SOLVING VESSEL EQUATIONS.pdf

8/11/2019 SOLVING VESSEL EQUATIONS.pdf

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gineering book, such as Perrys Chem-ical Engineers Handbook, revealednothing useful for this problem.

We had better luck conducting In-

ternet-based research, but it was notuntil poring through many searchresults that we came across the fol-lowing article by Dan Jones Cal-culating Tank Volume (http://www.webcalc.com.br/blog/Tank_Volume.pdf). Also see (Chem. Eng., Sept. 2011,pp 5563).

Using the equations provided inJones article for practical calcula-tions proved to be a problem in itself.First, the equations had to be as-sembled in a sensible way to account

for all the shapes containing liquid inthe vessel. In addition, depending onthe level of the liquid you are workingwith, there are different equationsthat have to be used.

Another common frustration forchemical engineers is that the datafound online must be validated as well.Often with research conducted online,the reliability and validity of the the in-formation found is not clear or defined.Checking the validity of the equationsthat are found can be complicated. Tobe sure that an equation is validated,engineers may need to recalculate ev-erything from scratch which we did

CHEMICAL ENGINEERING WWW.CHE.COM JUNE 2013 31

The Tafel equation is an equation in electrochemical

kinetics relating the rate of an electrochemical reaction to

the overpotential. The Tafel equation was first deduced

experimentally and was later shown to have a theoretical

justification. The equation is named after Swiss chemist

Julius Tafel (1862-1918)

Tafel equation

GENERAL Tafel equation

Tafel Equation

+ x

010101

if

for linewhile

Arithmetic

Matrices

Boolean

Functions

Plot

Programming

Symbols

Plot

Vis the overpotential, V

Ais the so-called Tafel slope, V

iis the current denisity, A/m2and

i0is the so called exchange current density

Calc 1

NEW UPLOAD DOWNLOAD

Tafel diagram n vs log i

2

1

log i0

log i

0110

6110

5110

40.001

+

xx Calc 2x Calc 3x

V A i

i=

ln

0

fx

contributed by Jane Chemist

references Publication One, Publication Two is Longer

citations Electrochemical Methods, Fundementals and Applications

FIGURE 3. Cloud-based calculation tools can improve engineering workflow

Time

Conceptdevelopment

High-levelrequirements

Detailedrequirements

High-level

design

Detaileddesign

Scale-up, inte-gration and testing

Implementation

Subystemverification

Acceptance

Operation andmaintenance

Part/unit replacement

andprocess improvements

Initial design stages:sizing, conceptualizing,

material selection

Equation library(corporate/Wiki)

Databases(materials/components)

Life engineering calculation tools (SMath-based)

Optional PLM integration layervia API

Codes andstandardsFIGURE 2. A Web-based equation li-

brary can help in vessel calculations


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in this case and of course, it endedup costing us even more time.

Once we found and validated theequations and vessel dimensions, thenext step was to use a calculation tool

that is easy to integrate with the data.We first turned to Microsoft Excel,probably the most-often-used tool inmany engineers toolboxes. For mostcalculations and analyses, an Excelspreadsheet would suffice. Severalgenerations of engineers now havegrown up using Excel its a common,inexpensive software that is readilyavailable on most desktops and lap-tops. In addition to its familiarity, itsrelatively easy to input large amountsof data into Excel.

However, in this case of calculatingvolume in an irregularly shaped ves-sel, it was not. It became clear that itwould become an exceedingly time-consuming process just to enter theequations and variables.

Other reasons why Excel was not theright calculation tool in this case is thatprogramming is required with externaldata. Second, all calculations must beperformed in a consistent system ofunits with conversion factors embed-ded in equations. This is because Exceldoes not automatically understand theunits of measurement and does notsupport calculations in different unit

systems unless additional program-ming is introduced. Third, we plannedto create a browser-based application,but the Internet version of Excel hasexhibited performance issues and is

not highly rated by many users.Beyond Excel, there are engineer-

ing calculation tools available suchas PTCs (Needham, Mass.; www.ptc.com) Mathcad, which has automaticunit conversion and can check equa-tions for mathematical errors. How-ever, a browser version of Mathcad isnot available, and that limits its use-fulness in cloud-based applications.

SMathTo calculate the volume of a liquid in a

vessel of a complex shape, a task thatshould take only minutes, we testeda tool that is readily available onlineand that could integrate our data. Wefound an engineering desktop calcu-lation tool that is both powerful anddistributed free of charge SMathStudio (http://en.smath.info/forum/yaf_topics12_Download-SMath-Stu-dio.aspx).

SMath has a browser version calledSMath Live. While it is function-ally similar to the desktop version, itneeds further development. SMath,developed specifically for engineeringcalculations, is now used by thousands

of engineers and engineering studentsaround the world.

