Introduction

Mechanical stability

Once candidate lining materials have beenselected based on chemical stability in theprocess environment, the designer mustensure that the lining system is mechanicallystable. Mechanical stability is traditionallydetermined by ensuring that the hot facerefractory layer is in compression through alloperating conditions and that the stresses donot exceed the material’s failure strength.

An equally important consideration is thecalculated overlap between the brick lining andthe membrane. This new stability factorrequires that the overlap should be positive,

that is, that the steel shell should be in contactwith the refractory lining throughout alloperating conditions. A negative overlap (i.e.gap) between the brick lining and themembrane could have the followingconsequences:

➤ Liquid can accumulate in the gap; rapiddepressurization could vaporize thisliquid, leading to high stresses on theback of the brick lining

➤ The brick and the shell would no longerbe acting together during processvariations. The brick lining could shift,inducing high stresses when the steelshell depressurizes

➤ In the case of lining systems where thebrick lining is bonded to the membrane(such as with a fibreglass-reinforcedvinyl ester lining), a calculated gapwould induce tensile stresses in themembrane, possibly leading to failure ofthe membrane (note that the classicalstress calculations are in the hoopdirection, not the radial direction).

Based on these mechanical stabilitycriteria, the component strains and stressesmust be calculated for all operating conditions.This is undertaken first in one dimension, thenas required, in two and three dimensions toaccount for more complicated shapes.

One-dimensional spreadsheet model

Initially in the design process, one-dimensional thermal conduction and stressanalyses are completed with a spreadsheetbased on classic stress models. Some of theparameters considered for the one-dimensionalanalysis include:

Fundamentals of designing refractorylinings for hydrometallurgy autoclavesby A. Koning*

SynopsisPressure hydrometallurgy operations require vessels to be lined withan impermeable membrane for corrosion protection and one or morecourses of refractory or ceramic brick. Examples of unit operationsthat utilize composite lining systems include pressure oxidationautoclaves, sulphide precipitation autoclaves, chloride leach reactors,flash vessels, cyclone separators, and direct contact condensers(heater vessels and quench vessels). The refractory lining mustsatisfy multiple requirements: it must thermally insulate themembrane from process fluid, be structurally stable, provide erosionresistance, be chemically compatible with process fluid, and providean economic service life.

New hydrometallurgical processes are pushing the pressure, andtemperature with each new generation of plants. A fundamentalunderstanding of all factors affecting the mechanical stability of thelining system is essential as lining designs move further away fromthe industry’s experience base.

The method of designing a refractory lined vessel is examinedtaking into account the impact of irreversible chemical swell,operating factors, design factors, and installation factors. The effectof geometry and incorporating additional degrees of freedom to theanalysis is explored using two-dimensional and three-dimensionalfinite element analysis (FEA). The effect of these additional degreesof freedom on the results of the one-dimensional model arediscussed.

Keywordsrefractory lining design,autoclave, finite element analysis.

* Hatch Associates, South Africa.© The Southern African Institute of Mining and

Metallurgy, 2013. ISSN 2225-6253. This paperwas first presented at the, Refractories 2013Conference, 23–24 April 2013, Misty Hills Country Hotel and Conference Centre, Cradle ofHumankind, Muldersdrift, South Africa.

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Fundamentals of designing refractory linings for hydrometallurgy autoclaves

➤ Modelling thermal conduction and stress in cylindricalcoordinates (r, θ, z)

➤ Placing mortar layers between brick in a given layer➤ Including properties that are not temperature/pressure-

dependent, such as brick chemical swell➤ Calculating the brick/mortar lining separately from the

membrane/shell lining so that the theoretical overlapbetween the brick lining and membrane can bedetermined

➤ Pre-stressing the lining, either by adjusting the shelltemperature or brick temperature during installation

➤ Considering the membrane cure temperature➤ Breaking the layers into several sub-layers so that

temperature- and process-dependent values (such asthermal expansion coefficient and chemical swell) canbe incorporated into the appropriate sub-layer

➤ Incorporating an installation gap, such as thatpotentially occurring when the layer of insulating paperinstalled between a lead-lined shell and the brick layersdissolves.

