Composite Washing of Coals fromComposite Washing of Coals fromMultiple SourcesMultiple Sources

dr kalyan sen, Director,dr kalyan sen, Director,Central Fuel Research Institute,Central Fuel Research Institute,

Dhanbad, 2001Dhanbad, 2001

Actual ProblemActual Problem

Washery

Engineer

Management Customer

More Quantity

Best Quality

what is optimizationwhat is optimization ? ?

To maximize or minimize the objective functionTo maximize or minimize the objective function

Objective Function

Maximize

or

Minimize

Max --- Yield, Quantity, Profit, etc.Max --- Yield, Quantity, Profit, etc.

Min --- Undesired product, Loss, Production cost, etcMin --- Undesired product, Loss, Production cost, etc

Optimization parameters

Variable that governs the objective function.

Like, temperature, pressure, concentration, mass, density, etc.

Obj. function = function (Opt. Parameters)

Types of Problem

Linear

Non-linear

Unconstrained

Constrained

Multi level multi variable

Problems

in the

Coal preparation plants

Problems

Variation of raw coal sources

Deterioration of feed coals

Evaluation of Wash. Charac. & Size distribution

Frequent variation in feed

Control of Individual Eqpt.

Variation in product

Quality

Quantity

ResultingResulting

How it is solved

presently ?

Existing Procedure

Graphical method can handle :

Upto three coals or sizes at a time

Requires skilled personnel

Time consuming

Limitations

Frequent evaluation & control

Practical limitation imposed from the equipment (e.g. Jig cannot be run at low gravity or HMC / HMB difficult to run at higher gravities)

What to do ?

Problem Problem

Sp. Gr. 2Ratio R2

Feed1

Feed2

Ratio R1 Sp. Gr. 1

Overall

Y, A

Two Coals -

feed proportion - m1 : m2

Yield of coals - Y1 and Y2

Overall ash content - A1 and A2

Elementary ash content - and

Cumulative Yield & Ash of two coals

1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15

Relative density

0

20

40

60

80

100Cumulative % (Yield or Ash)

0

20

40

60

80

100

Coal 1 Yield Coal 2 Yield Coal 1 Ash Coal 2 Ash

QuestionQuestion ? ?

At what condition

Overall yield (Y) is maximum

at the desired quality (Ash, A)

Solution

From material balance,

Y (m1 +m2) = Y1 m1 + Y2 m2

Y1 m1 + Y2 m2 Y = --------------------- (1) (m1 +m2)

From ash balance,

Y A (m1 +m2) = Y1 A1 m1 + Y2 A2 m2 (2)

Y1 A1 m1 + Y2 A2 m2 A = ------------------------------ (3) Y1 m1 + Y2 m2

when the ratio of two coals are given and quality of overall product is fixed, we may assume that,

m1 and m2 = constant

and A = constant

we are to find the relation between Y1 and Y2 so that the overall yield Y is maximum.

L = (Y1m1 + Y2m2) A - Y1 A1 m1 - Y2 A2 m2 = 0 …… (4)

using differential equations as per Lagrange’s theorem for maximization,

dY / dY1 + dL / dY1 = 0

dY / dY2 + dL / dY2 = 0

where, = Lagrangian multiplier

Differentiating equations (1) & (4) and

substituting the derivatives, we get,

{1/(m1+m2)} + [A - (d(Y1 A1)/dY1] = 0

{1/(m1+m2)} + [A - (d(Y2 A2)/dY2] = 0

But we know that,

d(Y1 A1)/dY1 = 1

d(Y2 A2)/dY2 = 2

Thus,

{1/(m1+m2)} + [A - 1] = 0

{1/(m1+m2)} + [A - 2] = 0

or,

1 = 2 and at this condition a maximum overall yield can be achieved. But, it is to be noted that individual overall ash of the two coals may not be equal.

Conclusion

Necessary condition :

Equalization of elementary ash at the cut points

0

20

40

60

80

100

Yield%

0 20 40 60 80 100

Ash%

A

Y

Advantage

Any number of feed coals & sizes

Any number & type of restrictions

Operable by washery supervisors

Shop floor quick decision

Accuracy & reliability of operating conditions

Very useful for modern on-line controls

Methodology for Optimization

Develop equation on the basic concept

(F&S test)

Mathematical formulation of

optimization problem

Selection of necessary condition for

optimization

ConceptCFRI’s Publication

Composite washing of coals from multiple sources :

Optimization by numerical technique

Int. J. Mineral Processing, 41 (1994) 147-160.

Limit for Characteristic AshLimit for Characteristic Ash

Basis Petrographic study

Coke property

limiting value 26-28%

Composite washing of FeedsChar. Ash vs. Relative density

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Relative density

0

10

20

30

40

50

60

70

80

Ch

ar.

Ash

%

1.52 1.

63

Comparison with

coals from western

origin

CHAR..ASH LEVEL ?

1.3 1.4 1.5 1.6 1.7 1.8 1.9 20

5

10

15

20

25

30

0

10

20

30

40

50

60

70

80

Relative density

Cu

m. A

sh

%C

ha

r.As

h%

Western coal vs. Indian coal

Indian COALWESTERN COAL

26-28%

CLEANS ASH

17.0%

9.0%

cum.Ash

cum.Ash