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d e l o s C e m e n t o s

d e E n t r e n a m i e n t o A c e l e r a d o p a r a

S u p e r v i s o r e s d e P o z o

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e s l a c i e n c i a q u e e s t u d i a e l f l u j o y l a d e f o r m a c i n d e l a m a t e r i a .

e n C e m e n t a c i n :

E v a l u a r m e z c l a y b o m b e a b i l i d a d d e l e c h a d a s D e t e r m i n a r t a s a s d e d e s p l a z a m i e n t o a p r o p i a d o s p a r a u n a r e m o c i n d e l o d o e f e c t i v a y c o l o c a c i n d e l e c h a d a

E s t i m a r p r e s i o n e s d e f r i c c i n C a l c u l a r l o s H H P r e q u e r i d o s

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F l u j o d e F l u i d o s e n T u b e r a s

E n M e c n i c a d e F l u i d o s d o s t i p o s d e f l u j o s o nd e f i n i d o s :

1 . F l u j o L a m i n a r

2 . F l u j o T u r b u l e n t o

F l u j o T a p n e s u n f l u j o s u b - l a m i n a r

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F l u j o L m i n a r

M o v i m i e n t o S u a v e , d e s l i z a n t e ( * ) V e l o c i d a d e n l a p a r e d = C e r o V e l o c i d a d e s m x i m a e n e l c e n t r o V m a x = 2 V

A d o n d e V = V e l o c i d a d p r o m e d i a d e p a r t c u l a

V = 0

V = 0

V max

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F l u j o T u r b u l e n t o

M o v i m i e n t o T o r t u o s o

V e l o c i d a d p r o m e d i o d e l a p a r t c u l a e s u n i f o r m e at r a v e s d e l a t u b e r a

DIRECTION OF FLOW

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E L F l u j o d e l o s F l u i d o s

d e C o r t e = FA

V e l o c i d a d d e C o r t e d v = V 2 - V 1d r r

V i s c o s i d a d = = E s f u e r z o d e c o r t eV e l o c i d a d d e c o r t e

r

V2

F AA

AA

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NEWTONIAN or NON-NEWTONIAN..

Shear rate

LAMINARFLOW

TURBULENTFLOW

ShearStress

NEWTONIAN NON-NEWTONIAN

POWERLAW

BINGHAMPLASTIC

TRANSITION

ZONE

TRANSITION

ZONE

Stress

HERSCHELBULKLEY

d e F l u j o - C l a s i f i c a c i n d e F l u i d o s

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M o d e l o s d e F l u j o

P a r a r e p r e s e n t a c i n m a t e m t i c a , l o s s i g u i e n t e s m o d e l o s s o nu s a d o s :

1 . M o d e l o N e w t o n i a n o

2 . M o d e l o B i n g h a m p l a s t i c

3 . M o d e l o L e y d e P o t e n c i a( P s e u d o - P l a s t i c o )

4 . M o d e l o d e H e r s c h e l B u l k l e y

N e w t o n i a n

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M o d e l o N e w t o n i a n o

F l u i d o f l u y e t a n p r o n t o u n a f u e r z a e s a p l i c a d a E s f u e r z o d e C o r t e e s p r o p o r c i o n a l a l aV e l o c i d a d d e C o r t e

L a V i s c o s i d a d e s c o n s t a n t e = . d v

d r = v i s c o s i d a d = C o n s t a n t e

dvdvdrdr

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M o d e l o P l s t i c o d e B i n g h a m F l u i d o P l s t i c o d e B i n g h a m e s c a r a c t e r i z a d o p o r :

y : P u n t o C e d e n t e ( B i n g h a m y i e l d )

p : V i s c o s i d a d P l s t i c a

= y + p d vd r

= + pd v / d r

y

dvdr

a

p

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dvdr

RELACION EXPONENCIAL

dvdr

nK

Escala LOG-LOG :

El Fluido se caracteriza por:Indice de Comportamiento, nIndice de Consistencia, K

M o d e l o L e y d e P o t e n c i a

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M e d i c i o n e s d e l a s P r o p i e d a d e s d e l o s F l u i d o s

P R O P I E D A D E S M E D I D A S :

E s f u e r z o d e C o r t e

V e l o c i d a d d e c o r t e

F u e r z a d e G e l

E Q U I P O U S A D O :

F a n n V G 3 5 ( 6 v e l o c i d a d e s o 1 2 v e l o c i d a d e s )

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d e C i l i n d r o s C o a x i a l e s

Cilindro Interno

Eje

Rotor

Bob

Taza de Muestra

Resorte de Torsion

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V i s c o s i m e t r o F A N N

C a s i t o d o s t i e n e n 6 r o t a c i o n e s .

