Prebaked Carbon Anodes
Calcined coke and recycled anode butts are crushed and screened/sized to pre-determined size fractions in anode plants. This dry aggregate mix is then preheated to 110-165 ºC and mixed with 13-18 wt.% pitch at temperatures around 150 ºC to form anode paste. The obtained paste then experiences a forming step by vibratory compaction or hydraulic pressing, to form green anode blocks. Green anodes are then baked at temperatures between 1100 and 1200 ºC to obtain the required mechanical strength.
Baked anode properties are influenced by the physical and chemical properties of its raw materials (coke and pitch). In the last three decades, there has been a continuous decline in the quality of calcined cokes in parameters such as sulfur impurity and bulk density [12, 15, 16]. On the other hand, coal tar pitch continues to decrease in quinoline insolubles (QI) and to increase in softening point as a result of coal tar quality changes from cookeries [16, 17]. Blending raw materials from different sources has been a technique for anode plants to offset the raw materials quality variation. This, in turn, can raise homogeneity concerns for anode pastes. Thus, it is very important to understand the influence of different properties of coke aggregates and binder pitch on final quality indices of anodes.
Effects of coke properties on anode quality
Coke particles make up around 65 wt.% of an anode and thus physical, chemical and mechanical properties of coke have a considerable impact of anode quality. Coke porosity (experimentally measured by means of bulk density) has a direct effect on the apparent density of anode. Fischer and Perruchoud  reported an increase of 0.06 kg/dm3 in anode apparent density for a 0.12 kg/dm3 increase in coke bulk density. Lower air permeability of anode has also been observed with increasing coke density . K.A. Dorche et al.  investigated the effects of physical properties of coke particles on the compaction behavior of green anode paste and reported a pronounced effect of coke particles shape on compaction curves and final apparent density of anode paste. They showed that using more spherical particles enhances the density of the compacted anode pastes. Dion et al.  in 2015 proposed a method to separate high- and low-density calcined cokes. High-density particles were used in medium and coarse size fractions of anode recipe and low-density particles were crushed and used as fine particles. As shown in Figure 2.1, it has been shown that use of separated high-density coke fractions leads to higher baked density of anodes with the same amount of pitch.
Figure 2.1. Baked density of laboratory anodes made with as-received and separated cokes. (reproduced from )
Effects of pitch properties on anode quality
Pitch acts as a binder in anode paste to bond the coke particles together. It also penetrates into the open pores of coke particles. Wettability of coke by binder pitch affects the bonding strength between them and so the final anode properties. It has been shown  that temperature has a positive effect in wettability of coke by pitch. Coking value and softening point are also important properties of pitches. A part of pitch is lost during baking as volatiles release, leaving behind a pitch coke. This characteristic of pitch is measured as coking value. The remaining pitch coke acts as binder between the coke particles. As shown in Figure 2.2, baked apparent density (BAD) of anodes increases with the increase in softening point of pitch. It is believed that this is because of the positive effect of softening point on the coking value of pitch .
Figure 2.2. Effect of softening point of pitch on density and baking loss of anodes (reproduced from )
Rheological properties of anode paste
Pitch is a thermoplastic amorphous material and thus it does not have a melting point. The change from the solid state to a viscous liquid is gradual and the term softening point is used to describe it. Pitches used in carbon anode plants have a softening point of 100-120 ºC. Above the softening point, pitch is a liquid and based on its chemical composition it can exhibit Newtonian , non-Newtonian  and viscoelastic  behavior. A combination of pitch and coke fine particles (also called fines) can make up a viscous granular phase representing 38-60% of the anode content . This phase is called Binder Matrix, in which large coke aggregates are dispersed. There is an optimum content of pitch in the paste to have the best combination of quality factors in final baked anode. Overpitching results in cracking and extreme shrinkage in the anode block, due to excessive mass loss during baking. The most important result of underpitching is anodes with low apparent density, high electrical resistivity and poor mechanical properties . Figure 2.3 schematically shows the optimum pitch content, which bonds the aggregates and also provides enough space for pitch expansion during baking. Since pitch wets the coke particles and penetrates into the open pores of the particles, the structure and porosity of coke are important factors determining the pitch demand in anode paste.
