ajustes - regresion lineal y cuadratica

0.00

0.01

0.02

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0.63

-0.5

-0.5

-0.4

-0.4

-0.3

-0.3

-0.2

-0.1

-0.1

0.0

0.0

0.1

0.1

0.2

0.2

0.3

0.3

0.4

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0.5

0.5

0.6

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0.7

0.7

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0.8

0.9

0.9

1.0

1.0

1; 0.387

2; -0.257

1; 0

2; 0.387

1; -0.257

2; 0.652

1; 0

2; 0.652

1; 0.846

2; -0.257

1; 0.985

2; -0.257

1; 0.408

2; -0.257

1; 0

2; 0.846

1; 0.018

2; 0.237

1; 0.985

2; 0.408

1; 0.3332; 0.302

3; 0.2724; 0.242

5; 0.2136; 0.182

7; 0.1498; 0.115

1; 0

2; 0.387

1; -0.257

2; 0.652

1; 0

2; 0.652

1; 0.846

2; -0.257

1; 0.985

2; -0.257

1; 0.408

2; -0.257

1; 0

2; 0.846

1; 0.018

2; 0.237

1; 0.985

2; 0.408

1; 0.3332; 0.302

3; 0.2724; 0.242

5; 0.2136; 0.182

7; 0.1498; 0.115

1; 0

2; 0.387

1; -0.257

2; 0.652

1; 0

2; 0.652

1; 0.846

2; -0.257

1; 0.985

2; -0.257

1; 0.408

2; -0.257

1; 0

2; 0.846

1; 0.018

2; 0.237

1; 0.985

2; 0.408

1; 0.3332; 0.302

3; 0.2724; 0.242

5; 0.2136; 0.182

7; 0.1498; 0.115

1; 0

2; 0.387

1; -0.257

2; 0.652

1; 0

2; 0.652

1; 0.846

2; -0.257

1; 0.985

2; -0.257

1; 0.408

2; -0.257

1; 0

2; 0.846

1; 0.018

2; 0.237

1; 0.985

2; 0.408

1; 0.3332; 0.302

3; 0.2724; 0.242

5; 0.2136; 0.182

7; 0.1498; 0.115

NUMERO DE ETAPAS

VSLINEA 1LINEA 0COINSIDIENDO 1:LINEA 2LINEA 3LINEA 4LINEA 5LINEA 6LINEA 7VSLINEA 1LINEA 0COINSIDIENDO 1:LINEA 2LINEA 3LINEA 4LINEA 5LINEA 6LINEA 7VSLINEA 1LINEA 0COINSIDIENDO 1:LINEA 2LINEA 3LINEA 4LINEA 5LINEA 6LINEA 7VSLINEA 1LINEA 0COINSIDIENDO 1:LINEA 2LINEA 3LINEA 4LINEA 5LINEA 6LINEA 7LINEA 8

FRACCION PESO SOLUTO

FRAC

CIO

N P

ESO

SO

LVEN

TE

POR CUESTIONES REDONDE EN DECIMALES SE CONSIDERA 4 ETAPAS

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80.50

0.51

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

0.60

0.61

0.62

0.63

CONCENTRACION DE SOLUTO

Fn

DATOS DE PRUEBA COMPOSICION CALCULADA

1/Fn

Lb/Lb intertes fraccion masa underflowSOLUTO solvente

underflow SOLUTO SOLVENTE

0.500 2.000 0.000 0.000 0.500 1.500 0.000 0.3330.505 1.980 0.100 0.051 0.455 1.505 0.034 0.3020.515 1.942 0.200 0.103 0.412 1.515 0.068 0.2720.530 1.887 0.300 0.159 0.371 1.530 0.104 0.2420.550 1.818 0.400 0.220 0.330 1.550 0.142 0.2130.571 1.751 0.500 0.286 0.286 1.571 0.182 0.1820.595 1.681 0.600 0.357 0.238 1.595 0.224 0.1490.620 1.613 0.700 0.434 0.186 1.620 0.268 0.115

