Advanced Production Accounting of a Flotation Plant

Advanced Production Accounting of a Flotation Plant Industrial Modeling Framework (APA-FP-IMF)

i n d u s t r IAL g o r i t h m s LLC. (IAL)

www.industrialgorithms.com August 2014

Introduction to Advanced Production Accounting, UOPSS and QLQP Presented in this short document is a description of what we call "Advanced" Production Accounting (APA) applied to a small Tin-Iron Flotation Plant found in Woollacott and Stange (1987) where their “smoothing” algorithm used can be partially found in Hodouin (2010). APA is the term given to the technique of vetting, screening or cleaning the past production data using statistical data reconciliation and regression (DRR) when continuous-processes are assumed to be at steady-state (Kelly and Hedengren, 2013) i.e., there is no significant material accumulation. For this case, the model and data define a simultaneous quantity and quality bilinear DRR problem (Kelly, 2004b). Figure 1a shows the Flotation Plant using names for the nodes and simple number indices for its streams where Figure 1b depicts the same problem configured in our unit-operation-port-state superstructure (UOPSS) (Kelly, 2004a, 2005; Zyngier and Kelly, 2012).

Figure 1a. Flotation Plant Flowsheet (Woollacott and Stange, 1987).

Figure 1b. Flotation Plant UOPSS Flowsheet. The diamond shapes or objects are the sources and sinks known as perimeters, the rectangle shapes with the cross-hairs are continuous-process units and as mentioned these units should have a steady-state detection algorithm (SSD) installed to determine if the units are steady or stationary. The circle shapes with no cross-hairs are in-ports which can accept one or more inlet flows and are considered to be simple or uncontrolled mixers. The cross-haired circles are out-ports which can allow one or more outlet flows and are considered to be simple or uncontrolled splitters. The lines, arcs or edges in between the various shapes are known as internal and external streams and represent in this context the flows or transfers of materials from one shape to another. This example and its flow and assay data are taken directly from Woollacott and Stange (1987) as mentioned but is mapped to our UOPSS modeling framework which includes only one time-period typically defined for one business or calendar day. For this problem the configuration is as follows. There are nine (9) mass flows, six (6) components in mass percent (representing the size distributions of >44.3, >30.2, >22.3, >15.8, >12.4 and <12.4 micro-meters) and two (2) properties (tin and iron) in mass percent. The components and properties are called assays in metallurgical accounting applications. Each continuous-process unit-operation is configured as a blackbox subtype with a “%” character suffixed (or prefixed) indicating that an overall quantity balance is applied (see Appendix A) and each quality also has a “%” character suffixed (or prefixed) indicating that an overall quality balance is to applied (see Appendix B). More details and discussion on these types of bilinear data reconciliation problems can be found in Kelly (2004b). Industrial Modeling Framework (IMF), IMPL and SSIIMPLE To implement the mathematical formulation of this and other systems, IAL offers a unique approach and is incorporated into our Industrial Modeling Programming Language we call IMPL. IMPL has its own modeling language called IML (short for Industrial Modeling Language) which is a flat or text-file interface as well as a set of API's which can be called from any computer programming language such as C, C++, Fortran, C#, VBA, Java (SWIG), Python (CTYPES) and/or Julia (CCALL) called IPL (short for Industrial Programming Language) to both build the model and to view the solution. Models can be a mix of linear, mixed-integer and nonlinear variables and constraints and are solved using a combination of LP, QP, MILP and NLP solvers such as COINMP, GLPK, LPSOLVE, SCIP, CPLEX, GUROBI, LINDO, XPRESS, CONOPT, IPOPT, KNITRO and WORHP as well as our own implementation of SLP called SLPQPE

