Algorithm v1.0 Β· Mineral Processing Β· Kenya

Graphite Ore Processing
Algorithm

Decision framework for beneficiation route selection β€” Concentration Criterion (Gaudin, 1939), equipment matching, density delta verification, and electrode-grade reliability assessment for East African flake graphite. Separation Efficiency evaluated per Schulz (1970); equipment thresholds after Wills & Finch (2016, Ch. 10).

Interactive Process Evaluator

Enter ore characterization data from mineralogical and chemical analysis. Use the Proximate Analysis panel to calculate Fixed Carbon from raw lab data, then run the full 6-step algorithm.

Proximate Analysis β†’ Fixed Carbon Calculator

Enter the four values from your lab proximate analysis report (ASTM D3172 / ISO 17246). FC% is calculated automatically and fed into the algorithm below.

Moisture β€” M (%) 2.0
Ash β€” A (%) 80.0
Volatile Matter β€” VM (%) 3.0
Calculated FC%
15.0
= 100 βˆ’ M βˆ’ A βˆ’ VM
= 100 βˆ’ 2.0 βˆ’ 80.0 βˆ’ 3.0
Formula (ASTM D3172):   FC% = 100 βˆ’ Moisture(%) βˆ’ Ash(%) βˆ’ Volatile Matter(%)  |  All values on air-dried basis  |  Ref: Wills & Finch (2016); ASTM D3172
Ore Characterisation Inputs
Graphite Density (ρg, g/cm³) 2.10
Gangue Density (ρf, g/cm³) 2.65
Fluid Density (ρfluid, g/cm³) 1.00
Feed Grade – Fixed Carbon (%) 15.0
Target Fixed Carbon (%) 98.0
Target Ash Content (%) 3.0
Particle Size & Recovery
Primary Particle Size
Mass Recovery Target (%) 85
Operation Scale
Ore Type
Liberation Size (Β΅m) 150
Computed Parameters
Concentration Criterion (CC)
β€”
β€”
Density Delta (Δρ)
β€”
g/cmΒ³
Enrichment Ratio (ER)
β€”
β€”
Separation Efficiency (SE)
β€”
R_m βˆ’ R_g [Schulz, 1970]
Calculated FC% (Proximate)
β€”
100 βˆ’ M βˆ’ A βˆ’ VM
Algorithm Decision Steps
Formal Algorithm Specification

Pseudocode representation of the six-step decision framework for gravity separation route selection in Kenyan graphite ore processing. CC thresholds: Gaudin (1939) / Wills & Finch (2016). SE derivation: Schulz (1970). Equipment ranges: Pattanaik & Venugopal (2021). Graphite trials: Patil et al. (1999), Vasumathi et al. (2023).

CC = (ρgangue βˆ’ ρfluid) / (ρgraphite βˆ’ ρfluid) Concentration Criterion β€” Gaudin, A. M. (1939). Principles of Mineral Dressing. McGraw-Hill. Tabulated in Wills & Finch (2016), Table 10.1. CC > 2.5: effective to fine sizes; 1.25–2.5: coarse/medium; < 1.25: gravity not viable.
SE (%) = Rm βˆ’ Rg  [Schulz, 1970] Computed only for the method CC confirms in Step 1.
Gravity / Hybrid β€” Two-product mass balance [Wills & Finch, 2016, Ch. 3]:
yield = feed_FC / target_FC  Β·  Rm = min(yield Γ— 100, recovery%)  Β·  Rg = (yield Γ— gangue_in_conc%) / gangue_in_feed%
Flotation β€” Literature benchmarks [Vasumathi et al., 2023]: Column flotation SE β‰ˆ 80%; Mechanical cell SE β‰ˆ 63%
Cite: Schulz (1970); Wills & Finch (2016, Ch. 1 & 3); Vasumathi et al. (2023); Patil et al. (1999)
ER = Cproduct / Cfeed Enrichment Ratio β€” ratio of target FC% to feed FC%. ER β‰₯ 10: 3+ stage regrind circuit; ER 5–10: two-stage + optional flotation polish; ER < 5: single stage sufficient. Ref: Vasumathi, N., et al. (2023). Int. J. Chemical Engineering, 2023, 1007689. https://doi.org/10.1155/2023/1007689
FC (%) = 100 βˆ’ Moisture (%) βˆ’ Ash (%) βˆ’ Volatile Matter (%) Fixed Carbon by Proximate Analysis β€” ASTM D3172 / ISO 17246. All values on air-dried basis. Feed grade is calculated from this formula using lab assay data before running the algorithm.
Algorithm Pseudocode