Rheological behavior of anode paste is termed as granulo-viscoelastic . The viscous part comes from the pitch and the elasticity and granular behavior come from the coke particles. Increased temperature, shear rate and pitch amount increase the viscous behavior of the paste compared to its elastic response. This behavior has an important effect on the compaction behavior of the paste during vibro-forming process, thus on the final density of anode.
Figure 2.3. Concept of optimum pitch content in anode paste (reproduced from )
Theory and measurement
External load on a material causes an internal rearrangement. These rearrangements require a finite time in any material. Materials with significant amount of time-dependent stress-strain response are called viscoelastic . Time dependency in response of materials to external loads can be represented as shown in Figure 2.4. When a step load is applied to the materials for time duration of t0 to t1, the ideal elastic material (b) exhibits an instantaneous response and deformation immediately returns to zero by unloading. This response needs only Young’s modulus to be defined. Pure viscous material (c) deforms with a constant rate with time during loading and leaves a non-zero constant deformation at the end. Viscoelastic material (d) however, has a more complex response; instantaneous deformation followed by gradual time-dependent deformation up to t1. It also shows an immediate partial recovery followed by a time-dependent deformation recovery by unloading.
Dynamic mechanical testing is a well-established method to study the rheological properties of viscous and viscoelastic materials including bituminous binders . Dynamic Shear Rheometer (DSR) is the laboratory equipment used for this purpose.
Figure 2.4. Idealized response of a viscoelastic material compared to pure elastic and pure viscous material.
Viscoelastic behavior of a material is normally presented by two parameters of a complex shear modulus, G*, and phase angle, . Dynamic Shear Rheometer (DSR) provides an experimental method to measure these parameters. As schematically shown in Figure 2.5, in DSR, a disk of material is sandwiched between two plates and a sinusoidal stress (or strain) is applied to the upper plate while the lower plate is fixed. When a material is subjected to a sinusoidal straining, the material’s response as the induced stress will also have a sine form. The time lag between the two curves, as shown in Figure 2.6(a), is called phase angle. For pure elastic materials, the phase angle is zero and that of pure viscose materials is 90º. Viscoelastic materials have phase angles between 0º and 90º.
Numerical Methods in Modeling of Anode Paste and Similar
Anode paste is a composite material composed of a viscoelastic matrix, a particulate phase and voids. Binder pitch itself has a temperature and strain rate dependent behavior and its chemical composition also affects its rheological properties. Coke aggregates with different sources may have different apparent density, shape and so packing density. Besides, since both binder and aggregates are carbon materials, their light reflection under the microscope is such similar that studying the microstructural homogeneity is very difficult. Therefore, it is not surprising that characterization and modeling of anode paste and especially predicting its performance under complex processing techniques such as vibro-compaction under elevated temperature, load and frequency effects is very challenging.
Since there have been very limited published works on numerical modeling of anode paste, continuum mechanical methods used to model similar materials such as asphalt concrete and ramming paste are also reviewed here.
In continuum models, each constituent of a composite material is considered as a single continuum and then the response of the constituents is super-posed using constitutive laws. Koneru et al. in 2008  developed a constitutive model of compaction for asphalt mixes using the theoretical framework of multiple natural configurations proposed by Rajagopal  for large deformations of dissipative bodies. In this work, the constitutive law for mechanical energy dissipation is proposed by taking appropriate assumptions concerning the manner in which a body stores and dissipates energy. In this model, for each current configuration ( ) a natural configuration ( ) (stress-free state) is associated. In Figure 2.7, is a reference configuration, ( ) is the configuration currently occupied by the material and ( ) is the natural configuration. By considering only one relaxation mechanism, only one natural configuration is associated to each current configuration.
