Recomendaciones - – SEGUIMIENTO, CONCLUSIONES Y RECOMENDACIONES

CAPITULO V – SEGUIMIENTO, CONCLUSIONES Y RECOMENDACIONES

5.3 Recomendaciones

The r e gression equa t i o n s d e s c r i b i n g t he cha r a c te r i s t i c s o f the s k im mi l k conc entr a te and the spr a y drier have been combined to form a c omput e r s i mul ation mod e l of the d r y i n g proc e s s. Th i s model may be us e d t o s imul ate a wide v a r i e t y o f drier ope r a t i n g modes a n d i ncorpo r a t e s provi sion for i n troduc ing c ha n g e s i n m i l k compo s i t i o n and pr e he a t treat- ment . The f o l lowing se c t ion e x amine s t he structure o f t h i s mode l whi le t he second sec t ion descr ibes t he s i mu l ation pro g ram .

5 . 1 - The Mod e l Str uc ture

A s t r uc t ural a r r a y s i m i l ar to that in Tab l e 3-3 was used to d e te r

m i n e t h e o r d e r in whi c h t he r e g r e ss i o n e qua t i o n s mus t b e so l v e d t o give t he unknown powde r prope r t i e s r e s ul ting f rom an y given se t of input v a r i ab l e s . T h i s order depe n d s o n whi c h o f t he input s are f i x ed , w h i c h a r e manipu l ate d and wh i c h are dependent o n t h e inputs a l r e a d y spec i f i e d . Some of the po ss i b l e opt ions a r e g i v en in Tab l e 5 - 1 . _The _{V d r l a b l e}

s ymbo l s a r e those o f Ta ble 3 - 1 . In b o t h c a s e s t he f o l l owing V d r l ab l e s a r e a s s umed t o have been fixed :

- mi l k compo s i t i o n - pre he a t t e mpe r a t ure - pre he a t ho l di ng time - drier a i r flowrate - the number of no z z l e s - the no z z l e o r i f i c e s i ze

- the no z z l e swi r l chamber or core

The options mar ked wi th a n a s t e r i s k

( * )

are use d in no z z l e a tomis i n g spra y d r ie r s . Re gar d l e s s o f whi c h opt i o n i s cho s e n ,· f i ve ope r a t i n g v a r i ab l e s m us t b e spe c i f ie d b e f o r e the produc t qua l i t y var i a b l e s c a n be c a l cul a ted . There a r e three d i f fe re n t se t s o f dependent var i a b l e s l i s t e d i n Tab l e S - 1 , s o the simulation mod e l s ho ul d have prov i s i o n for t h e f o l l ow i n g c a l c ulation s .

TABLE 5 - 1 Options for Operating Spr a y Dr ier s Op tion Deg rees o f Fixed No . F r eedom Variab l e s * ₄ 2 4 3 4 4 * ₃

_T

_c 5 * ₃ _{T c} 6 3

T

7 2

T ,

T _c 8 * ₂

T ,

T c

Vi sco s i ty sen s i t i v e no z z l e s ( 1 )

_p

f rom F , p ( 2 )

_}1

f rom TS , 'I c ( 3 )

_p

f rom TS ,

T

c Vi scosity insensi t i ve ( 4 ) P f r om F ( 5 ) F f r om P and then and then and then nozzles M a n ipul aterl varictbl e s

T ,

TS ,

F , p

T ,

TS ,

F , 'r

T ,

TS ,

P ,

'I

T ,

TS ,

F T ,

TS ,

p

TS ,

P ,

T

TS ,

p

T

f r om

_{p ,}

TS

c p f rom

_{p ,}

F F from

f '

p

8 1 Depe n d t= n t V a r i a b l e s

J-l t

T c.;

Jl t

p c

f '

F c

f '

Jl t

}l t

}J t

The conc entrate v i scosity i s a n intermed iate var i a b l e in the c a l c u l ati o n s and may b e c a l c ulate d f rom the concentr ate to tal so l i d s and t empe r a t ur e in the l a st two c a s e s e v en though i t is not r e qui r e d . Th i s s impl i f i e s the programmin g , a s t he n onl y t h e f i r st three c a s e s n e e d be c o n sidered .