Six-step decision framework. Steps 1–4 use ore characterisation data only. Step 5 (SE) is derived mathematically from CC, feed grade, and mass recovery β€” no pilot trial needed. Step 6 (ER) determines circuit staging.

// GRAPHITE GRAVITY SEPARATION DECISION ALGORITHM β€” 6 STEPS
// Kenyan Flake Graphite β†’ Electrode Grade Production
// Sources: Gaudin (1939), Schulz (1970), Wills & Finch (2016), Patil et al. (1999), Vasumathi et al. (2023)

FUNCTION GravitySelectionAlgorithm(ore_data):

// ── STEP 1: Concentration Criterion ──────────────────────────────
// Source: Gaudin (1939); Wills & Finch (2016, Ch. 10, Table 10.1)
CC ← (ρ_gangue βˆ’ ρ_fluid) / (ρ_graphite βˆ’ ρ_fluid)

IF CC > 2.5:
gravity_viability ← "HIGH" // all sizes viable
equipment_pool ← {DMS, jig, shaking_table, centrifugal, spiral}
ELSE IF CC > 1.25:
gravity_viability ← "MODERATE" // coarse/medium only; add flotation polish
equipment_pool ← {jig, shaking_table, spiral}
ELSE:
gravity_viability ← "LOW"
RECOMMEND "Froth Flotation as primary method"
RETURN {route: "FLOTATION", gravity: "SECONDARY"}

// ── STEP 2: Particle Size β†’ Equipment Selection ───────────────────
// Source: Pattanaik & Venugopal (2021); Patil et al. (1999)
IF particle_size > 4000 Β΅m:
primary_equipment ← "Dense Media Separation (DMS)"
ELSE IF particle_size >= 100 Β΅m:
primary_equipment ← "Wilfley Shaking Table / Jig"
ELSE: // < 100 Β΅m
primary_equipment ← "Centrifugal Concentrator (Falcon / Knelson)"
FLAG "Flake damage risk β€” use gentle regime"

// ── STEP 3: Density Delta Verification ───────────────────────────
// Source: Simonsen & Potgieter (2023); Wills & Finch (2016)
Δρ ← ρ_gangue βˆ’ ρ_graphite

IF Δρ > 0.8: CONFIRM "Gravity highly suitable"
ELSE IF Δρ > 0.3: CONFIRM "Gravity suitable with optimised parameters"
ELSE: RECOMMEND "Hybrid: Gravity + Flotation / Magnetic / Leaching"

// ── STEP 4: Electrode Grade Reliability Check ─────────────────────
// Source: ASTM D4422; Vasumathi et al. (2023); Udaya Bhaskar et al. (2002)
IF target_FC >= 98% AND target_ash <= 5%:
electrode_grade ← "TRUE"
IF gravity_viability == "HIGH":
RECOMMEND "Multi-stage gravity β†’ thermal purification"
ELSE:
RECOMMEND "Gravity rougher + Flotation cleaner + acid leach"
ELSE:
electrode_grade ← "FALSE" // industrial/battery grade β€” relaxed criteria

// ── STEP 5: Separation Efficiency β€” optimal conditions for selected method ─
// Source: Schulz (1970); Wills & Finch (2016, Ch. 1 & 3); Vasumathi et al. (2023)
// SE is computed at THEORETICAL OPTIMAL yield for the CC-confirmed method.
// Mass recovery (user input) is used only in Step 6 for staging decisions.

