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MATLAB as a ool as Analysis and P oblem Sol ing
Compe ency De elopmen in Chemical Enginee ing
Deg ee using MATLAB
Ma ía-Fe nanda López-Pé ez, S.C. Ca dona, J. Lo a, A. Abad
Depa amen o de Ingenie ía Química y Nuclea . Uni e si a Poli ècnica de València
(UPV). Plaça Fe àndiz i Ca bonell, s/n 03801 Alcoy, Alican e (Spain).
* Co esponding au ho : Email: [email p o ec ed].es; Phone: + 34 966528586
Recei ed: 2016-05-06; Accep ed: 2016-08-18
Abs ac
Analysis and sol ing p oblems is a Chemical Enginee ing s uden capabili y.
In o de o de elop his abili y, ac i i ies ha encompass p oblem-sol ing by
s uden s may in ol e p oblems in eal-wo ld se ings.
In Chemical Enginee ing deg ee, MATLAB is a nume ical so wa e package
ha helps in he p ocess o designing, e alua ing and implemen ing a s a egy
o answe an open-ended ques ion o achie e a desi ed goal. In his con ex ,
Ma lab is so wa e used in p ocess simula ion. Se e al lec u es o Escuela
Poli écnica Supe io d’Alcoi p esen ed an inno a ion and imp o emen
educa ional esea ch p ojec (PIME) in o de o used MATLAB, like
coo dina ion eaching ool be ween some subjec s.
The p incipal pu pose o his wo k is he s uden s imp o emen using, as has
been men ioned p e iously, MATLAB in a p oblem-based lea ning
me hodology. This me hodology allows a mo e e ec i e coo dina ion in he
deg ee. The p esen pape p esen s a eal- wo ld p oblem and he common
elemen s o mos p oblem-sol ing con ex s and how is designed o unc ion
ac oss all disciplines.
Keywo ds
Analysis and sol ing p oblems, p oblem-sol ing lea ning, MATLAB,
coo dina ion
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1. In oduc ion
Due o he p o ound change ha mus ake place in lea ning in he uni e si y con ex , he
mos impo an s ep is educa ion-based aining and e alua ion o compe encies. The UPV,
in line wi h he Bologna p ocess has launched a numbe o s a egies o e alua ing hem,
s a ing wi h gene ic compe encies, linked o nume ous subjec s o uni e si y deg ees (V.
Yepes, 2014).
The gene ic compe encies ha ha e de ined he UPV a e:
• Unde s anding and in eg a ion.
• Implemen a ion and p ac ical hinking.
• Analysis and p oblem sol ing.
• Inno a ion, c ea i i y and en ep eneu ship.
• Design and p ojec .
• Teamwo k and leade ship.
• E hical, en i onmen al and p o essional esponsibili y.
• E ec i e communica ion.
• C i ical hinking.
In he p esen case, he gene ic compe ency o be ea ed in his wo k is he compe ence o
Analysis and P oblem sol ing. Acco ding o he UPV, his compe i ion can be de ined as
"analyze and sol e p oblems e ec i ely, whe e signi ican elemen s a e iden i ied and de-
ined”. Th ee le els o complexi y can be es ablished: i s demons a ion p o iciency,
p oblem sol ing using knowledge lea ned in he class oom o in books. A second le el,
which is de eloping i s own c i e ia in o de o sol e he p oblems, using e lec ion and
expe ience. And a hi d, mo e de eloped, when he s uden is able o de elop and p opose
solu ions in unusual and un amilia opics (A Villa, 2007). In he Deg ees, he equi ed
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le els would be he i s wo, he i s le el o yea s 1s and 2nd and he second le el o
de elopmen would be aken in o 3 d 4 h. The nex le el would co espond o Mas e
s udies.
The subjec s need a coo dina ion ollowing EEES amewo k (C. A mengol, 2009). This
coo dina ion mus be add essed bo h ho izon ally and e ically le el, ocusing on
coo dina ion o con en and e alua ion o speci ic and gene ic subjec compe encies o he
same cou se o special y, and ensu e he co ec dis ibu ion o esou ces (D. Cazo la, 2010;
JF Mo ales, 2013). This equi es a lo o dedica ion on he pa o academic commi ees o
Deg ee and his complex wo k mus be well planned, so ha he c ea ion o ools o
acili a e he coo dina ion wo k will be needed (Y. Ga cia, 2013).