(Successive Linear & Quadratic Programming Engine) which is a very competitive alternative to the other nonlinear solvers and embeds all available LP and QP solvers. In addition and specific to DRR problems, we also have a special solver called SECQPE standing for Sequential Equality-Constrained QP Engine which computes the least-squares solution and a post-solver called SORVE standing for Supplemental Observability, Redundancy and Variability Estimator to estimate the usual DRR statistics. SECQPE also includes a Levenberg-Marquardt regularization method for nonlinear data regression problems and can be presolved using SLPQPE i.e., SLPQPE warm-starts SECQPE. SORVE is run after the SECQPE solver and also computes the well-known "maximum-power" gross-error statistics (measurement and nodal/constraint tests) to help locate outliers, defects and/or faults i.e., mal-functions in the measurement system and mis-specifications in the logging system. The underlying system architecture of IMPL is called SSIIMPLE (we hope literally) which is short for Server, Solvers, Interfacer (IML), Interacter (IPL), Modeler, Presolver Libraries and Executable. The Server, Solvers, Presolver and Executable are primarily model or problem-independent whereas the Interfacer, Interacter and Modeler are typically domain-specific i.e., model or problem-dependent. Fortunately, for most industrial planning, scheduling, optimization, control and monitoring problems found in the process industries, IMPL's standard Interfacer, Interacter and Modeler are well-suited and comprehensive to model the most difficult of production and process complexities allowing for the formulations of straightforward coefficient equations, ubiquitous conservation laws, rigorous constitutive relations, empirical correlative expressions and other necessary side constraints. User, custom, adhoc or external constraints can be augmented or appended to IMPL when necessary in several ways. For MILP or logistics problems we offer user-defined constraints configurable from the IML file or the IPL code where the variables and constraints are referenced using unit-operation-port-state names and the quantity-logic variable types. It is also possible to import a foreign *.ILP file (row-based MPS file) which can be generated by any algebraic modeling language or matrix generator. This file is read just prior to generating the matrix and before exporting to the LP, QP or MILP solver. For NLP or quality problems we offer user-defined formula configuration in the IML file and single-value and multi-value function blocks writable in C, C++ or Fortran. The nonlinear formulas may include intrinsic functions such as EXP, LN, LOG, SIN, COS, TAN, MIN, MAX, IF, NOT, EQ, NE, LE, LT, GE, GT and CIP, LIP, SIP and KIP (constant, linear and monotonic spline interpolations) as well as user-written extrinsic functions (XFCN). It is also possible to import another type of foreign file called the *.INL file where both linear and nonlinear constraints can be added easily using new or existing IMPL variables. Industrial modeling frameworks or IMF's are intended to provide a jump-start to an industrial project implementation i.e., a pre-project if you will, whereby pre-configured IML files and/or IPL code are available specific to your problem at hand. The IML files and/or IPL code can be easily enhanced, extended, customized, modified, etc. to meet the diverse needs of your project and as it evolves over time and use. IMF's also provide graphical user interface prototypes for drawing the flowsheet as in Figure 1 and typical Gantt charts and trend plots to view the solution of quantity, logic and quality time-profiles. Current developments use Python 2.3 and 2.7 integrated with open-source Gnome Dia and Matplotlib modules respectively but other prototypes embedded within Microsoft Excel/VBA for example can be created in a straightforward manner.

However, the primary purpose of the IMF's is to provide a timely, cost-effective, manageable and maintainable deployment of IMPL to formulate and optimize complex industrial manufacturing systems in either off-line or on-line environments. Using IMPL alone would be somewhat similar (but not as bad) to learning the syntax and semantics of an AML as well as having to code all of the necessary mathematical representations of the problem including the details of digitizing your data into time-points and periods, demarcating past, present and future time-horizons, defining sets, index-sets, compound-sets to traverse the network or topology, calculating independent and dependent parameters to be used as coefficients and bounds and finally creating all of the necessary variables and constraints to model the complex details of logistics and quality industrial optimization problems. Instead, IMF's and IMPL provide, in our opinion, a more elegant and structured approach to industrial modeling and solving so that you can capture the benefits of advanced decision-making faster, better and cheaper. Flotation Plant "Advanced" Production Accounting Synopsis At this point we explore further the purpose of "advanced" production accounting in terms of its diagnostic capability of aiding in the detection, identification and elimination of "bad" production data where "bad" really implies inconsistent data. The major advantage of DRR is its ability to use redundant data which is sometimes referred to as over-determined or over-specified problems. The redundancy primarily occurs because of the inclusion of a model i.e., equations or equality constraints relating all of the quantity and quality variables together including the laws of conservation of matter (i.e., a mass, volume or mole basis). It interesting to quote a recent trade magazine article on “metal accounting risks” (Lothian, 2012) regarding assessing the accuracy of metallurgical balances: “attempting to achieve this without a statistical data reconciliation engine is impossible”. From our Table 1, taken directly from Woollacott and Stange (1987)’s Table I, all 9 stream assays are measured where we use their Error Model 1 which applies a 10% standard error uncertainty to all components and properties (i.e., the standard-deviation equals 0.10 times its actual, raw or measured value). In addition, shown in their Table II are the measured flowrates with estimates of their uncertainty.

Table 1. Flotation Plant’s Measurements (Woollacott and Stange, 1987).

After modeling and solving this bilinear DRR problem in twenty-five (25) iterations using IMPL’s SECQPE, we arrive at a solution with an objective function of 8.92 which has a Hotelling statistic of 21.66 at 95% confidence and 36 – 2 = 34 degrees-of-freedom indicating that no gross-errors are present. There are thirty-six (36) equations (i.e., 4 nodes times (1 quantity + 8 qualities)), seventy-nine (79) measured variables of which all are declared to be redundant and the two (2) unmeasured quantity or flow variables are declared to be observable for a total of eighty-one (81) variables. Unfortunately Woollacott and Stange (1987) do not report the objective function value of their “smoothed” algorithm, which is somewhat similar to other well-known data reconciliation algorithms except that it uses a hierarchical solution strategy briefly described in Hodouin (2010). However, they present the solutions for several Error Models (except Error Model 1 which is the one we use) in their Table VII and our Table 2. Fortunately, our reconciled results found in our Table 3 using Error Model 1 are relatively close to their smoothed results using Error Models 2, 3, 4 and 5 which confirms that our model and data are consistent.