SOLU/INT 0.06

SOLV/INT 0.43857143SOLV/INT SOLV/INT

0.238 0.357INSERTAR

0.186 0.434

SOLIDO SOLIDO LIXIVIADO

CANTIDAD 1425 CANTIDAD 1498.571SOLUTO 400 0.281 SOLUTO 60.000 0.040

SOLVENTE 25 0.018 SOLVENTE 438.571 0.293INERTE 1000 0.702 INERTE 1000 0.667

SOLUCION LIXIVIADA SOLUCION LIXIVIANTE

CANTIDAD 591.429 CANTIDAD 680SOLUTO 350.000 0.592 SOLUTO 10 0.015

SOLVENTE 241.429 0.408 SOLVENTE 655 0.963

2105 = 2090

85

PERDIDA 15

SOLIDO%

CANTIDAD 1425.000SOLUTO 400.000 0.281 28.070

SOLVENTE 25.000 0.018 1.754INERTE 1000.000 0.702 70.175

SOLIDO LIXIVIADO%

CANTIDAD 1498.571SOLUTO 60.000 0.040 4.004

SOLVENTE 438.571 0.293 29.266

SOLUCION LIXIVIADA%

CANTIDAD 591.429SOLUTO 350.000 0.592 59.179

SOLVENTE 241.429 0.408 40.821

SOLUCION LIXIVIANTE%

CANTIDAD 680.000SOLUTO 10.000 0.015 1.471

SOLVENTE 655.000 0.963 96.324

POR REGRESION LINEAL

Fn = (Lb solucion/Lb

inertes)

CONCENTR

SOLUTO/SOLUCION

SOLUTO/ inertes

solvente/ inertes

FRACCION MASA

FRACCION MASA

FRACCION MASA

FRACCION MASA

RECUPERACION

FRACCION MASA

FRACCION MASA

FRACCION MASA

FRACCION MASA

BALANCE GENERAL

ABxnFn 1

SALETONENTRATON __

DONDE:A = 2.036B = -0.577

ENTOCNES: 1/Fn = 2.036 + -0.577 Xn

DESPEJANDO "X" :

α = 0.060

X = 0.118

Fn = 0.508

1.338

a = 10.377

b = -13.614

c = -1.027

13.258

10.733

V1=

β1 =

β2 =

n

menor

mayor

menor

mayor

menor

mayor

blixiviantesolsolutodeley

blixiviantesolsolutodeley

badescsolutodeley

badescsolutodeley

)()()____(

)()()____(

)()()arg___(

)()()arg___(

ABxnFn 1

))((

))((

toninerteFn

tonperdidatonsolutoX

)(

))((*)(

eleydeinert

tonperdidatoleydelsoluBxAX

)(

))((

eleydeinert

tonperdidatoleydelsolu

B

AX

1

)_)((

___1 inertestonFn

lixiviantesoldetonV

)1)((

))(_____)((

1

1

VB

BlixiviantesolensolutodeleyVAa

)1)((

))(())((

1

1

VB

XBVAb

)1)((

)_____)(()()(

1

1

VB

lixiviantesolensolutodeleyVXAc

2

4)()( 2 cbaba

menor

mayor

menor

mayor

menor

mayor

blixiviantesolsolutodeley

blixiviantesolsolutodeley

badescsolutodeley

badescsolutodeley

n

log

)()()____(

)()()____(

)()()arg___(

)()()arg___(

log

ϴ = 0.029

ɸ = 0.070

δ = 1.235

n = 4.152

SOLIDO LIXIVIADO SOLIDO LIXIVIADO

SOLIDO LIXIVIADO CANTIDAD 1593.02899 CANTIDAD 1549.25317CANTIDAD 1425 SOLUTO 350.947105 0.22030177 SOLUTO 217.650283

FRACCION MASA

FRACCION MASA

menor

mayor

menor

mayor

menor

mayor

blixiviantesolsolutodeley

blixiviantesolsolutodeley

badescsolutodeley

badescsolutodeley

n

log

)()()____(

)()()____(

)()()arg___(

)()()arg___(

log

)()()arg___(

)()()arg___(

menor

mayor

badescsolutodeley

badescsolutodeley

)()()____(

)()()____(

menor

mayor

blixiviantesolsolutodeley

blixiviantesolsolutodeley

menor

mayor

log

log

n

SOLUTO 400 0.28070175 SOLVENTE 242.081881 0.15196326 SOLVENTE 331.60289SOLVENTE 25 0.01754386 INERTE 1000 0.62773497 INERTE 1000

INERTE 1000 0.70175439 SOLU TOTAL 593.028986 SOLU TOTAL 549.253173SOLU/INT 0.59302899 SOLU/INT 0.54925317

0.571 0.5 0.53 0.30.595 0.6 0.55 0.4

SOLUCION LIXIVIADA SOLUCION LIXIVIANTE SOLUCION LIXIVIANTECANTIDAD 591.428571 CANTIDAD 759.457557 CANTIDAD 715.681744SOLUTO 350 0.59178744 SOLUTO 300.947105 0.39626586 SOLUTO 167.650283

