracted from rheometry was successful in predicting the trends in heel mass in the gel tank and the velocity field in contraction flow. The model predictions were validated by gel tank experiments and MRI velocity measurements. The following conclusions can be drawn from the experiments and modeling.

- The effect of the gel composition was studied by testing gels composed of two polymers with very different

Declaration of Competing Interest

The authors declared that there is no conflict of interest.

Acknowledgements

The authors gratefully acknowledge the Rutgers Molecular Imaging Center for providing assistance with MRI scanning. The help of Gregg Marron in performing some of the drainage tests reported in this paper is highly appreciated.

References (16)

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