Table 2. Flotation Plant’s “Smoothed” Flow Results from Woollacott and Stange (1987).

Table 3. Flotation Plant’s Reconciled Flow Results from IMPL-SECQPE.

1. Feed 6.47

2. PyriteConcentrate 0.61

3. PyriteTailings 5.86

4. RougherFeed 11.48

5. ScavengerConcentrate 1.70

6. RougherConcentrate 4.03

7. FinalTailings 5.74

8. CleanerTailings 3.91

9. FinalConcentrate 0.12

In summary, we have highlighted the advanced production accounting of a small Flotation Plant with both mass quantity and quality data and no statistically detectable gross-errors are present. References Woollacott, L.C., Stange, W., “Guidelines for the derivation of reliable material balances from plant data”, Journal of South Africa Institute of Mining and Metallurgy, 87, 207-217, (1987). Kelly, J.D., "Production modeling for multimodal operations", Chemical Engineering Progress, February, 44, (2004a). Kelly, J.D., "Formulating large-scale quantity-quality bilinear data reconciliation problems", Computers & Chemical Engineering, 357-362, (2004b). Kelly, J.D., "The unit-operation-stock superstructure (UOSS) and the quantity-logic-quality paradigm (QLQP) for production scheduling in the process industries", In: MISTA 2005 Conference Proceedings, 327, (2005).

Hodouin, “Process observers and data reconciliation using mass and energy balance equations”, Chapter 2 in Advanced Control and Supervision of Mineral Processing Plants, editors Sbarbaro, D., del Villar, R., Springer, (2010). Zyngier, D., Kelly, J.D., "UOPSS: a new paradigm for modeling production planning and scheduling systems", ESCAPE 22, June, (2012). Lothian, K., “Is your business safe from metal accounting risks”, Global Mining, www.energydigital.com, November, (2012). Kelly, J.D., Hedengren, J.D., "A steady-state detection (SDD) algorithm to detect non-stationary drifts in processes", Journal of Process Control, 23, 326, (2013). Appendix A – APA-FP-IMF.UPS (UOPSS) File

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checksum,80

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Unit-Operation-Port-State-Superstructure (UOPSS) *.UPS File.

! (This file is automatically generated from the Python program IALConstructer.py)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sUnit,&sOperation,@sType,@sSubtype,@sUse