This tool consists of a powerful mathengine core, user-friendly worksheet-based graphical user interface (GUI)

and plug-ins some of which areopen source software that connectthe core with GUI. SMath has the fol-lowing features: The ability to handle numeric and

symbolic calculations Capabilities for 2-D and 3-D graphs Software versions designed for differ-

ent platforms and operating systems Partial support of Mathcad files

(*.xmcd) The ability to use mathematical units

(either built-in or user defined)

Multi-language worksheets Multi-language interface (28 lan-

guages) The capacity to use programming

functions directly on the worksheet Infrastructure to support third-

party plug-ins An auto-complete feature with de-

scription of all supported entries The ability to use the tool in collabo-

ration (via server) Equation snippets

Improved volume calculationsThe tools chemical engineers have attheir disposal are critical for main-

Cover Story

32 CHEMICAL ENGINEERING WWW.CHE.COM JUNE 2013

FIGURE 4. (AH) Various standard shapes that can be combined includecylinders, cones, ellipsis and hemispherical. The diagrams and equationsshow some of the possible situations for volume measurement that engi-neers might face

V Hh+Rhh

H

D

2

3H:=

where R :=

2

2

A. Conical top:

H

h

D

Vb

h H

6 R3 Rh:=

2

B. Elliptical head:

D

2where R :=

h

H

D

R

C. Elliptical bottom:

V h

3 H

D

R3 H h:=

2

2

2

2where R :=

h

H

D

R

Note: := means

is defined to be

Hh

W

L

D. Horizontal elliptical vessel:

V L (hb) (hb)hba

b:= b asin

22 2

+ bb

2+ b

2

H

2b :=

W

2where a := Note: := means

is defined to be


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taining high levels of productivity. Ide-ally, engineers should use tools thatare seamless, can save time, and avoidcostly errors in the workflow. One way

to accomplish this is through cloudcomputing, where software programsand data that have traditionally re-sided on company servers are now lo-cated on a third partys remote serversand are accessed via the Web.

Cloud computing assures todays en-gineers quick and easy access to datafrom anywhere on a variety of devices.It also allows engineers to easily sharedata with their peers across the globe.Fortunately, as technology continuesto move into the cloud, engineers will

have more effective and reliable toolsto integrate data, such as equationswith calculation software, into theirdesign and workflow.

Currently in the early stages of de-velopment, there is an engineeringcloud-based productivity tool (Figure2) comprising of SMath Live inte-

E. Hemispherical head:

Vb h

6 (1.5 D h):=

2

h

D

F. Hemispherical top:

h

D

V h

3 (D+ h):=

23

4

D

2

D

G. Horizontal cylinder:

D

R

L

h

V LRh

:= R acos (R h)2 2

R

D

2where R :=

2 R hh

H. Horizontal hemicylindtrical top:

R

L

h

V Lh

:= R acos h22 2 2

RR h0.5 R

CHEMICAL ENGINEERING WWW.CHE.COM JUNE 2013 33

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Cover Story

34 CHEMICAL ENGINEERING WWW.CHE.COM JUNE 2013

grated with a searchable and brows-able library of common engineeringequations, including those for par-tially filled shapes, that could help

you calculate liquid volume as a func-tion of liquid level much faster thanbefore. A chemical engineer coulduse this cloud-based product to findshapes and assemble them in any

reasonable combination to calculatethe volume of liquid in any partiallyfilled vessel. Such a product will beuseful when integrated into engineer-

ing workflow as an early-stage designtool. The stages of a typical engineer-ing workflow where this tool can beintegrated can be seen in Figure 3.

This type of Web-based product

would enable users to find and selectequations for various shapes and thenassemble them like Lego blocks ontoan SMath Live worksheet. If you are

working with any unusually shapedshells, bottoms or heads, you can buildany vessel from them using smallerpieces (Figure 4). You can continueto build up to more complex shapesand calculate the volume of the entireshape or the volume of liquid in par-tially filled shape. The same approachcould be used for calculating the vol-ume of dry particulates, suspensionsand so on.

Initial results are encouraging andcan be seen in Figure 1, which shows

an example of a calculation for a verti-cal cylindrical vessel with conical bot-tom and elliptical top. This examplewas assembled from calculations forthree basic shapes: cone bottom, el-liptical top and vertical cylinder. Eachcalculation contains limiting condi-tions and validation routines, as wellas graphic representation of a shape.These conditions and validation rou-tines are easily adoptable for the ves-sel shown in the example.

A prototype of this cloud-based

calculation tool is now underway. Webelieve that the future of engineer-ing will be characterized by toolsthat integrate data and calculationsoftware and are available in thecloud. Development and deploymentof these sophisticated tools will becritical for maintaining high levelsof engineering productivity in thechemical industry.

Edited by Scott Jenkins

Author

Sasha Gurke is engineer-ing technical fellow at KnovelCorp. (240 West 37th Street,New York, NY 10018; Email:[email protected]; Phone:617-803-8344). A chemist andchemical engineer, Gurke hasmore than 30 years of experi-ence in the technical infor-mation field. He co-foundedKnovel in 1999 and as senior

vice president, he was activelyinvolved in product development and manage-ment. Knovel was acquired by Elsevier in 2012,and Gurke continues to play an important rolein new product development and strategy. Priorto Knovel, he spent 15 years with Chemical Ab-stracts Service/American Chemical Society inproduct development and editorial positions.His industrial experience includes working as a

chemist at water treatment and paint manufac-turing plants. Gurke holds a masters degree inchemical technology from St. Petersburg StateUniversity of Technology and Design.

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