3 , 6 , 1 0 0 , 2 0 0 , 3 0 0 a n d 6 0 0 r p m .

L e c t u r a s 3 , 6 y 6 0 0 r p m , y a n o s o n u s a d o s e n l a s p r u e b a s A P I .

V e l o c i d a d r o t a c i o n a l e s p r o p o r c i o n a l a l a V e l o c i d a d e C o r t e

D e f l e c c i n d e l B o b e s p r o p o r c i o n a l a l E s f u e r z o d e C o r t e

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R e s i s t e n c i a d e G e lEl comportamiento reologico de los fluidos es tiempo-dependiente

)

Y i e l d p o i n t ( l b / 1 0 0 f t 2 )DECREASINGSHEARRATE

DECREASINGSHEARRATE

INCREASINGSHEARRATE

INCREASINGSHEARRATE

GELSTRENGTHGELSTRENGTH

YIELD POINTYIELD POINT

SHEARSTRESSSHEARSTRESS

SHEAR RATESHEAR RATE

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P r o c e d i m i e n t o s p a r a d e t e r m i n a r l a s P r o p i e d a d e sd e l o s f l u i d o s

R o t a r F a n n 3 5 a 3 0 0 r p m , 2 0 0 r p m y 1 0 0 r p m p o r 2 0 s e g c a d a l e c t u r a .

R e g i s t r a r d e f l e c c i n d e l B o b ( ) e n g r a d o s .

G r a f i c a r d e f l e c c i n v s r p m .

C o m p a r a r r e p r e s e n t a c i n g r f i c a c o n t e r i c a y d e t e r m i n a r e lm o d e l o r e o l o g i c o :

a . N e w t o n i a n

b . B i n g h a m P l a s t i c

c . L e y d e P o t e n c i a ( S i e s L e y d e P o t e n c i a , h a c e r g r f i c a L o g - L o g ) .

C a l c u l a r l o s p a r m e t r o s d e f l u i d o

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C o r r e c c i o n e s d e l e s f u e r z o y v e l o c i d a d d e C o r t e

= x SCF x 1002 )

dvdr

= rpm x

RBR =

22 260

.. RBR

-1

2 )n'

(

2 )n'

(n'R B R = R O T O R , B O B R A T I O

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F a c t o r C o r r e c c i n d e l R e s o r t e ( S C F )

0.2

0.5

1

2

3

4

5

10

0.002121

0.005302

0.0106

0.02121

0.03181

0.04241

0.05302

0.106

0.004181

0.01045

0.02091

0.04181

0.06272

0.08363

0.1045

0.2091

0.00848

0.0212

0.0424

0.0848

0.1272

0.1696

0.212

0.424

0.01831

0.04578

0.09156

0.1831

0.2747

0.3662

0.4578

0.9156

SPRING No.SPRING No.

BOB NoBOB No

11 22 33 44

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R o t o r - B o b R a t i o ( R B R )

1

2

3

BOB NoBOB No11 22 33

ROTOR NoROTOR No

1.068

1.5

2.136

1.022

1.544

2.04

1.5

3.107 3

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C a l c u l o s d e P r o p i e d a d e s d e F l u i d o s : N e w t o n i a n o

1. NEWTONIAN:

VISCOSITY =SHEAR STRESS

SHEAR RATE

= = x scf x 47880rpm x

(cp)

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E j e m p l o 1

C o n l o s s i g u i e n t e s d a t o s :

R P M L e c t u r a d e l D i a l ( )3 0 0 1 0 02 0 0 6 61 0 0 3 3

G r a f i c a r ( ) v e r s u s R P M y d e t e r m i n a r e l t i p o d e f l u i d o H a c e r u n a g r f i c a d e s h e a r r a t e C a l c u l a r l a v i s c o s i d a d d e l f l u i d o T o m a r S p r i n g N o 1 , B o b N o 1 a n d R o t o r N o 1

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S o l u c i n E j e m p l o 1

RPM

300

200

100

RPM

300

200

100

dv/dr

511

340

170

dv/dr

511

340

170

100

66

33

100

66

33

106

70

35

106

70

35

120120

100100

8080

6060

4040

2020

100100 200200 300300

xx

xx

xx

Newtonian: = dvdr

, = dv/dr

= x scf x 47880rpm x = 100 x 0.0106 x 47880

300 x 1.6991= 99.5 cp

or = dv/dr

= 106511

x 47880100

= 99.3 cp

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C a l c u l o s P r o p i e d a d e s d e F l u i d o : P l s t i c o d e B i n g h a m