Cleaners,Recleaners,processc,blackbox%,

Conditioner,,processc,blackbox%,

Feed,,perimeter,,

FinalConc,,perimeter,,

FinalTails,,perimeter,,

PyriteCircuit,,processc,blackbox%,

PyriteConc,,perimeter,,

Roughers,Scavengers,processc,blackbox%,

&sUnit,&sOperation,@sType,@sSubtype,@sUse

! Number of UO shapes = 8

&sAlias,&sUnit,&sOperation

ALLPARTS,Cleaners,Recleaners

ALLPARTS,Conditioner,

ALLPARTS,Feed,

ALLPARTS,FinalConc,

ALLPARTS,FinalTails,

ALLPARTS,PyriteCircuit,

ALLPARTS,PyriteConc,

ALLPARTS,Roughers,Scavengers

&sAlias,&sUnit,&sOperation

&sUnit,&sOperation,&sPort,&sState,@sType,@sSubtype

Cleaners,Recleaners,6,,in,

Cleaners,Recleaners,8,CleanerTails,out,

Cleaners,Recleaners,9,,out,

Conditioner,,3,,in,

Conditioner,,4,RougherFeed,out,

Conditioner,,5,,in,

Conditioner,,8,,in,

Feed,,1,,out,

FinalConc,,9,,in,

FinalTails,,7,,in,

PyriteCircuit,,1,,in,

PyriteCircuit,,2,,out,

PyriteCircuit,,3,PyriteTails,out,

PyriteConc,,2,,in,

Roughers,Scavengers,4,,in,

Roughers,Scavengers,5,ScavengerConc,out,

Roughers,Scavengers,6,RougherConc,out,

Roughers,Scavengers,7,,out,

&sUnit,&sOperation,&sPort,&sState,@sType,@sSubtype

! Number of UOPS shapes = 18

&sAlias,&sUnit,&sOperation,&sPort,&sState

ALLINPORTS,Cleaners,Recleaners,6,

ALLINPORTS,Conditioner,,3,



ALLINPORTS,FinalConc,,9,

ALLINPORTS,FinalTails,,7,

ALLINPORTS,PyriteCircuit,,1,

ALLINPORTS,PyriteConc,,2,

ALLINPORTS,Roughers,Scavengers,4,

http://www.energydigital.com/

ALLOUTPORTS,Cleaners,Recleaners,8,CleanerTails

ALLOUTPORTS,Cleaners,Recleaners,9,

ALLOUTPORTS,Conditioner,,4,RougherFeed

ALLOUTPORTS,Feed,,1,

ALLOUTPORTS,PyriteCircuit,,2,

ALLOUTPORTS,PyriteCircuit,,3,PyriteTails

ALLOUTPORTS,Roughers,Scavengers,5,ScavengerConc

ALLOUTPORTS,Roughers,Scavengers,6,RougherConc

ALLOUTPORTS,Roughers,Scavengers,7,

&sAlias,&sUnit,&sOperation,&sPort,&sState

&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState

Cleaners,Recleaners,8,CleanerTails,Conditioner,,8,

Cleaners,Recleaners,9,,FinalConc,,9,

Conditioner,,4,RougherFeed,Roughers,Scavengers,4,

Feed,,1,,PyriteCircuit,,1,

PyriteCircuit,,2,,PyriteConc,,2,

PyriteCircuit,,3,PyriteTails,Conditioner,,3,

Roughers,Scavengers,5,ScavengerConc,Conditioner,,5,

Roughers,Scavengers,6,RougherConc,Cleaners,Recleaners,6,

Roughers,Scavengers,7,,FinalTails,,7,

&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState

! Number of UOPSPSUO shapes = 9

&sAlias,&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState

ALLPATHS,Roughers,Scavengers,6,RougherConc,Cleaners,Recleaners,6,

ALLPATHS,PyriteCircuit,,3,PyriteTails,Conditioner,,3,

ALLPATHS,Roughers,Scavengers,5,ScavengerConc,Conditioner,,5,

ALLPATHS,Cleaners,Recleaners,8,CleanerTails,Conditioner,,8,

ALLPATHS,Cleaners,Recleaners,9,,FinalConc,,9,

ALLPATHS,Roughers,Scavengers,7,,FinalTails,,7,

ALLPATHS,Feed,,1,,PyriteCircuit,,1,

ALLPATHS,PyriteCircuit,,2,,PyriteConc,,2,

ALLPATHS,Conditioner,,4,RougherFeed,Roughers,Scavengers,4,

&sAlias,&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState

Appendix B – APA-FP-IMF.IML File

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Copyright and Property of i n d u s t r I A L g o r i t h m s LLC.

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Calculation Data (Parameters)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sCalc,@sValue

!Miscellaneous Constants.

NNON,-99999

LARGEBOUND,1E+3

!Horizon and Period Times.

START,-1.0

BEGIN,0.0

END,1.0

PERIOD,1.0

! Measured Quality Tolerance Fraction (Error Model 1)

TOL,0.10

!Measured Stream Flows.

F1_V,NNON

F2_V,0.61

F3_V,6.94

F4_V,NNON

F5_V,1.7

F6_V,4.14

F7_V,5.75

F8_V,3.42

F9_V,0.11

F1_L,0.0

F1_U,LARGEBOUND

F1_T,F1_V

F1_W,0.0

F2_L,0.0

F2_U,LARGEBOUND

F2_T,F2_V

F2_W,NE(F2_V;NNON)* 1.0/(0.02)^2

F3_L,0.0

F3_U,LARGEBOUND

F3_T,F3_V

F3_W,NE(F3_V;NNON)* 1.0/(2.12)^2

F4_L,0.0

F4_U,LARGEBOUND

F4_T,F4_V

F4_W,0.0

F5_L,0.0

F5_U,LARGEBOUND

F5_T,F5_V

F5_W,NE(F5_V;NNON)* 1.0/(0.10)^2

F6_L,0.0

F6_U,LARGEBOUND

F6_T,F6_V

F6_W,NE(F6_V;NNON)* 1.0/(2.0)^2

F7_L,0.0

F7_U,LARGEBOUND

F7_T,F7_V

F7_W,NE(F7_V;NNON)* 1.0/(0.18)^2

F8_L,0.0

F8_U,LARGEBOUND

F8_T,F8_V

F8_W,NE(F8_V;NNON)* 1.0/(2.14)^2

F9_L,0.0

F9_U,LARGEBOUND

F9_T,F9_V

F9_W,NE(F9_V;NNON)* 1.0/(0.03)^2

&sCalc,@sValue

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Constant Data (Parameters)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sData,@sValue

! Measured Stream Component Assays in %mass (>44.3, >30.2, >22.3, >15.8, >12.4, <12.4 microns).