SOLVENTE 241.428571 0.40821256 SOLVENTE 458.510452 0.60373414 SOLVENTE 548.031461

DATOS DE PRUEBA COMPOSICION CALCULADA

1/Fn

Lb/Lb intertesSOLUTO solvente

underflow SOLUTOSOLVENTE

0.500 2.000 0.000 0.000 0.500 1.500 0.0000.505 1.980 0.100 0.051 0.455 1.505 0.034 0.3330.515 1.942 0.200 0.103 0.412 1.515 0.068 0.3020.530 1.887 0.300 0.159 0.371 1.530 0.104 0.2720.550 1.818 0.400 0.220 0.330 1.550 0.142 0.2420.571 1.751 0.500 0.286 0.286 1.571 0.182 0.2130.595 1.681 0.600 0.357 0.238 1.595 0.224 0.1820.620 1.613 0.700 0.434 0.186 1.620 0.268 0.149

0.115

SOLIDO LIXIVIANTE

CANTIDAD 1425.000FRACCION

SOLUTO 400.000 0.281SOLVENTE 25.000 0.018% INERTES 1000.000 0.702

SOLUCION LIXIVIANTE

CANTIDAD 665.000FRACCION

SOLUTO 10.000 0.015SOLVENTE 655.000 0.985

SOLUCION LIXIVIADA

CANTIDAD 591.428571FRACCION

SOLUTO 350.000 0.592SOLVENTE 241.429 0.408

% RECUPER. 85.000

BASE DE CALCULO 100.000 KgSOLUTO EN EL SOLIDO LIXIVIANTE 28.070 Kg

SOLVENTE EN EL SOLIDO LIXIVIANTE 1.754 KgINERTE EN EL SOLIDO LIXIVIANTE 70.175 Kg

total 100.000 Kg

Descarla del Underflow contiene: SOLU/INT 0.0685 % RECUPERACION15 % RECIRCULANTE

INSERTE DATOS PARA

ITERPOL

FRACCION MASA

FRACCION MASA

Fn = (Lb solucion/Lb

inertes)