2. BINGHAM PLASTIC:

(a) y = (intercept) x scf x 100

Plastic viscosity =(1 - ) x scf x 47880

rpm1- rpm

where slope of straight line curve

(b)

rpm1- rpm

( )( 1 - )==

(cp)(

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M e t o d o S i m p l i f i c a d oa. BINGHAM PLASTIC

p = (300 - 100) 1.5

y = 300 - p

b. POWER LAW

n' = 2.16 Log (300 / 100)

K'= scf x 300 x 1.068(511) n'

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E j e m p l o I I

D a d o l a s s i g u i e n t e s l e c t u r a s :

F A N N R P M L e c t u r a d e l D i a l ( )3 0 0 1 3 0

2 0 0 9 6

1 0 0 6 3

G r a f i c a r ( ) v e r s u s r p m y d e t e r m i n a r e l t i p o d e f l u i d o ( m o d e l o ) H a g a u n a g r f i c a d e l a v e l o c i d a d d e c o r t e v s E s f u e r z o d e C o r t e

C a l c u l a r l a s p r o p i e d a d e s d e l f l u i d o

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S o l u c i o n E j e m p l o I I

100100

120120

140140

2020

4040

6060

8080

100100 200200 300300

X

X

X

= x scf x 100

(300 100

x 1.5 = 130 - 63 x 1.5 = 100.5 cp- ))

= y + p x dv/drdv/dr = rpm x =

(300 100 ) scf x 47880(p =

(300 - 100) x 1.6991

S x scf x 47880==

1.6991

2 POINT METHOD:

S = slope

...... y = 30 x 0.0106 x 100 = 31.8 lbf/100ft22

SLOPE = 130 - 63

300 - 100= 0.335 = 100.06 cp

0.335 X 0.0106 x 47880

1.6991... p =..

PLASTIC VISCOSITY: yp =dv/dr

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C a l c u l o s P r o p i e d a d e s d e F l u i d o : L e y d e P o t e n c i a

3 . L E Y D E P O T E N C I A :( a ) n = p e n d i e n t e h o r i z o n t a l d e l a c u r v a

( b ) k = 1 0 x s c f

D O N D E I = I n t e r c e p t c u a n d o l o g r p m = 0

P a r a c a l c u l o s d e F l u j o u n K m o d i f i c a d o e s u s a d o , q u e e s K m u l t i p l i c a d o p o r u n f a c t o r d e c o r r e c c i o n d e a c u e r d o a S a v i n s .

))K'(pipe) = K'K'(pipe) = K'(3n' + 1)(3n' + 1)

4n'4n'

n'n'

((

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D e r i v a c i o n d e K = K' dv

drn'

= x scf , dvdr

= rpm x

x scf = K' (rpm x )n'

I = Log K' + n' log - Log scf

K' = 10I x scfn'

10 I = K' x n'scf

K' = 10Log I x scf

n'

Log + log scf = Log K' + n' log rpm + n' Log

Note: If plot is made on Log-log paper,

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E j e m p l o I I I

D a d o e l s i g u i e n t e :

F A N N R P M D I A L L E C T U R A

3 0 0 5 6

2 0 0 4 7

1 0 0 3 5

U s a n d o e l m e t o d o g r f i c o , d e t e r m i n e e l t i p o d e f l u i d o y c a l c u l a r l o s p a r m e t r o s r e o l o g i c o s d e l f l u i d o .

B o b N o 1 , R o t o r N o 1 , S p r i n g N o 1

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S o l u c i n E j e m p l o I I I

6060

5050

4040

3030

2020

1010

100100 200200 300300

xx

xxxx

rpm11 22 33

11

22

0.610.61

xxxxxx

Log

Log rpm

Log

1.75

1.67

1.54

Log

1.75

1.67

1.54

RPM

300

200

100

RPM

300

200

100

Logrpm

2.47

2.30

2.0

Logrpm

2.47

2.30

2.0

56

47

35

56

47

35

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S o l u c i n E j e m p l o I I I

0.033 lbf sec /ft

INTERCEPT = 0.61

n' = 0.46 BEHAVIOUR INDEX

10I x scfIK' =

()'( '

==2 2

60

= 1.84=

0.46 -1-1

.. ..1.068 0.460.46

22(( ))

0.460.4622(( ))