C1,2.6

,5.2

,2.4

,1.9

,1.7

,1.2

,1.9

,1.1

,2.3

C2,15.9

,15.4

,17

,11.3

,6.8

,6.3

,17.1

,6.8

,4.5

C3,29.6

,26

,29.7

,21

,16.3

,15.9

,30.8

,16.2

,14.8

C4,22.3

,22

,21.2

,21.3

,20.9

,22.4

,22.4

,21.5

,27.4

C5,7.5

,7.6

,6.9

,8.4

,9

,9.9

,7.1

,9.6

,12.7

C6,22.1

,23.8

,22.8

,36.1

,45.3

,44.4

,20.7

,44.8

,38.3

! Measured Stream Property Assays in %mass (Tin, Iron).

P1,0.795

,1.095

,0.78

,2.455

,3.18

,5.26

,0.26

,4.70

,25.35

P2,5.5

,11.87

,4.61

,6.79

,9.69

,10.78

,3.88

,10.58

,19.66

&sData,@sValue

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Chronological Data (Periods)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

@rPastTHD,@rFutureTHD,@rTPD

START,END,PERIOD

@rPastTHD,@rFutureTHD,@rTPD

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Construction Data (Pointers)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Include-@sFile_Name

APA-FP-IMF.ups

Include-@sFile_Name

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Capacity Data (Prototypes)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sUnit,&sOperation,@rRate_Lower,@rRate_Upper

ALLPARTS,0.0,LARGEBOUND

&sUnit,&sOperation,@rRate_Lower,@rRate_Upper

&sUnit,&sOperation,&sPort,&sState,@rTeeRate_Lower,@rTeeRate_Upper

ALLINPORTS,0.0,LARGEBOUND

ALLOUTPORTS,0.0,LARGEBOUND

&sUnit,&sOperation,&sPort,&sState,@rTeeRate_Lower,@rTeeRate_Upper

&sUnit,&sOperation,&sPort,&sState,@rTotalRate_Lower,@rTotalRate_Upper



&sUnit,&sOperation,&sPort,&sState,@rTotalRate_Lower,@rTotalRate_Upper

&sUnit,&sOperation,&sPort,&sState,@rYield_Lower,@rYield_Upper,@rYield_Fixed



&sUnit,&sOperation,&sPort,&sState,@rYield_Lower,@rYield_Upper,@rYield_Fixed

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Constituent Data (Properties)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sComponent

C1

C2

C3

C4

C5

C6

&sComponent

&sTemplate,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target

CT,C1,0.0,100.0,100.0

,C2,0.0,100.0,100.0

,C3,0.0,100.0,100.0

,C4,0.0,100.0,100.0

,C5,0.0,100.0,100.0

,C6,0.0,100.0,100.0

&sTemplate,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target

&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target

ALLINPORTS,CT%

ALLOUTPORTS,CT%

&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target

&sProperty

P1

P2

&sProperty

&sTemplate,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target

PT,P1,0.0,100.0,100.0

,P2,0.0,100.0,100.0

&sTemplate,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target

&sUnit,&sOperation,&sPort,&sState,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target

ALLINPORTS,PT%

ALLOUTPORTS,PT%

&sUnit,&sOperation,&sPort,&sState,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Cost Data (Pricing)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState,

@rFlowPro_Weight,@rFlowPer1_Weight,@rFlowPer2_Weight,@rFlowPen_Weight

Cleaners,Recleaners,8,CleanerTails,Conditioner,,8,,,,F8_W,

Cleaners,Recleaners,9,,FinalConc,,9,,,,F9_W,

Conditioner,,4,RougherFeed,Roughers,Scavengers,4,,,,F4_W,

Feed,,1,,PyriteCircuit,,1,,,,F1_W,

PyriteCircuit,,2,,PyriteConc,,2,,,,F2_W,

PyriteCircuit,,3,PyriteTails,Conditioner,,3,,,,F3_W,

Roughers,Scavengers,5,ScavengerConc,Conditioner,,5,,,,F5_W,

Roughers,Scavengers,6,RougherConc,Cleaners,Recleaners,6,,,,F6_W,

Roughers,Scavengers,7,,FinalTails,,7,,,,F7_W,


@rFlowPro_Weight,@rFlowPer1_Weight,@rFlowPer2_Weight,@rFlowPen_Weight

&sUnit,&sOperation,&sPort,&sState,&sComponent,

@rComponentPro_Weight,@rComponentPer1_Weight,@rComponentPer2_Weight,@rComponentPen_Weight