The s i mul ation model a l so inc orporate s two out l e t a i r tempe r a t ur e contro l le r s. One man ip ul ate s the i n l e t a i r temperature and the o t he r man ipul ate s t h e conc entrate feedrate or atom i s i n g pre s s ur e .

The str ucture o f t he s i mulation prog ram i s i l l u s t r a te d i n F i g ur e 5 . 1 by means of a f l owc hart.

5 . 2

-

The Simulation Pr ogram

Eac h o f the mod ul e s s hown i n F i gure 5 . 1 w i l l now be con s i le r e d i n deta il. Some o f the regressio n mode l s g i v en i n Chapt e r 4 a r e used directly, but some fur the r a n a l y s i s wa s r e qu i r ed be f o r e all the n e c e s s a r y e qua t i o n s could be derived.

5 . 2 . 1 Th e Press ure , F l owrate , Viscosit y Re l a t i o n

The viscos i t y o f t he c o nc e n t r a te a t t he n o z z l e i s n o t t he same a s tha t me a s ured w i t h t he Contr a v e s v t scome te r a s t h e conc e n t r a t(' l e a ve s

the heat excha nger in t he feed l i n e t o the h i '::J h pressure pump . The a g e

a n d t empe r a tur e o f the conc e n t r a t e a r e d if f e rent, a n d the s h e a r r a te i s 1 0 0 0 t im e s grea te r at t he nozzle. U s i n g t he v i sco s i t y mod e l i n C hapt e r

4 to obta i n the viscosi ty a s a funct i o n o f t he conc e n t r a te tu tal sol i d s

a n d t empe r a ture , and then c a l c uJ a t 1. n g the p r e s s ure a t a g 1.v •2 n f l o<rn ate f rom t he no z z l e e qua tion gives ver y poor agreement with t he expe r i men t a l observations. Instead, a pseudo-visco sity w a s c a l c ul a ted f rom the p r e s s ur e and flowrate readin gs for t he two season's data as fo l l ows.

For the S B 5 4 noz z l e

P F 2 • 3 4 5 ( 2 . 3 6 7 9 + 5.3 0334 exp ( - 0 . 0 3 4 64

f ) )

x 1 0 -4

l n

( (

1 0 0 0 0 p 1 p 2 . 3 4 5 2.3 67 9) I 5 . 3 0 3 3 4 l

-0.03464

for a sugar sol ution with an average density 1 . 1 03 time s that of the concentrate . The pressures mea sured on concentrate wer e mul tipl i e d by 1 . 1 0 3 b e fore being used in this equation , on the assumption that at constant vol umetr ic flowrate , the pre s s ure i s directly proportional to t he fluid density ( Masters , 1 9 7 2 p . 1 7 0 )

MILK COMPO S I T ION

( % Prote i n )

SELECT OPTION

( 1 ) spe c i f y F , _P _{( 2 )} _sp_ecif y _{F ,} Tc ( 3 ) _{spe c i f y} _{P , Tc}

OPT ION 1

INPUT O PERAT I NG VARIABLES T , F , p ( 2 ) T , F , Tc

( 3 ) T , P , _Tc

CHECK E XP L I C IT CONS'l'kA I I'<T� ·rmi n < T < 'lma x _Tmin < T < Tmax

Fmi n < F < _Fmax ( 2 ) Fm � n _< F < Fma x Pmi n < p < _Pmax _{( 3 )}Pmi n < p < _{Pma x}

SOLVE NOZ ZLE E QUATION SOLVE V I SCOS IT Y E

Q

UATION

Get

p

f r o m F , _p G e t

p

f r om _{1'S ,}

Tc P r o te l n C HECK IMPL I C IT CONSTIU\ IN'l'S SOLVE NOZZLE E\._!U/\T l UN

p

}Jlll

i n _{( 2 )}_{Ge t} _p _{f r}_om

p ,

_F ( 3 ) Get F f rom

p ,

p SOLVE VISCOSITY E

Q

UATION

CHECK I l'IP L I C IT CONSTRA I N T S

Ge t Tc f rom

p ,

'l'S I Pr ote i n

( 2 ) Pml r1 < p < _Pmax ( 3 ) Fmin < F < Fmax

SCALE T , TS , F , P , Tc

SOLVE QUALI T Y EQUATIONS

Ge t moi s ture , S I , bulk densi t y f r om T , ·rs , F ,

ADD MEASUREMENT NOI SE AND ROUND ING

POWDER QUALITY

FIGURE 5 . 1 A Flowc ha r t o f the Drier Simul at ion Mode l P , T

8 4

5 . 2 . 2 The V i scosity , To tal So l id s , Tempe ra ture Re l ation

The pse udo- viscosity c al c ul ate d above wa s then regre s s e d against t h e c oncentrate total sol ids , tempe r atur e and prote i n content to g i v e :