IF gravity_viability == "HIGH" OR "MODERATE":
// Two-product mass balance at optimal yield [Wills & Finch, 2016, Ch. 3]
optimal_yield ← feed_FC / target_FC // correct mass pull for this grade split
R_m ← 100% // at optimal yield, all graphite reports to concentrate
R_g ← (optimal_yield Γ— gangue_in_conc%) / gangue_in_feed% // gangue misplacement
SE_gravity ← R_m βˆ’ R_g // Schulz (1970) β€” high value confirms method is correct
IF gravity_viability == "MODERATE": // hybrid β€” weighted combination
SE_flotation ← 80% // graphite flotation benchmark [Vasumathi et al., 2023]
SE ← w_gravity Γ— SE_gravity + w_flotation Γ— SE_flotation
ELSE: SE ← SE_gravity
ELSE: // flotation primary β€” benchmarks only
SE ← {column: 80%, mechanical_cell: 63%} // [Vasumathi et al., 2023]

// Diagnostic flags raised if inputs need attention (not method failure)
FLAG IF feed_FC < 5%: "Very low grade β€” check liberation"
FLAG IF target_FC > 99%: "Chemical purification required beyond mechanical separation"
FLAG IF ER >= 10: "Multi-stage regrind mandatory β€” see Step 6"

IF SE >= 60%: CONFIRM "Selected method is effective β€” proceed to Step 6"
ELSE IF SE >= 40%: RECOMMEND "Marginal β€” reduce liberation size or add cleaning stage"
ELSE: FLAG "Check inputs β€” feed grade may be below reliable liberation threshold"

// ── STEP 6: Enrichment Ratio β€” Number of Stages ──────────────────
// Source: Schulz (1970); Zhang et al. (2022); Vasumathi et al. (2023)
ER ← target_FC / feed_FC

IF ER >= 10:
RECOMMEND "3+ stage circuit with inter-stage regrinding"
ELSE IF ER >= 5:
RECOMMEND "Two-stage gravity + optional flotation polish"
ELSE:
RECOMMEND "Single-stage gravity sufficient"

// ── FINAL OUTPUT ──────────────────────────────────────────────────
RETURN {
primary_route: primary_equipment,
gravity_viability: gravity_viability,
electrode_grade: electrode_grade,
CC: CC, Δρ: Δρ, SE: SE, ER: ER, FC: feed_FC
}
END FUNCTION
Process Decision Flowchart

Visual decision tree from ore characterisation through equipment selection to final route recommendation. Each decision node is anchored to peer-reviewed sources. The five-step framework follows the logical structure of Wills & Finch (2016, Ch. 10), with CC thresholds from Gaudin (1939), SE evaluation per Schulz (1970), centrifugal equipment benchmarks from Pattanaik & Venugopal (2021), and graphite-specific trials from Patil et al. (1999) and Udaya Bhaskar et al. (2002).

High-Resolution Flowchart Image
Graphite Ore Gravity Separation Decision Flowchart

Figure 1. Five-step gravity separation decision algorithm for Kenyan flake graphite ore. Adapted from Gaudin (1939), Wills & Finch (2016), Schulz (1970), Patil et al. (1999), and Pattanaik & Venugopal (2021).