The one-dimensional spreadsheet model allows manyparameters to be evaluated quickly. A wide variety ofvariables can be changed independently. The spreadsheetprovides the following benefits:

➤ Sensitivity analyses—Most brick properties are notaccurately known. Either there is no test standardwhich accurately reflects the in-service conditions orthere is wide variability in manufactured properties dueto the nature of the raw material supply andbrickmaking process. Spreadsheets provide a means ofdetermining rapidly the sensitivity of temperature andstresses to material properties

➤ Material selection—For each process plant there will bespecific lining requirements. The spreadsheet allowsrapid determination of the key mechanical designvariables so that materials can be properly selected

➤ Installation specifications—The conditions duringinstallation can influence the mechanical stability of thelining during operation and shutdown. The requirementfor specific installation conditions such as the shelltemperature and brick temperature can be determinedand specified to the installation contractor

➤ Operating conditions—Wide variations in operatingconditions can be modelled. These provide guidelinesfor incorporation into the operating and maintenancemanuals.

The approximate thicknesses of the refractory aredetermined within the one-dimensional spreadsheet prior toproceeding with FEA modelling.

The use of FEA in vessel design

One-dimensional calculations assume a cylindrical vessellining that is thin relative to the radius of the vessel. Theaddition of attachments, supports, nozzles and hemi-heads,or thick-walled vessels to the analysis requires considerablymore complex mathematical analysis. A designer must resortto finite element analysis (FEA) in these cases as exactformulae are difficult or impossible to obtain. FEA increasesthe number of degrees of freedom of the one-dimensionalanalysis by allowing heat to flow in multiple directions and

allowing the material to move in multiple directions. An FEAanalysis will highlight hot-spots in the vessel or stressconcentrations that will lead to failures. The designer canthen focus on these hot-spots or stress concentrations andparameters such as gaps, geometry, and material selection inorder to eliminate the hot-spots or stress concentrations.

Two-dimensional FEA analysis

The primary drawback to a full three-dimensional FEA modelis that it is more time-intensive than one-dimensionalanalysis, as a geometry must be built in three dimensionsand meshed. An intermediate step between the one-dimensional analysis and the full three-dimensional analysisis a two-dimensional axisymmetric model, where thegeometry and boundary conditions are assumed to berevolved 360° about an axis. This model is relatively easy toconstruct and is used primarily to determine nozzle sizingand insert layout before proceeding to a three-dimensionalmodel. A typical axisymmetric model for a nozzle is shown inFigure 1. In this example the membrane temperature variesfrom 93°C on the flange face to 90°C at the nozzle and vesselbody interface to 70°C within the vessel body. A designer canmodify the thickness and type of materials used and theirlocation to reduce these temperatures to acceptable levels.

Three-dimensional FEA analysis

Once the vessel has been sized in accordance with coderequirements and the nozzles have been sized in accordancewith process flow, thermal membrane temperature, and coderequirements in a two-dimensional analysis, a full three-dimensional model is created. In Figure 2 the geometry of ahorizontal autoclave operating at 200°C is shown with itsassociated mesh. The model consists of steel, membrane, gap,and brick materials. With the three-dimensional model,interferences between components and weights of thedifferent components are easily calculated.

In order to determine the thermal profile within thevessel, material properties and thermal loads are assigned.The thermal conductivity of each of the materials is enteredas it varies with temperature. When the thermal model is

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Figure 1—Two-dimensional axisymmetric model of nozzle with thermalprofile

solved, the thermal conductivity of the material at a particularlocation is based upon the temperature of that material atthat location. The convection coefficient on the inside andoutside is also varied with the temperature of the surface thatthe heat is flowing from or into. With thermal imaging wecan calibrate the material properties and loading conditions.For known materials, the results of thermal FEA analysis areextremely accurate.

Owing to the three-dimensional nature of the modelbelow, heat flows towards the junction between the nozzleand the vessel body from the inside of the nozzle and thevessel itself. It is because of the heat flux coming frommultiple directions that we see an increased temperature atthe junction between the nozzle and the vessel body. Inaddition, the proximity of nozzles to each other allows heatto come from adjoining nozzles which creates localized hot-spots between the nozzles. In Figure 2, although the vesselbody temperature is 50°C, the junction between the nozzleand the vessel body is at 70°C. The designer is at liberty tomove nozzles and change materials and thickness in order toreduce these localized hot-spots.