P '

1 8 . 4 6 + 7 . 4 0 TS - 8 . 54 T _c+ 2 . 5 0 T 2 - 0_c .8 2 T . TS c

- 0 . 4 5 Prot - 1 . 1 9 T S . Pr ot - 1 . 64 Prot 2 cp

w i t h 0 . 6867 and roo t mean square r e s i dua l 5 . 1 cp .

wher e TS total solids - 4 7 . 7

) I

T H i gh pr e s s ur e cone . temp. - 43 . 7

₎

_I

1 0 c

a n d Prot Prote in - 3 9 . 7 4

Th i s model wa s s i gn i f i c an t l y better tha n one i n wh i c h the natur a l l o ga r i t hm of t h e vi scos i t y wa s used a s the re sponse var i ab l e , but the rms of the r e s i dua l s wa s s t i l l 2 2 % of t he mean pse udo- v i sco s i t y .

Th i s pse udo- vi scosity pa s s e s through a minimum a s t he tempe r ature o f the concentr ate is rai sed . The tempe ranure wh i c h m i n im i s e �. the v i s co s i ty is found by s e t t i n g to zero the f i rst der ivative of t he e qua t i o n with r e spect to tempe r a t ure , g i v in g :

Tc ( min

p'l

( 0 . 82 T S + 8 . 54

) I

( 2 X 2 . 5 0 )

The min imum v i s c o s i t y may now b e cal cul ate d , and used to check for an impl i c i t constr a i n t violation whe n opt ion 1 of the simul ation pro g ram i s cho s e n. I n thi s option the conc e n tr a te f l owr a te and atom i s i n g pre s s ur e are s pe c i f i e d , so t h a t the pse udo- vi sco s i t y may be c a l c ul ated f rom the noz z l e e qua t ion . F i gure 5 . 2 gives the e qua ti o n s use d in the s i mul ation mod e l for each of t he three opt i on s .

5 . 2 . 3 The Powder Qual i t y Equa t io n s

T h e e quations p r e s e n t e d in Chapter 4 a r e use d to c a l c ul a te the moistur e , So l ub i l i t y In dex , b ul k d en s i t y and othe r qua l i t y v ar i ab l e s . The t hr o ughput o f m i l k sol i d s i s a l so c a l c ul ated at t h i s s t a g e , using t he f o l lowing equa t i o n .

8 5

p

989 + 0 . 0 1 6 6 T S2 - ₍ ₀_._{0 0 7 6} _T _{- 3 . 7 5}

)

_{T S}

c c

(

0 . 0 64 + _{0 . 0 0 2 4} _T ) _T

c c

where Pc concentrate dens i ty ( k g/m3 )

TS conc entrate total sol i ds

_{( % )}

T _c concentrate temperature ( C )

T h i s i s a r e gression e qua tion f i tted to the data o f Ha l l a n d Hed r i c k 3

( 1 9 6 6 ) with t he i

n

te rcep

t

( 9 89 kg/_m ) a_{d J}u_{s t}ed _to g i ve bette r a g reement w i th data from New Ze a l and s k i m m i l k concen t r a te s . The so l l d s throughput

i s then :

G F

( p

/ 1 0 0 0 ) ( T S/ 1 0 0

)

c k g / h whe r e F i s i n 1/h.

Thi s quanti ty is needed i f t he proce s s i n g r

a te

s o f t he d r i e r a n d

e va po r a tor a r e t o b e matched. At the evapor a tor f i n a l e f f e c t temp-

e r at ur e of 44 C , the tota l s o l i d s - d en s i t y e q ua t ion is approx imate l y :

In document Factibilidad para el traslado y la mejora de la planta operativa de la comercializadora avícola Andrea en Bogotá (página 69-78)