Interactive Flowchart
β–Ά START: Ore Sample Received
STAGE 1 β€” Characterisation
XRD Β· TGA Β· SEM-EDS Β· Screen Analysis
Determine: ρgraphite, ρgangue, Feed Grade (FC%)
[Wills & Finch, 2016; Zhang et al., 2022, Chem. Eng. J.]
CC Concentration
Criterion (ρg βˆ’ ρf)/(ρm βˆ’ ρf) [Gaudin, 1939]
CC < 1.25
⬑ Froth Flotation
Primary method
Gravity secondary only
[Vasumathi et al., 2023]
CC > 2.5: HIGH
All sizes viable
All gravity equipment
1.25 < CC < 2.5
⚑ Gravity + Flotation
Coarse/medium only
Flotation polish for fines
STEP 2 β€” Size-Based Equipment Selection
Screen analysis from characterisation β†’ map to equipment
> 4 mm Β· Coarse
Dense Media
Separation (DMS)
FeSi medium
High capacity
[Wills & Finch, 2016]
100 Β΅m – 4 mm
Middlings
Wilfley Shaking
Table / Jig
Dual-stage recommended
Regrind between stages
[Patil et al., 1999]
< 100 Β΅m Β· Fines
Centrifugal
Concentrator
Falcon / Knelson
⚠ Gentle β€” flake damage risk
[Pattanaik & Venugopal, 2021]
Δρ Check ρgangue βˆ’ ρgraphite > 0.3 g/cmΒ³? [Simonsen & Potgieter, 2023]
YES β€” Δρ > 0.3
βœ“ Gravity Confirmed
Proceed to Step 4
NO β€” Δρ ≀ 0.3
⚠ Gravity Unreliable
Switch to Flotation
or Magnetic / Leaching
STEP 4 β€” Electrode Grade Reliability
Target FC β‰₯ 98% AND Ash ≀ 5%?
[ASTM D4422; Vasumathi et al., 2023; Udaya Bhaskar et al., 2002]
YES
Multi-stage Gravity Circuit
+ Thermal Purification
If CC HIGH β†’ gravity alone
If CC MODERATE β†’ add flotation cleaner
NO β€” Industrial Grade
Single-stage Gravity
Sufficient
Battery / industrial carbon
FC 90–97% acceptable
STEP 5 β€” Enrichment Ratio Staging
ER = Target FC / Feed FC β†’ Determine number of stages
ER β‰₯ 10
3+ Stage Circuit
+ Regrind Loops
Inter-stage attrition
scrubbing required
5 ≀ ER < 10
2-Stage Gravity
+ Optional Flotation
Scavenger tails
return to circuit
ER < 5
Single-Stage
Gravity Sufficient
High-grade feed
straightforward upgrade
⬛ OUTPUT: Separation Route + Equipment Specification
Reference Tables & Benchmark Data

Standardised thresholds, equipment selection criteria, and Kenyan graphite ore benchmarks for algorithm calibration.

Kenya Graphite Context

Kenyan flake graphite (Kwale, Kilifi, Taita-Taveta) typically occurs in meta-pelitic gneisses. Feed grades range 5–25% FC. Gangue includes quartz, feldspar, mica and silicates with densities 2.6–2.9 g/cmΒ³. Flake graphite CC values typically fall 1.4–2.2 β€” moderate gravity range.

Electrode Grade Requirements

Lithium-ion battery anode: FC > 99.95%, Ash < 0.5% (requires chemical purification post-gravity). Conventional electrode: FC β‰₯ 98%, Ash ≀ 5%. Industrial refractory: FC β‰₯ 90%, Ash ≀ 10%. Gravity alone rarely achieves electrode purity without downstream steps.

Flake Preservation Priority

Large flake graphite (+80 mesh) commands 2–4Γ— price premium. Algorithm must account for attrition damage in centrifugal concentrators. Shaking tables preserve flake integrity better than flotation at coarse sizes. Liberation size should be matched carefully to avoid over-grinding.

Concentration Criterion Decision Table
CC Range Viability Effective Size Range Recommended Equipment Notes
> 2.5 HIGH All sizes incl. fines DMS, Jig, Shaking Table, Centrifugal, Spiral Gravity primary route; flotation optional polish
1.75 – 2.5 MODERATE-HIGH Coarse + medium (>100 Β΅m) Jig, Shaking Table, Spiral Fine fraction needs flotation or centrifugal
1.25 – 1.75 MODERATE Coarse only (>500 Β΅m) Jig, DMS for coarsest fraction Flotation cleaner essential for target grade
< 1.25 LOW / INFEASIBLE Not viable β€” Use Froth Flotation as primary; gravity secondary
Size-Based Equipment Selection Table
Particle Range Primary Equipment Secondary / Polishing Flake Risk Capacity
> 4 mm Dense Media Separation Jig LOW High (100+ t/h)
1 mm – 4 mm Jig (Baum / Batac) Shaking Table LOW Medium
100 Β΅m – 1 mm Wilfley Shaking Table Spiral Concentrator MEDIUM Low-medium
38 Β΅m – 100 Β΅m Centrifugal (Falcon/Knelson) Enhanced Gravity Sep. HIGH Low
< 38 Β΅m (ultra-fines) Column Flotation Selective flocculation VERY HIGH Low
Density Reference Values β€” Kenyan Ore Minerals
Mineral Phase Density (g/cmΒ³) Occurrence
GraphiteValuable2.09 – 2.23Flake β€” primary target
QuartzGangue2.65Dominant gangue
Feldspar (K/Na)Gangue2.55 – 2.76Common in gneisses
Muscovite / MicaGangue2.76 – 3.00Common β€” platy, problematic
BiotiteGangue2.80 – 3.40Common in meta-pelites
IlmeniteHeavy mineral4.72Accessory β€” easy to reject
PyriteSulphide5.02Trace β€” remove via flotation
Water (processing)Fluid1.00Standard medium
Full Reference List