Cleaners,Recleaners,8,CleanerTails,C1,,,1.0/(C1[8]*TOL)^2.0,

,,,,C2,,,1.0/(C2[8]*TOL)^2.0,

,,,,C3,,,1.0/(C3[8]*TOL)^2.0,

,,,,C4,,,1.0/(C4[8]*TOL)^2.0,

,,,,C5,,,1.0/(C5[8]*TOL)^2.0,

,,,,C6,,,1.0/(C6[8]*TOL)^2.0,

Cleaners,Recleaners,9,,C1,,,1.0/(C1[9]*TOL)^2.0,

,,,,C2,,,1.0/(C2[9]*TOL)^2.0,

,,,,C3,,,1.0/(C3[9]*TOL)^2.0,

,,,,C4,,,1.0/(C4[9]*TOL)^2.0,

,,,,C5,,,1.0/(C5[9]*TOL)^2.0,

,,,,C6,,,1.0/(C6[9]*TOL)^2.0,

Conditioner,,4,RougherFeed,C1,,,1.0/(C1[4]*TOL)^2.0,

,,,,C2,,,1.0/(C2[4]*TOL)^2.0,

,,,,C3,,,1.0/(C3[4]*TOL)^2.0,

,,,,C4,,,1.0/(C4[4]*TOL)^2.0,

,,,,C5,,,1.0/(C5[4]*TOL)^2.0,

,,,,C6,,,1.0/(C6[4]*TOL)^2.0,

Feed,,1,,C1,,,1.0/(C1[1]*TOL)^2.0,

,,,,C2,,,1.0/(C2[1]*TOL)^2.0,

,,,,C3,,,1.0/(C3[1]*TOL)^2.0,

,,,,C4,,,1.0/(C4[1]*TOL)^2.0,

,,,,C5,,,1.0/(C5[1]*TOL)^2.0,

,,,,C6,,,1.0/(C6[1]*TOL)^2.0,

PyriteCircuit,,2,,C1,,,1.0/(C1[2]*TOL)^2.0,

,,,,C2,,,1.0/(C2[2]*TOL)^2.0,

,,,,C3,,,1.0/(C3[2]*TOL)^2.0,

,,,,C4,,,1.0/(C4[2]*TOL)^2.0,

,,,,C5,,,1.0/(C5[2]*TOL)^2.0,

,,,,C6,,,1.0/(C6[2]*TOL)^2.0,

PyriteCircuit,,3,PyriteTails,C1,,,1.0/(C1[3]*TOL)^2.0,

,,,,C2,,,1.0/(C2[3]*TOL)^2.0,

,,,,C3,,,1.0/(C3[3]*TOL)^2.0,

,,,,C4,,,1.0/(C4[3]*TOL)^2.0,

,,,,C5,,,1.0/(C5[3]*TOL)^2.0,

,,,,C6,,,1.0/(C6[3]*TOL)^2.0,

Roughers,Scavengers,5,ScavengerConc,C1,,,1.0/(C1[5]*TOL)^2.0,

,,,,C2,,,1.0/(C2[5]*TOL)^2.0,

,,,,C3,,,1.0/(C3[5]*TOL)^2.0,

,,,,C4,,,1.0/(C4[5]*TOL)^2.0,

,,,,C5,,,1.0/(C5[5]*TOL)^2.0,

,,,,C6,,,1.0/(C6[5]*TOL)^2.0,

Roughers,Scavengers,6,RougherConc,C1,,,1.0/(C1[6]*TOL)^2.0,

,,,,C2,,,1.0/(C2[6]*TOL)^2.0,

,,,,C3,,,1.0/(C3[6]*TOL)^2.0,

,,,,C4,,,1.0/(C4[6]*TOL)^2.0,

,,,,C5,,,1.0/(C5[6]*TOL)^2.0,

,,,,C6,,,1.0/(C6[6]*TOL)^2.0,

Roughers,Scavengers,7,,C1,,,1.0/(C1[7]*TOL)^2.0,

,,,,C2,,,1.0/(C2[7]*TOL)^2.0,

,,,,C3,,,1.0/(C3[7]*TOL)^2.0,

,,,,C4,,,1.0/(C4[7]*TOL)^2.0,

,,,,C5,,,1.0/(C5[7]*TOL)^2.0,

,,,,C6,,,1.0/(C6[7]*TOL)^2.0,

&sUnit,&sOperation,&sPort,&sState,&sComponent,

@rComponentPro_Weight,@rComponentPer1_Weight,@rComponentPer2_Weight,@rComponentPen_Weight

&sUnit,&sOperation,&sPort,&sState,&sProperty,

@rPropertyPro_Weight,@rPropertyPer1_Weight,@rPropertyPer2_Weight,@rPropertyPen_Weight