With the addition of heat capacitance the model can besolved in a transient manner in order to determine the heat-up time required. The transient model and the thermal modelare subsequently used in the stress analysis.

Once the thermal analysis has been completed, themechanical properties varying with temperature are placed inthe model. Loads or combinations of loads including pipingloads, gravity, hydrostatic head due to vessel contents,internal pressure or vacuum, thermal expansion, and swellare applied to the mesh and the stresses and distortionswithin the vessel are calculated.

In the vessel shown in Figure 3 the stress analysisreveals that there are localized compressive stress concen-trations on the hot face of the nozzle/body juncture in thebrick lining. There are also tensile localized stresses betweenthe nozzle and body on the cold face. This is confirmed byinspections of failed brick linings. The use of thicker shellmaterials instead of repads, gaps, and self-reinforced nozzlescan help to reduce these stresses.

DIN 28 060 stipulates the dimensional tolerances forbrick-lined vessels. This standard is very useful fordetermining the allowable distortions in the fabricated vessel,but does not take into consideration the distortions resultingfrom the applied loads, which can be several magnitudeshigher that the DIN 28 060 standards. In addition, the ASMEcode will provide a vessel which is acceptable, but due tosteel stress and fatigue levels may not provide a uniformsupport frame for the brick lining. An area of interest is theknuckle in a hemi-head. The knuckle is a high stress area forthe vessel and is often allowed to yield during hydrotesting.The distortion of the steel shell in the knuckle can compoundthe already high stresses in the brick lining. The use ofthicker shell materials instead of repads in the head of thevessel can reduce the stresses in the knuckle area of thevessel.

In addition to the nozzle and vessel-body juncture, thehead and supports are known to be localized points forfrequent brick-lining failures. These failures can be attributedto the vessel steel shell restraining the brick lining unevenly,which causes excessive tensile stresses on the cold face of the

brick lining and compressive stresses on the hot face. InFigure 4, for example, a vessel is supported at eight locationsby a ring beam. If the support points are not allowed toexpand with the addition of thermal expansion and pressurethe vessel will not deform uniformly. This would in turncause stresses on the lining. These stresses on the lining canbe reduced with the use of gaps, sliding supports, or differentgeometries for the support. Similar effects are seen withsaddle supports around horizontal autoclaves.

FEA allows the designer to compare different materialsand geometries to determine the primary stressors for thelining system. To aid in these comparisons the models arebuilt parametrically. Through these comparisons, thedependence of the model results on geometry and materialcan be determined. In particular, while the material propertiesfor steel are well known, the material properties for ceramics,especially chemical swell, are not well documented. This willlead to inaccuracies in the magnitudes of the stresses, butwill still allow one to compare different designs and thenselect the best designs given all material properties being thesame. After the vessel has been built, the model can be

Fundamentals of designing refractory linings for hydrometallurgy autoclaves

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Figure 2—Membrane temperature within autoclave

Figure 3—First and third principal stresses around nozzles

Figure 4—Distortion in shell due to fixed support

Fundamentals of designing refractory linings for hydrometallurgy autoclaves

calibrated with strain gauges attached to the vessel steel shelland then compared to the calculated values.

Conclusions

With the aid of computers, more comprehensive calculationsare being completed prior to the construction of brick-linedvessels. The use of FEA has given the designer a way ofpredicting thermal profiles more accurately than the classicalone-dimensional analysis. The use of gaps, swell, and three-dimensional geometry can now be balanced to engineer amore stable and reliable brick lining system.

References

FALCKE, F.K. and LORENTZ, G. 1985. Handbook of Acid-Proof Construction. VCHVerlagsgesellschaft, Weinheim, Germany, pp.163–171.

KONING, A. and LAUZON, P. 2004. Design fundamentals for hydrometallurgypressure vessel refractory lining. Pressure Hydrometallurgy 2004: 34thAnnual Hydrometallurgy Meeting of CIMI. Papangelakis, V. and Collins,M. (eds).: Canadian Institute of Mining, Metallurgy and Petroleum.Montréal. pp. 617–638.

LAUZON, P., KONING, A., AND DONOHUE, I. 2008. Stress development in refractorydue to the rate of temperature change: a pressure vessel refractory liningconsideration. Southern African Hydrometallurgy Conference 2009.Southern African Institute of Mining and Metallurgy, Johannesburg. pp. 57–64. ◆

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