CONCENTR

SOLUTO/SOLUCION

fraccion masa

underflow

SOLUTO/ inertes

solvente/ inertes

1º 2º

inertePeso

solutopesoperdidasolutoKg

_

)_*(%_

Kg soluto = 0.00375

PESO DEL SOLVENTE EN LA DESCARGA 4.211

10% * Peso del Solvente en el underflow de alimentado

Interpolacion en la tabla

soluto solvente

0.000 0.3330.004 x 0.32958088 solvente/ inertes0.034 0.302

SOLUCION LIXIVIANTECOMPONENTES Kg Fracción

SOLUTO EN EL SOLIDO LIXIVIANTE 4.211 0.043SOLVENTE EN EL SOLIDO LIXIVIANTE 23.128 0.237

INERTE EN EL SOLIDO LIXIVIANTE 70.175 0.720

total 97.514 1

Composición del OverflowENTRANTE SALIENTE

COMPONENTES % Frac Masa % Frac MasaSoluto 1.471 0.015 59.179 0.592

Solvente 98.529 0.985 40.821 0.408TOTAL 100.000 1.000 100.000 1.000

ORIGEN LINEA DE OPERACIÓNX 0 1 0Y 0 0 1

ECUACIONES DE RECTAS

LINEA 1

Y = 1 + -1 X

PRIMERA LINEA

Y = 0 + 5.493 X

COINSIDIENDO 1: LINEA 1 Y PRIMERA LINEA

X = 0.154Y = 0.846

LINEA 2

INSERTE DATOS

inertePeso

solutopesoperdidasolutoKg

_

)_*(%_

Y = -0.335 + 1.256 X

LINEA 3

Y = 1.372 + -26.275 X

COINSIDIENDO 2: LINEA 2 Y LINEA 3

X = 0.062Y = -0.257

LINEA 4

Y = -1.000 + 11.988 X

LINEA 0

Y = 0.277 + -0.925 X

COINSIDIENDO 3: LINEA 4 Y LINEA 0

X = 0.099Y = 0.186

LINEA 5

Y = 0 + 1.876 X

COINSIDIENDO 4: LINEA 5 Y LINEA 1

X = 0.348Y = 0.652

LINEA 6

Y = -0.454 + 3.184 X

COINSIDIENDO 4: LINEA 6 Y LINEA 0

X = 0.178Y = 0.112

LINEA 7

Y = 0 + 0.631 X

COINSIDIENDO 5: LINEA 7 Y LINEA 1

X = 0.613Y = 0.387

LINEA 8

Y = -0.330 + 1.169 X

COINSIDIENDO 6: LINEA 8 Y LINEA 0

X = 0.290Y = 0.009

LINEA 9

Y = 0 + 0.032 X

COINSIDIENDO 6: LINEA 9 Y LINEA 1

X = 0.969Y = 0.031

LINEA 10

Y = 0 + 0.317 X

)1)((

)_____)(()()(

1

1

VB

lixiviantesolensolutodeleyVXAc

SOLIDO LIXIVIADOCANTIDAD 1498.571SOLUTO 60

SOLVENTE 438.571429INERTE 1000

SOLIDO LIXIVIADO SOLIDO LIXIVIADO

CANTIDAD 1520.13788 CANTIDAD 14950.14048723 SOLUTO 121.843633 0.08015301 SOLUTO 51.7977508 0.03464732

FRACCION MASA

FRACCION MASA

FRACCION MASA

0.21404048 SOLVENTE 398.294252 0.26201192 SOLVENTE 443.202249 0.296456350.64547229 INERTE 1000 0.65783506 INERTE 1000 0.66889632

SOLU TOTAL 520.137884 SOLU TOTAL 495 SOLU TOTALSOLU/INT 0.52013788 SOLU/INT 0.495

0.515 0.2 0.505 0.10.53 0.3 0.515 0.2

SOLUCION LIXIVIANTE SOLUCION LIXIVIANTECANTIDAD 686.566456 CANTIDAD 661.428571

0.23425256 SOLUTO 71.8436327 0.10464192 SOLUTO 1.79775078 0.002717980.76574744 SOLVENTE 614.722823 0.89535808 SOLVENTE 659.630821 0.99728202

SOLUCION LIXIVIANTECANTIDAD 680SOLUTO 10

SOLVENTE 655

INSERTE DATOS PARA

ITERPOL

INSERTE DATOS PARA

ITERPOL

INSERTE DATOS PARA

ITERPOL

FRACCION MASA

FRACCION MASA

FRACCION MASA

3º 4º

0.040038130.292659680.66730219

SOLIDO LIXIVIADO

CANTIDAD 1500SOLUTO 1.35899087 0.00090599

FRACCION MASA

FRACCION MASA

SOLVENTE 498.641009 0.33242734INERTE 1000 0.66666667

SOLU TOTAL 500SOLU/INT 0.5

0.5 00.505 0.1

SOLUCION LIXIVIANTECANTIDAD 666.428571SOLUTO -48.6410091 -0.07298758

SOLVENTE 715.069581 1.07298758

0.014705880.96323529

INSERTE DATOS PARA

ITERPOL

FRACCION MASA

FRACCION MASA

5º

y x X^2 x*y0.500 2.000 0.000 0 00.505 1.980 0.100 0.01 0.19800.515 1.942 0.200 0.04 0.38830.530 1.887 0.300 0.09 0.56600.550 1.818 0.400 0.16 0.72730.571 1.751 0.500 0.25 0.87570.595 1.681 0.600 0.36 1.00840.620 1.613 0.700 0.49 1.1290suma 14.672 2.800 1.400 4.893

m = -0.57704989b = 2.035943567

y = -0.57704989 x + 2.035943567

REGRECION LINEAL

22 )()(

))((

xxn

yxxynmpendiente

n

xmybcióner

)(secint

bmxy

X Y XY0.000 0.333 0.000 0.000 0.000 0.0000.034 0.302 0.001 0.000 0.000 0.0100.068 0.272 0.005 0.000 0.000 0.0180.104 0.242 0.011 0.001 0.000 0.0250.142 0.213 0.020 0.003 0.000 0.0300.182 0.182 0.033 0.006 0.001 0.0330.224 0.149 0.050 0.011 0.003 0.0330.268 0.115 0.072 0.019 0.005 0.031

n 0.000 0.000 0.000 0.0008 0.000 0.000 0.000 0.000S 1.021 1.808 0.192 0.041 0.009 0.181