Cleaners,Recleaners,8,CleanerTails,P1,,,1.0/(P1[8]*TOL)^2.0,

,,,,P2,,,1.0/(P2[8]*TOL)^2.0,

Cleaners,Recleaners,9,,P1,,,1.0/(P1[9]*TOL)^2.0,

,,,,P2,,,1.0/(P2[9]*TOL)^2.0,

Conditioner,,4,RougherFeed,P1,,,1.0/(P1[4]*TOL)^2.0,

,,,,P2,,,1.0/(P2[4]*TOL)^2.0,

Feed,,1,,P1,,,1.0/(P1[1]*TOL)^2.0,

,,,,P2,,,1.0/(P2[1]*TOL)^2.0,

PyriteCircuit,,2,,P1,,,1.0/(P1[2]*TOL)^2.0,

,,,,P2,,,1.0/(P2[2]*TOL)^2.0,

PyriteCircuit,,3,PyriteTails,P1,,,1.0/(P1[3]*TOL)^2.0,

,,,,P2,,,1.0/(P2[3]*TOL)^2.0,

Roughers,Scavengers,5,ScavengerConc,P1,,,1.0/(P1[5]*TOL)^2.0,

,,,,P2,,,1.0/(P2[5]*TOL)^2.0,

Roughers,Scavengers,6,RougherConc,P1,,,1.0/(P1[6]*TOL)^2.0,

,,,,P2,,,1.0/(P2[6]*TOL)^2.0,

Roughers,Scavengers,7,,P1,,,1.0/(P1[7]*TOL)^2.0,

,,,,P2,,,1.0/(P2[7]*TOL)^2.0,

&sUnit,&sOperation,&sPort,&sState,&sProperty,

@rPropertyPro_Weight,@rPropertyPer1_Weight,@rPropertyPer2_Weight,@rPropertyPen_Weight

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Content Data (Past, Present Provisos)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

! Command Data (Future Provisos)

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

&sUnit,&sOperation,@rSetup_Lower,@rSetup_Upper,@rBegin_Time,@rEnd_Time

ALLPARTS,1,1,BEGIN,END

&sUnit,&sOperation,@rSetup_Lower,@rSetup_Upper,@rBegin_Time,@rEnd_Time

&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState,@rSetup_Lower,@rSetup_Upper,@rBegin_Time,@rEnd_Time

ALLPATHS,1,1,BEGIN,END

&sUnit,&sOperation,&sPort,&sState,&sUnit,&sOperation,&sPort,&sState,@rSetup_Lower,@rSetup_Upper,@rBegin_Time,@rEnd_Time


@rRate_Lower,@rRate_Upper,@rRate_Target,@rBegin_Time,@rEnd_Time

Cleaners,Recleaners,8,CleanerTails,Conditioner,,8,,F8_L,F8_U,F8_T,BEGIN,END

Cleaners,Recleaners,9,,FinalConc,,9,,F9_L,F9_U,F9_T,BEGIN,END

Conditioner,,4,RougherFeed,Roughers,Scavengers,4,,F4_L,F4_U,F4_T,BEGIN,END

Feed,,1,,PyriteCircuit,,1,,F1_L,F1_U,F1_T,BEGIN,END

PyriteCircuit,,2,,PyriteConc,,2,,F2_L,F2_U,F2_T,BEGIN,END

PyriteCircuit,,3,PyriteTails,Conditioner,,3,,F3_L,F3_U,F3_T,BEGIN,END

Roughers,Scavengers,5,ScavengerConc,Conditioner,,5,,F5_L,F5_U,F5_T,BEGIN,END

Roughers,Scavengers,6,RougherConc,Cleaners,Recleaners,6,,F6_L,F6_U,F6_T,BEGIN,END

Roughers,Scavengers,7,,FinalTails,,7,,F7_L,F7_U,F7_T,BEGIN,END


@rRate_Lower,@rRate_Upper,@rRate_Target,@rBegin_Time,@rEnd_Time

&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target,@rBegin_Time,@rEnd_Time

