﻿ Predicting Coal Preparation Plant Performance # It takes a smart dog to find hidden treasures

## Predicting Coal Preparation Plant Performance

There are several tools available for modeling coal preparation plant performance.  And they all do a good job, but it is helpful to understand the basic principles to understand what the results mean.  The following is a brief overview of how I perform process simulation on a coal cleaning circuit.  This process was used for performing analysis of coal preparation circuits in Alberta, British Columbia, China, Illinois, India, Ohio, Pennsylvania, Utah, and West Virginia.  Several of these were comparing actual plant performance to a predicted performance both past, present, and future.  Others were used to model a new circuit during engineering and design.

The work is based on the fact that gravity based processes can be simulated mathe­matically with three pieces of information. Two of the pieces required to predict the clean coal yield and quality are washability or sink-float tests on the coal and partition curves for the various gravity cleaning devices.

COAL WASHABILITY

The washability of a coal is determined by sink-float testing.  The test is per­formed by placing a sample of coal in progressively heavier specific gravity baths and scooping off the material that floats.  This test shows how the quality and yield of the coal varies as the specific gravity changes.  The data shows how one coal would separate at various specific gravities.  The cumulative float at any float specific gravity is what a "perfect" (theoretical) specific gravity separation would produce in the way of clean coal yield and quality, with the cumulative sink being the refuse from the perfect separation.  This test result will be used as the example for this manual.

A typical washability data is shown in Table 1.  In general the information in the yellow highlighted sections comes from the analysis f the test data.  Other analysis information such as volatile matter or fixed carbon can also be used.  This is typical of a steam coal analysis from North America.

Table 1 Example Washability Data With the washability data and information about the preparation plant equipment the performance can be predicted with a fairly good accuracy.  The information needed on the equipment is the partition curves.

PARTITION CURVE

Each type of washing equipment has its own characteristic performance curve, com­monly referred to as a partition (distribution) curve. They are also known as Tromp curves from the work of Klaas F. Tromp from the Dutch State Mines Organization.  Typical curves are shown in Figure 1.  The term "partition" derives from the fact that the equipment separates or "partitions" the coal into two fractions, plus or minus the specific gravity of separation.  Each curve is substantially independent of the density distribution of the coal being washed.  The curve is dependent upon the size distribution of the feed coal.

Figure 1 – Typical Partition Curves There are two basic philosophies in dealing with the effect of different size feeds.  One philosophy requires a unique partition curve for each size feed and each separating gravity.  This procedure becomes very cumbersome and requires a large file of curves.  A new or changed feed size requires the development of a new curve or access to one in storage.  This is the procedure first developed by the USBM and continued by the DOE, which have proceeded to sample and test various plants and process equipment, and publish the results.

The second philosophy is based upon the work of the Dutch State Mines or­ganization which specifies that each family of curves can be reduced to a single curve that defines the effects at low and high gravities.  This curve can then be modified to any feed by adjusting the slope of the center section.  This is generally referred to as a normalized curve and is based on +/- X specific gravity units from a separating point, referenced as zero.

This second method is the method I and many others in the coal industry use.  As such, we have a set of partition curves for different types of processing equipment, and adjustment factors (called Ep's) for the center sections.  Ep is an abbreviation for Ecart Probable Error (or sometimes moen) and is a measure of the precision of separa­tion.  It is defined as the specific gravity at which 25% of the feed reports to clean coal (D25), minus the specific gravity at which 75% reports to clean coal (D75), all divided by 2, or:

Ep = (D25 - D75)/ 2

A low Ep (.02) indicates a very precise separation, and a high Ep (.20) indicates a very inefficient separation.  Other factors such as error area, imperfection, and Tromp area are, and have been, used by various preparation engineers.

From results experienced in the field, and comparing theoretical to actual plant performance, some adjustments to this method of Ep have been developed and a unique Ep calculation is done for each equipment based on some adjustment factors.

Ep =F1*F2*(F3*SG-F4)

Where:

F1:      Where F1 is calculated from the separating SG and the Ave Size

Where Ave Size       uses Ave = e((ln(top)+ln(bot))/2)

F2:      Prediction or guarantee, 1.0 if predicting performance, 1.25 if  guaranteeing performance

F3:      empirical factors determined by testing and unique for each equipment (generally)

F4:      empirical factors determined by testing and unique for each equipment (generally)

The raw data I use was taken from old notes, then a regression analysis was performed to fit a curve to the data to determine general characteristics.  This was then used to calculate curves for each device based on separating gravity and assumed Ep. This curve is then used to calculate a unique curve from the input data.          Regression analysis was also performed on the impact of average grain size to refine the F1 value.