All sources cited in the algorithm, pseudocode, flowchart, and reference tables. Formatted in APA 7th edition adapted for mineral engineering journals (Minerals Engineering, International Journal of Mineral Processing, Journal of Sustainable Metallurgy).

A β€” Foundational Theory & Textbooks
[1]
Gaudin, A. M. (1939). Principles of Mineral Dressing (1st ed.). McGraw-Hill. β€” Original source of the Concentration Criterion (CC) formula and CC threshold classifications used in Step 1 of this algorithm.
[2]
Schulz, N. F. (1970). Separation efficiency. Transactions of the Society of Mining Engineers, AIME, 247, 81–87. β€” Defines SE = Rm βˆ’ Rg; the standard metallurgical efficiency metric used in Step 5 and the Calculator. SE > 50% required for a viable gravity circuit.
[3]
Wills, B. A., & Finch, J. A. (2016). Mineral Processing Technology: An Introduction to the Practical Aspects of Ore Treatment and Mineral Recovery (8th ed.). Butterworth-Heinemann, Elsevier. β€” Chapter 10 (Gravity Concentration) provides CC Table 10.1; Chapter 1 reviews SE definitions including Schulz (1970). Primary reference for equipment size ranges and DMS operation.
[4]
Taggart, A. F. (1945). Handbook of Mineral Dressing: Ores and Industrial Minerals (1st ed.). John Wiley & Sons. β€” Classic reference for mineral density values and early gravity separation concepts; cited for historical mineral dressing context.
B β€” Gravity Separation Principles & Equipment
[5]
Pattanaik, A., & Venugopal, R. (2021). Application of enhanced gravity separators for fine particle processing: An overview. Journal of Sustainable Metallurgy, 7, 315–339. https://doi.org/10.1007/s40831-021-00343-5 β€” Comprehensive review of Falcon/Knelson centrifugal concentrators, MGS, jig, and shaking table performance for fine mineral systems. Directly supports Step 2 equipment selection and the centrifugal concentrator flake damage warning.
[6]
Simonsen, H., & Potgieter, J. H. (2023). Physical beneficiation of heavy minerals β€” Part 1: A state of the art literature review on gravity concentration techniques. PMC / National Library of Medicine. β€” Introduces the Modified Concentration Criterion (MCC) as an improvement on Gaudin's CC for partially liberated mineral systems; validates Δρ threshold logic in Step 3.
[7]
Ottley, D. J. (1986). Gravity concentration in modern mineral processing. In B. A. Wills & R. W. Barley (Eds.), Mineral Processing at a Crossroads (NATO ASI Series, Vol. 117, pp. 209–243). Springer. https://doi.org/10.1007/978-94-009-4476-3_11
[8]
Falconer, A. (2003). Gravity separation: Old technique/new methods. Physical Separation in Science and Engineering, 12, 31–48. https://doi.org/10.1080/1478647031000104293 β€” Reviews modern enhanced gravity methods including spirals, Knelson, and MGS; supports equipment pool definitions in Step 2.
C β€” Graphite-Specific Gravity & Enhanced Gravity Studies
[9]
Patil, D. P., Govindarajan, B., Rao, T. C., Kohad, V. P., & Gaur, R. K. (1999). Plant trials with the multi gravity separator for the reduction of graphite. Minerals Engineering, 12(10), 1127–1131. https://doi.org/10.1016/S0892-6875(99)00097-7 β€” Direct experimental evidence for MGS (enhanced centrifugal gravity) effectiveness on fine graphite (<100 Β΅m). Demonstrates combination of flotation + MGS achieves target graphite reduction. Underpins Step 2 fine-particle equipment selection and the hybrid route recommendation.