In he case o Enginee ing, he use o ma hema ical models ha desc ibe he beha io o
p ocesses is an impo an pa o he basic knowledge ha a s uden mus possess (S.C.
Ca dona, 2014). In enginee ing, he use o ma hema ical so wa e o s uden aining (J.M.
Gonzal ez, 2013) is necessa y and essen ial. Because he ma ke he e a e many so wa e
o sol ing ma hema ical models, a wide dispe sion o so wa e o he same pu pose
appea s, a s uden manages di e en so wa e o each subjec o sol e p oblems in a ious
a eas, bu ac ually use he same nume ical me hod (e.g., sol ing o dina y di e en ial
equa ions). One consequence o using wo o mo e so wa e o he same pu pose du ing
he deg ee is ha he s uden doesn’ domina e any o hem, because he ime is limi ed.
This lack o eache coo dina ion in he use o so wa e could cause g ea unce ain y o
s uden s abou he pu pose o he ma hema ical ools and ha educe ime o lea ning he
con en s o each subjec .
The e o e, he use o he same gene al pu pose ma hema ical so wa e can be a ool o
coo dina ion and in eg a ion o he con en s o many o he deg ee subjec s and his ool
could enhance a wo king me hod based on p oblem-examples (Ma ia-Fe nanda Lopez-
Pe ez, 2012.2013), o s eng hen he gene al compe ency de elop.
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A P ojec o Inno a ion and Educa ional Imp o emen o se e al eache s has been aised
o eal coo dina ion in he Deg ee o Chemical Enginee ing, and enhance analysis and
p oblem sol ing compe ency. The pu pose o he p ojec en i led "Using MATLAB as a
eaching s a egy and ho izon al and e ical coo dina ion be ween subjec s Chemical
Enginee ing Deg ee" is he use o his so wa e as a eaching ool ha se es as a link
be ween subjec s. To imp o e coo dina ion be ween he subjec s and pose a eaching
me hodology based on p oblem sol ing is he main objec i e.
2. P oposed me hodology: in eg a ion o di e en eaching me hods
In his P ojec , wo king me hod based on p oblem-examples ha ein o ce con en s ha
a e impo an in he applica ion o chemical enginee ing, using MATLAB as an in eg a ion
ool is he main objec i e.
Fo his, se e al asks we e de eloped:
1. In ol e Chemical Enginee ing Deg ee lec u es using single ma hema ical so wa e in
hei subjec s in he complex ma hema ical calcula ions.
2. Con e he s uden in an ad anced use in MATLAB.
3. De elop a lea ning me hodology based on ans e sal p oblems ha allows s uden s o
achie e he analysis and p oblem sol ing compe ency.
4. P omo e coo dina ion o he con en s o di e en subjec s, bo h ho izon ally and
e ically in he di e en cou ses. The coo dina ion p o ides g ea e cohesion o he deg ee.
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3. Discussion o he p oposal and esul s
3.1 Pa icipa ion o in e es ed lec u e s
The nex s ep was o in ol e di e en lec u es who each a he Chemical Enginee ing
Deg ee o pa icipa e in his coo dina ion p ojec using MATLAB. This ma hema ical so -
wa e would be used in p oblem sol ing and also should coo dina e he subjec con en s by
sol ing a complex p oblem in o de o he compe ency.
The subjec s we e a o al o eigh (Table 1), om he i s yea o ou h, whe e he equi ed
le el o knowledge and he ma hema ical complexi y inc eased.
Table 1. Subjec s in o Coo dina ion p ojec using MATLAB.
Subjec
Cha ac e
Yea
Semes e
Ma hs II
Basic o ma ion
1
B
Calcula ion me hods
Obliga o y
2
A
Chemical Kine ics
Obliga o y
2
B
Mass ans e
Obliga o y
2
B
Chemical eac o s
Obliga o y
3
A
Expe imen al Chemical Enginee ing II
Obliga o y
3
A
Analysis and simula ion o p ocesses
Obliga o y
3
B
Biological was ewa e ea men
Elec i e
4
B
The e o e, all subjec s we e adap ed o he eache s. The eache used MATLAB o sol e
p oblems. Because some eache s did no ha e he su icien le el ma hema ical so wa e,
se e al wo kshops we e conduc ed. Th ee wo kshops we e suppo ed by he Ins i u o en
Ciencias de la Educación (ICE) and we e augh by a deg ee o Chemical Enginee ing,
eache wi h high knowledge in MATLAB.