1.068

Consistency Index, K' =10 0.61 x 0.0106

1.840.46

= n'n 2

GRADIENT = 0.46

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S o l u c i n E j e m p l o I I I

K' (pipe) = K' 3n' + 14n'

n'

= 0.033 3 x 0.464 x 0.46

0.46

= 0.037 lb f sec n'/ft2

1+

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U n i d a d e s d e c a m p o

1. Shear ratedv

drDifference of vel. b/w 2 platelets

==( )) Distance b/w 2 platelets1

1sec -1-1 (Reciprocal second)==

2. Shear StressForce causing the shearSurface area of the platelet

= lbf/100ft 22

==

3. Apparent viscosity = Shear StressShear rate = lbf/100ft 2

Note: 1 poise = 100 centipoise = 0.2089 lbfsec/100ft22

4. Spring Correction factor scf = lbf/ft2

5. Bob Deflection = = degrees

6. Power Law Index = n' (dimensionless

7. Consistency Index = K' = lbfsn/ft2

2

n/ft

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C e m C A D E

A c t u a l m e n t e , s e u s a e l C e m C A D E p a r a :- D e t e r m i n a r e l m o d e l o i d e a l - C o n s t r u i r l o s g r a f i c o s r e o l o g i c o s

N u e v o m o d e l o r e o l o g i c o : H e r s h e l l B u k l e y

> > > = + k ( ) n

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D e f i n i c i o n e s . E s f u e r z o d e C o r t e ( S h e a r S t r e s s ) F u e r z a p o r u n i d a d d e r e a ( p r e s i n d e b o m b e o o c a d a d e l ap r e s i n e n e l f l u j o ) C a u s a q u e e l f l u i d o f l u y a a u n a v e l o c i d a d V 1 , c u a n d o l a V 2 = 0 . E l e s f u e r z o d e c o r t e e s u n i f o r m e a t r a v e s d e l f l u i d o y p u e d e ns e r e x p r e s a d o c o m o l i b r a s f u e r z a p o r p i e s c u a d r a d o s od i n a s p o r c e n t i m e t r o c u d r a d o .

M a r c h 1 0 , 2 0 0 4 J B

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D e f i n i c i o n e s . V e l o c i d a d d e C o r t e ( S h e a r R a t e ) G r a d i e n t e d e v e l o c i d a d ( m e d i d a d e l a v e l o c i d a d r e l a t i v a e n t r e l a s d o s p l a c a s E x p r e s a d a e n s e g u n d o s r e c p r o c o s ( s e g - 1 ) . S i n e m b a r g o l a v e r d a d e r a v e l o c i d a d d e c o r t e s e p u e d e e s t i m a r p o r a r r i b ad e u n 2 0 % u s a n d o l a v e l o c i d a d d e c o r t e d e u n f l u i d o n e w t o n i a n o .

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D e f i n i c i o n e s . V i s c o s i d a d A p a r e n t e . E s l a r e l a c i n e n t r e e l e s f u e r z o d e c o r t e y l a v e l o c i d a d d e c o r t e d e e lf l u i d o U n a p r o p i e d a d q u e d a l a f u e r z a n e c e s a r i a p a r a m o v e r e l f l u i d o d e t e r m i n a d o . E s u n a m e d i d a d e l a r e s i s t e n c i a i n t e r n a q u e o f r e c e e l f l u i d o a l f l u j o d e b i d oa s u s f u e r z a s i n t e r n a ( f r i c c i o n a l y e l e c t r o s t a t i c a ) . P a r a l o s f l u i d o s n e w t o n i a n o s d o n d e l a r e l a c i o n e n t r e e l e s f u e r z o yv e l o c i d a d d e c o r t e e s c o n s t a n t e , l a v i s c o s i d a e s a b s o l u t a . P a r a l o s f l u i d o s n o N e w t o n i a n o s e l e s f u e r z o y l a v e l o c i d a d d e c o r t e n o e s c o n s t a n t e y l a v i s c o s i d a d e s l l a m a d a v s i c o s i d a d a p a r e n t e y e s v l i d a s o l op a r a l a v e l o c i d a d d e c o r t e m e d i d a . L a v i s c o s i d a d p l s t i c a e s l a p e n d i e n t e d e l a p o r c i n d e l n e a r e c t a d e le s f u e r z o d e c o r t e y l a v e l o c i d a d d e c o r t e o b s e r v a d a c o n l o s f l u d o s p l s t i c o s d e B i n g h a n y e s c o n s t a n t e .