reología de las lechadas de cemento
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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 .
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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 .
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