0.128 0.226 0.024 0.005 0.001 0.023

1.808 = 8.000 a + 1.021 b0.181 = 1.021 a + 0.192 b0.030 = 0.192 a + 0.041 b

DESARROLLANDO POR MATRICES

8.00000 1.02086 0.19159 1.808421.02086 0.19159 0.04078 0.181220.19159 0.04078 0.00930 0.03022

1.56467 0.19966 0.03747 0.353701.56467 0.29365 0.06250 0.277761.56467 0.33301 0.07592 0.24682

1.56467 0.19966 0.03747 0.353700.00000 0.09399 0.02503 -0.075940.00000 0.03936 0.01343 -0.03094

1.56467 0.19966 0.03747 0.353700.00000 0.00370 0.00099 -0.002990.00000 0.00370 0.00126 -0.00291

1.56467 0.19966 0.03747 0.353700.00000 0.00370 0.00099 -0.002990.00000 0.00000 0.00028 0.00008

X2 X3 X4

1/nS

Ajuste de una función parabólica: Y* = a + b X + c X2

X cXb XaYX

X cXb XaXY

Xc X b Na Y

4322

32

2

c = 0.294b = -0.886a = 0.332

Y = 0.332 + -0.886 X + 0.294

2X c + X b +a = Y

0.0000.0000.0010.0030.0040.0060.0070.0080.0000.0000.0300.004

+ 0.192 c+ 0.041 c+ 0.009 c

X2Y

X cXb XaYX

X cXb XaXY

Xc X b Na Y

4322

32

2

X2

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700

-0.200

0.000

0.200

0.400

0.600

0.800

1.000

1.200

1; 0.373

2; -0.107

1; 0.373

2; 0.000

1; 0.501

2; -0.107

1; 0.501

2; 0.000

1; 0.625

2; -0.107

1; 0.625

2; 0.000

1; 0.744

2; -0.107

1; 0.744

2; 0.000

1; 0.857

2; -0.107

1; 0.857

2; 0.000

1; 0.294

2; 0.106

1; 0.408

2; -0.107

1; 0.963

2; -0.107

1; 0.408

2; 0.963

Chart Title

overflowSOLUTO vs SOLVENTELINEA 1LINEA 2AJUSTE LINEA 3LINEA 4LINEA 5LINEA 6LINEA 7LINEA 8LINEA 9LINEA 10LINEA 11LINEA 12

overflowSALIENTE ENTRANTE

SOLUCIONSOLUTO 0.592 0.015

SOLVENTE 0.408 0.963

underflowSALIENTE ENTRANTE

AJUSTEMINERAL SALIENTE ENTRANTESOLUTO 0.043 0.281 0.043 0.281

SOLVENTE 0.237 0.018 0.294 0.106

ORIGENX 0.000Y 0.000

ECUACION:

Y = 0.332 + -0.886 X + 0.294

DONDE:

Y: PORCENTAJE MASA DE SOLVENTEX: PORCENTAJE MASA DE SOLUTO

ECUACIONES DE RECTAS

overflow

Y = -0.962 X + 0.977

underflow

Y = 0.332 + -0.886 X + 0.294

AJUSTE

Y = -0.791 x + 0.329

LINEA 1

Y = -23.491 X + 1.309

LINEA 2

Y = 0.970 X + -0.166

INTERSECCION GENERAL

X 0.060Y -0.107

LINEA 3

Y = 6.818 X + 0.000

INTER 1 overflow Y LINEA 3

X 0.126Y 0.857

LINEA 4

Y = 14.748 X + -0.996

INTER 2 AJUSTE Y LINEA 4

X 0.085Y 0.261

LINEA 5

Y = 3.062 X + 0.000

INTER 3 overflow Y LINEA 5

X 0.243Y 0.744

LINEA 6

Y = 4.661 X + -0.388

INTER 4 AJUSTE Y LINEA 6

X 0.131Y 0.225

LINEA 7

Y = 1.708 X + 0.000

INTER 5 overflow Y LINEA 7

X 0.366Y 0.625

LINEA 8

Y = 2.395 X + -0.252

INTER 6 AJUSTE Y LINEA 8

X 0.182Y 0.184

LINEA 9

Y = 1.013 X + 0.000

INTER 7 overflow Y LINEA 9

X 0.495Y 0.501

LINEA 10

Y = 1.401 X + -0.192

INTER 8 AJUSTE Y LINEA 10

X 0.237Y 0.141

LINEA 11

Y = 0.593 X + 0.000

INTER 9 overflow Y LINEA 11

X 0.629Y 0.373

LINEA 12

Y = 0.845 X + -0.158

X2

X2