Cleaners,Recleaners,8,CleanerTails,C1,0.0,100.0,C1[8],BEGIN,END

,,,,C2,0.0,100.0,C2[8],BEGIN,END

,,,,C3,0.0,100.0,C3[8],BEGIN,END

,,,,C4,0.0,100.0,C4[8],BEGIN,END

,,,,C5,0.0,100.0,C5[8],BEGIN,END

,,,,C6,0.0,100.0,C6[8],BEGIN,END

Cleaners,Recleaners,9,,C1,0.0,100.0,C1[9],BEGIN,END

,,,,C2,0.0,100.0,C2[9],BEGIN,END

,,,,C3,0.0,100.0,C3[9],BEGIN,END

,,,,C4,0.0,100.0,C4[9],BEGIN,END

,,,,C5,0.0,100.0,C5[9],BEGIN,END

,,,,C6,0.0,100.0,C6[9],BEGIN,END

Conditioner,,4,RougherFeed,C1,0.0,100.0,C1[4],BEGIN,END

,,,,C2,0.0,100.0,C2[4],BEGIN,END

,,,,C3,0.0,100.0,C3[4],BEGIN,END

,,,,C4,0.0,100.0,C4[4],BEGIN,END

,,,,C5,0.0,100.0,C5[4],BEGIN,END

,,,,C6,0.0,100.0,C6[4],BEGIN,END

Feed,,1,,C1,0.0,100.0,C1[1],BEGIN,END

,,,,C2,0.0,100.0,C2[1],BEGIN,END

,,,,C3,0.0,100.0,C3[1],BEGIN,END

,,,,C4,0.0,100.0,C4[1],BEGIN,END

,,,,C5,0.0,100.0,C5[1],BEGIN,END

,,,,C6,0.0,100.0,C6[1],BEGIN,END

PyriteCircuit,,2,,C1,0.0,100.0,C1[2],BEGIN,END

,,,,C2,0.0,100.0,C2[2],BEGIN,END

,,,,C3,0.0,100.0,C3[2],BEGIN,END

,,,,C4,0.0,100.0,C4[2],BEGIN,END

,,,,C5,0.0,100.0,C5[2],BEGIN,END

,,,,C6,0.0,100.0,C6[2],BEGIN,END

PyriteCircuit,,3,PyriteTails,C1,0.0,100.0,C1[3],BEGIN,END

,,,,C2,0.0,100.0,C2[3],BEGIN,END

,,,,C3,0.0,100.0,C3[3],BEGIN,END

,,,,C4,0.0,100.0,C4[3],BEGIN,END

,,,,C5,0.0,100.0,C5[3],BEGIN,END

,,,,C6,0.0,100.0,C6[3],BEGIN,END

Roughers,Scavengers,5,ScavengerConc,C1,0.0,100.0,C1[5],BEGIN,END

,,,,C2,0.0,100.0,C2[5],BEGIN,END

,,,,C3,0.0,100.0,C3[5],BEGIN,END

,,,,C4,0.0,100.0,C4[5],BEGIN,END

,,,,C5,0.0,100.0,C5[5],BEGIN,END

,,,,C6,0.0,100.0,C6[5],BEGIN,END

Roughers,Scavengers,6,RougherConc,C1,0.0,100.0,C1[6],BEGIN,END

,,,,C2,0.0,100.0,C2[6],BEGIN,END

,,,,C3,0.0,100.0,C3[6],BEGIN,END

,,,,C4,0.0,100.0,C4[6],BEGIN,END

,,,,C5,0.0,100.0,C5[6],BEGIN,END

,,,,C6,0.0,100.0,C6[6],BEGIN,END

Roughers,Scavengers,7,,C1,0.0,100.0,C1[7],BEGIN,END

,,,,C2,0.0,100.0,C2[7],BEGIN,END

,,,,C3,0.0,100.0,C3[7],BEGIN,END

,,,,C4,0.0,100.0,C4[7],BEGIN,END

,,,,C5,0.0,100.0,C5[7],BEGIN,END

,,,,C6,0.0,100.0,C6[7],BEGIN,END

&sUnit,&sOperation,&sPort,&sState,&sComponent,@rComponent_Lower,@rComponent_Upper,@rComponent_Target,@rBegin_Time,@rEnd_Time

&sUnit,&sOperation,&sPort,&sState,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target,@rBegin_Time,@rEnd_Time

Cleaners,Recleaners,8,CleanerTails,P1,0.0,100.0,P1[8],BEGIN,END

,,,,P2,0.0,100.0,P2[8],BEGIN,END

Cleaners,Recleaners,9,,P1,0.0,100.0,P1[9],BEGIN,END

,,,,P2,0.0,100.0,P2[9],BEGIN,END

Conditioner,,4,RougherFeed,P1,0.0,100.0,P1[4],BEGIN,END

,,,,P2,0.0,100.0,P2[4],BEGIN,END

Feed,,1,,P1,0.0,100.0,P1[1],BEGIN,END

,,,,P2,0.0,100.0,P2[1],BEGIN,END

PyriteCircuit,,2,,P1,0.0,100.0,P1[2],BEGIN,END

,,,,P2,0.0,100.0,P2[2],BEGIN,END

PyriteCircuit,,3,PyriteTails,P1,0.0,100.0,P1[3],BEGIN,END

,,,,P2,0.0,100.0,P2[3],BEGIN,END

Roughers,Scavengers,5,ScavengerConc,P1,0.0,100.0,P1[5],BEGIN,END

,,,,P2,0.0,100.0,P2[5],BEGIN,END

Roughers,Scavengers,6,RougherConc,P1,0.0,100.0,P1[6],BEGIN,END

,,,,P2,0.0,100.0,P2[6],BEGIN,END

Roughers,Scavengers,7,,P1,0.0,100.0,P1[7],BEGIN,END

,,,,P2,0.0,100.0,P2[7],BEGIN,END

&sUnit,&sOperation,&sPort,&sState,&sProperty,@rProperty_Lower,@rProperty_Upper,@rProperty_Target,@rBegin_Time,@rEnd_Time

Advanced Production Accounting of a Flotation Plant

Data & Analytics

Transcript of Advanced Production Accounting of a Flotation Plant