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3.2 S uden s as ad anced use s in MATLAB.
In some subjec s, du ing he deg ee, (Expe imen al Enginee ing I, II, and III) s uden s ha e
planned MATLAB wo kshops. In hese wo kshops, a manual a e gi en o s uden s, wi h
he mos ep esen a i e MATLAB unc ions in o de o be used in sol ing he p oblems o
he cou se.
These wo kshops o e he possibili y ha s uden s lea n MATLAB along he deg ee, which
acili a es s uden s each educa ional compe encies. The e o e, he basic con en s
assimila ion in he subjec s o he deg ee is imp o ed. Also, be e cohesion in he
de elopmen o he i le is achie ed. Finally, s uden s will lea n, along he i le, an ad anced
le el in nume ical/symbolic so wa e, which will p o ide added alue he deg ee;
p o essional ma ke app ecia es his knowledge.
3.3 Analysis and p oblems sol ing compe ency de elopmen
All asks ha ha e been discussed abo e mus be e lec ed in he con en s o he deg ee
subjec s. Chemical enginee ing examples o p oblems will inc ease di icul y while
s uden s ad ance in hei s udies o achie e he compe encies.
The e o e, o he de elopmen o Analysis and p oblems sol ing compe ency, p oblem-
based lea ning me hodology we e used. This ype o lea ning has he highes "lea n o sol e
p oblems by sol ing p oblems". These p oblems mus be app op ia e o he le el o he
cou se, and should ca ee o managemen s a emen s, should be mo i a ing o he o ma ion
and de elopmen o concep s is acili a ed.
S uden s pe cei ed cohesion o con en and ue coo dina ion when he concep s a e ela ed
o eal examples along he cou ses, s uden s could also unde s and he concep s in a mo e
e ec i e way, inc easing hei mo i a ion o he subjec s.
Fi s , a complex p oblem ha is esol ed in semes e B du ing 4 h cou se was chosen. Tha
p oblem was he design o a Sequencing Ba ch Reac o SBR.
This p oblem is e y complex, since he design o such eac o s implies knowing:
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 Bac e ia ha emo e con aminan s, espi a ion and kine ics o mic oo ganism
g ow h.
 Kine ic o biodeg adable o ganic ma e .
 Oxygen ans e p ocess om he gas phase o he liquid
The e o e, in eac o design he s uden mus possess concep s s udied in many o he abo e
subjec s. This subjec s and concep s coo dina ion is e y di icul .
The p oblem s a emen migh be:
“In a milk company in --- own, SBR eac o is going o be ins alled o emo ing pollu an s
ha discha ged in o he was ewa e sewe . The discha ge low is 200 L/d and he con ol
pa ame e s discha ge mus be below discha ge limi s. Design he eac o ( olume) and
ope a ional pa ame e s”.
As you can see he s a emen is comple ely open, so ha each eache can adap i o you
needs and pu poses.
To be e unde s and how he p oblem a ises, we will be de eloping subjec by subjec ,
wha a e he p oblems associa ed wi h he design o he SBR and ha can be esol ed in
each o hem, hei complexi y and how o ela e wi h o he s.
Remembe ha o 1s and 2nd cou se, analysis and p oblem sol ing compe ency include
iden i y and analyze a p oblem o gene a e al e na i e solu ions. Fo 3 d and 4 h cou se he
le el o esul s equi ed inc eases, in which he s uden mus use he expe ience and
judgmen o analyze he causes o a p oblem and build a mo e e icien and e ec i e
solu ion.
In he i s cou se s uden s will deal wi h concep s ha should ha e o design he bio eac o .
The subjec Ma h II; as is well known is a discipline ha some imes is a s umbling block
o s uden s. Ma h is di icul , bu also s uden s do no see he use ul in he eal li e. In he
p esen case, sol ing sys ems o di e en ial equa ions a e needed o he de elopmen o
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SBR eac o design, because i is a ba ch p ocess whe e he a iables change o e ime.