Assuming that asphalt mixture has an instantaneous elastic response from the natural configuration, the gradient of the mapping from ( ) to and ( ) is defined. Energy dissipation is assumed to be only mechanical and finally a constitutive law for an isotropic homogeneous material in isothermal compaction is obtained. This model is a very simplified description of such a complex process of compaction of asphalt mix and it takes into account only two parameters of viscosity (representing the binder) and “shear modulus-like parameter” representing the characteristics of the aggregates. However, the model at the end provides a good prediction of compaction curves of asphalt mixes. An example of the predictions of this model is given in Figure 2.8.
Chaouki et al. in 2014  extended Koneru et al.’s model to a viscoplastic model of compaction behavior of green anode paste using the same concept of natural configuration. Nonlinear compressible behaviour of the anode paste was represented by Helmholtz free energy and a dissipation potential was introduced to characterize the irreversible deformation process. They conducted experimental compression tests on anode paste in a thin-wall steel mold at 150 ºC to identify the model parameters. Then, the model was implemented in ABAQUS software to run finite element simulations. It’s reported that the proposed model, as also shown in Figure 2.9 (for the circumferential strain), successfully predicts the compaction curves of the anode paste.
Table of contents :
1.2. Metallic Aluminum Production
1.3. Raw Materials for Carbon Anodes
1.4. Anode Quality and Cost
1.5. Problem statement, project overview and objectives
2. Literature Review
2.1. Prebaked Carbon Anodes
2.1.1. Effects of coke properties on anode quality
2.1.2. Effects of pitch properties on anode quality
2.1.3. Rheological properties of anode paste
2.2.1. Theory and measurement
2.3. Numerical Methods in Modeling of Anode Paste and Similar Materials
2.3.1. Continuum Methods
2.3.2. Discrete Method
3. Discrete Element Method
3.1. Fundamentals of DEM modeling
3.2. Time integration and time-step issue in DEM
3.3. Burger’s Contact Model
4. Experimental Procedure
4.3.1. Vibrated Bulk Density (VBD)
4.3.2. Coke Particles Modeling
4.3.3. Making coke and pitch mixtures
4.3.4. Rheological characterization
4.3.5. Electrical resistivity measurement
5. Simulation of Vibrated Bulk Density of Anode-Grade Coke Particles Using Discrete Element Method
5.4. The Numerical Model
5.4.1. Principles of DEM
5.4.2. Movement of non-spherical particles
5.5. Materials and Methods
5.6. Results and Discussion
5.6.1. Friction coefficient estimation
5.6.2. Experimental and simulated Vibrated Bulk Density of coke particles
5.6.3. Effects of friction and sphericity
6. Packing Density of Irregular Shape Particles: DEM Simulations Applied to Anode-Grade Coke Aggregates
6.4. The Numerical Model
6.5. Case study
6.6. Experimental details
6.7. Results and Discussion
7. Discrete Element Method Modeling of Rheological Properties of Coke/Pitch Mixtures
7.6. Numerical Method
7.7. Results and discussion
7.7.1. DSR of Pitch and model verification
7.7.2. DEM simulation of coke/pitch pastes
8. Numerical Modeling of Compaction and flow of Coke/pitch Mixtures using Discrete Element Method
8.4. Numerical Modeling
8.5. Experimental Procedure
8.6. Results and Discussion
8.6.1. DSR experiments
8.6.2. DEM simulation of DSR tests
8.6.3. Compaction and flow modeling of pitch-coke and binder matrix-coke mixtures
9. Discrete Element Method Investigation of Bulk Density and Electrical Resistivity of Calcined Coke Mixes
9.4. Numerical Model
9.5. Experimental Procedure
9.6. Results and Discussion
9.6.1. Vibrated Bulk Density
9.6.2. Electrical Resistivity
10. Conclusions & Recommandations
10.1. Packing density of dry coke mixtures
10.2. Rheology of pitch and pitch/coke mixtures
10.3. Electrical resistivity of coke mixtures
10.4. Discrete element method and carbon anodes
10.5. Future works