The following pages present information for major equipment types commonly found in coal preparation plants.  The attached spreadsheet ( SDM Process Sim) shows this data in use with the typical washability presented above. Using this information and assuming a dense media vessel for the coarse and a water-only cyclone circuit for the fines the results are

 Dense Media Vessel Sep.Gr. % Wt % Ash % S 1.55 Predicted 78.70 8.67 1.16 Theoretical 80.38 8.99 1.17 Water-only Cyclone (2 Stage sink reclean) % Wt % Ash % S 1.70 Predicted 69.66 8.77 1.01 Theoretical 81.87 8.39 1.00 Plant % Wt % Ash % S Predicted 67.42 8.71 1.09 Theoretical 73.56 8.69 1.08

PROCESS EQUIPMNENT

Baum Jig

Figure 2 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 2: Normaized Baum Jig Partition Curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 0.0118x3 + 0.1364x2 + 0.5221x + 0.6656

Middle: y = 0.2455x + 0.5032

Tail:      y = 0.0043x3 - 0.0606x2 + 0.2896x + 0.5174

Using these functions and the following unique values for Baum jigs:

F1:      y = 0.0002x2 - 0.0243x + 1.2129

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.11

F4:      0.01

Fine Coal (Batac) Jig

Figure 3 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 3: Normaized Baum Jig Partition Curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 0.0007x3 + 0.015x2 + 0.1185x + 0.3482

Middle: y = 0.25x + 0.5

Tail:      y = 0.0051x3 - 0.064x2 + 0.2935x + 0.512

Using these functions and the following unique values for Fine Coal (Batac) jigs:

F1:      y = 0.0013x2 - 0.063x + 1.513

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.114

F4:      0.1

Mineral (Diaphragm) Jig

Figure 4 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 4: Normaized Baum Jig Partition Curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 0.0118x3 + 0.1364x2 + 0.5221x + 0.6656

Middle: y = 0.2455x + 0.5032

Tail:      y = 0.0043x3 - 0.0606x2 + 0.2896x + 0.5174

Using these functions and the following unique values for Mineral (Diaphragm) jigs:

F1:      y = 0.0013x2 - 0.063x + 1.513

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.11

F4:      0.1

Dense Medium Vessels

Figure 5 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 5 Normalized Dense Media Vessel Partition curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 0.0002x5 + 0.0042x4 + 0.0436x3 + 0.2231x2 + 0.5784x + 0.645

Middle: y = 0.25x + 0.5

Tail:      y = -0.002x5 + 0.0236x4 - 0.0779x3 - 0.0265x2 + 0.5319x + 0.2983

Using these functions and the following unique values for dense media vessels:

F1:      y = 3.7425x-0.4676

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.047

F4:      0.05

Dense Medium Cyclones

Figure 6 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 6 Normalized Dense Media Cyclone Partition curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 1E-05x6 + 0.0005x5 + 0.0082x4 + 0.0685x3 + 0.3092x2 + 0.7224x + 0.7231

Middle: y = 0.25x + 0.5

Tail:      y = 0.0004x5 - 0.0091x4 + 0.0882x3 - 0.4074x2 + 0.9152x + 0.1633

Using these functions and the following unique values for dense media cyclones:

F1:      y = -0.0028x3 + 0.0598x2 - 0.3723x + 1.5081

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.37

F4:      0.15

Water-only Cyclone

Figure 7 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 7 Normalized Water-only Cyclone Partition curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 0.0051x3 + 0.0645x2 + 0.2954x + 0.5026

Middle: y = -0.0068x3 + 0.0265x2 + 0.2646x + 0.4971

Tail:      y = 0.0062x3 - 0.0745x2 + 0.3301x + 0.5125

Using these functions and the following unique values for water-only cyclones:

F1:      y = -0.142Ln(x) + 0.8912

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.33

F4:      0.31

Tables

Figure 6 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 6 Normalized Dense Media Cyclone Partition curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 3E-06x6 + 0.0001x5 + 0.0018x4 + 0.0147x3 + 0.0651x2 + 0.1498x + 0.347

Middle: y = 0.25x + 0.5

Tail:      y = 0.0004x3 - 0.0109x2 + 0 0.095x + 0.6813

Using these functions and the following unique values for concentrating tables:

F1:       y = -0.0983Ln(x) + 1.1566

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.25

F4:      0.08

Spirals

Figure 6 shows normalized partition curves for a heavy media vessel at increasing separating gravities.  These curves are for ad­justed by changing the Ep. Figure 6 Normalized Spiral Concentrator Partition curve

By using regression analysis, functions for the both tails and the mid section were determined.

Head:   y = 3E-06x6 + 0.0001x5 + 0.0018x4 + 0.0147x3 + 0.0651x2 + 0.1498x + 0.347

Middle: y = 0.25x + 0.5

Tail:      y = 0.0004x3 - 0.0109x2 + 0.095x + 0.6813

Using these functions and the following unique values for dense media vessels:

F1:      y = -0.0983Ln(x) + 1.1566

F2:      1.00    Prediction or guarantee,

1.0 if predicting performance, 1.25 if guaranteeing  performance

F3:      0.25

F4:      0.08 o   40+ years’ experience in the mining industry with strong mineral processing experience in Precious metals, copper, industrial minerals, coal, and phosphate

o   Operational experience in precious metals, coal, and phosphate plus in petrochemicals.

o   Extensive experience studies and feasibility in the US and international (United States, Canada, Mexico, Ecuador, Columbia, Venezuela, Chile, China, India, Indonesia, and Greece).