One o he hema ic uni s in Ma h II is o dina y di e en ial equa ions and hei analy ically
sol ing.
When he ma h concep s ha e been explained, he p oblem can be p esen ed o he s uden .
Bu , his p oblem should be p esen ed as a eal si ua ion, he eache explain he impo ance
o was ewa e ea men and he used eac o s o his pu pose. The lec u es each
was ewa e p oblem can be he ma h lec u e o a pe son amilia wi h was ewa e ma e .
Some ideos o biological eac o ope a ion could be p esen ed. The ideo leng h would
be a maximum o 15 minu es, because he subjec can’ be in alida ed.
A his poin he eache will gi e he bac e ia g ow h di e en ial equa ion, oxygen and
pollu an a ia ion di e en ial equa ions. Such p ocesses can be modeled and a e o dina y
di e en ial equa ions which can be sol ed analy ically (Laplace). A he i s he eache
uses only a a iable, i can bac e ia, o la e , o e s he s uden s a mo e complex p oblem
, which a ies no only bac e ia a iable, bu also he subs a e and oxygen, hen he eache
p esen s he comple e sys em o o dina y di e en ial equa ions (Eq. sys em 1).
 
02
11
1
1max
1
1
1
*
2
02
11
1
1max
011
11
1
1max
1
1
CC(0)
1
·
)0( )(
)0(
1
)(












endoTOTAL
H
S
O
HH
endoH
H
S
H
H
S
OX
SK
S
Y
Y
CCKla
d
Cd
XX OX
SK
S
d
dX
SSX
SK
S
Y
d
dS

(Sis . Eq. 1)
Whe e S1 is subs a e, XH a e he e o ophic bac e ia and C is oxygen concen a ion.
All cons an s nume ic alue is p o ided, because he aim objec i e is he sys em esolu ion
and no he physical concep s.
When s uden s sol e he p oblem on he pape manually, he p oblem should be sol ed wi h
MATLAB, wi h he ele an unc ions, dsol e o ODE. The eache has seen a e y simple
esolu ion and a eal applica ion o he subjec .
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The nex subjec is Calcula ion Me hods in Chemical Enginee ing (2nd yea , semes e A),
whe e equa ions and sys ems o o dina y di e en ial equa ions a e sol ed nume ically by
he me hods o Eule , Runge-Ku a and mul is ep. In his poin , bo h subjec , Ma h II and
Calcula ion Me hods a e ela ed. The same p oblem can sol e wi h MATLAB, now
nume ically, once s uden s ha e lea ned o sol e sys ems manually. I is in e es ing ha
s uden s lea n o do wi h MATLAB and can see he sa ings in ime. In hese wo subjec s
hey ha e lea ned concep s and ha e go a way o sol ing sys ems wi h MATLAB. S uden s
ha e also seen he use ulness o he concep s lea ned.
In his momen , s uden s ha e seen he ma hema ical pa o he SBR eac o design, so ha
enginee ing concep s can be in oduced. In o de o make a ma hema ical model, whe e
he e a e chemical eac ions, he eac ion a e has o be s udied o ob ain a kine ic equa ion
whe e ela es he eac ion a e wi h ope a ional condi ions and composi ion.
- A=[K(T)][ (CA,CB,…) (eq. 2)
– A is eac ion a e (mol/l.·h), K is a cons an (is Tempe a u e unc ion) and CA, CB, eac i e
concen a ion.
Calcula ion o he kine ic cons an and he eac ion o de a e desc ibed in his subjec .
MATLAB is used in his subjec o sol e hese p oblems, using in e pola ion as poly i o
linea izing. S uden s ha e expe imen al da a o kine ic equa ion esol e, e.g. O ganic
ma e educ ion o bac e ia ac ion.
The e a e se e al models, such as: he i s o de model Monod. Speci ic a e cons an
(usually exp essed by k) is ob ained in i s o de kine ics, while o he model Monod,
h ee cons an s ha e o be e alua ed: he a ini y cons an (Ks), he speci ic a e (μmax/Y)
and inally, he maximum g ow h cons an (μ). In his pa , he eache would gi e s uden s
expe imen al da a (subs a e concen a ion e sus ime), and s uden s could use he
equa ions p esen ed abo e o ob ained hese cons an s using MATLAB.