[10]
Udaya Bhaskar, K., Govindarajan, B., Barnwal, J. P., Venugopal, R., Jakhu, M. R., & Rao, T. C. (2002). Performance and modeling studies of an MGS for graphite rejection in a lead concentrate. International Journal of Mineral Processing, 67(1–4), 59–70. https://doi.org/10.1016/S0301-7516(02)00017-0 β€” Mathematical modeling of MGS performance for graphite processing; validates SE values achievable in gravity circuits for graphite. Referenced in Step 4 multi-stage circuit recommendation.
[11]
Yerriswamy, P., Barnwal, J. P., Govindarajan, B., Gupta, B. K., & Rao, T. C. (2002). Influence of variables of multi gravity separator on rejection of graphite from a lead concentrate. Mineral Processing and Extractive Metallurgy (Trans. IMM Section C), 111, C156–C159. https://doi.org/10.1179/037195502766647084
D β€” Graphite Beneficiation Reviews (Flotation & Hybrid)
[12]
Vasumathi, N., Vijaya Kumar, T. V., & Subba Rao, S. (2023). A mini review on flotation techniques and reagents used in graphite beneficiation. International Journal of Chemical Engineering, 2023, Article 1007689. https://doi.org/10.1155/2023/1007689 β€” Reviews gravity, flotation, and hybrid beneficiation routes; affirms gravity as cost-effective pre-concentration method. Discusses the grade ceiling (~97% FC) achievable without chemical purification. Directly informs Step 4 electrode grade threshold and the "Flotation cleaner" recommendation for moderate CC ores.
[13]
Vasumathi, N., et al. (2023). Literature quest and survey on graphite beneficiation through flotation. Renewable and Sustainable Energy Reviews, 189, Article 113908. https://doi.org/10.1016/j.rser.2023.113908 β€” Master flowsheet for graphite beneficiation across a range of feed grades. Confirms multi-stage regrind requirements for high-ER scenarios (ER β‰₯ 10). Supports the circuit complexity logic in Step 5.
[14]
Zhang, X., Gu, X., Han, Y., Parra-Álvarez, N., Claremboux, V., & Kawatra, S. K. (2022). Flotation of graphite. Chemical Engineering Journal, 453, Article 139830. https://doi.org/10.1016/j.cej.2022.139830 β€” Comprehensive review of standard beneficiation methods including gravity, magnetic, electric, and flotation separation. Reviews Falcon, Knelson, MGS, and Kelsey Jig as representative gravity machines. Directly cited in flowchart Stage 1 characterisation node.
[15]
MesΓ­as-Figueroa, V., Quero-Arias, D., Leiva-Estay, G., & Toro, N. (2025). Advances in the potential application of froth flotation for the recovery of graphite from spent alkaline and Zn/C batteries. Journal of Material Cycles and Waste Management. https://doi.org/10.1007/s10163-025-02402-5 β€” Provides graphite physical property benchmarks (hardness 1–2 Mohs, specific gravity 2.2) and flotation process parameters for benchmark comparison.
E β€” Separation Efficiency Evaluation
[16]
Irannajad, M., & Mehdilo, A. (2018). A new approach in separation process evaluation: Efficiency ratio and upgrading curves. Physicochemical Problems of Mineral Processing, 54(3), 847–857. https://doi.org/10.5277/ppmp18109 β€” Extends Schulz (1970) SE definition to include efficiency ratio (ER) and upgrading curves; introduces OE and SI indices. Informs the ER classification thresholds in Step 5.
[17]
Finch, J. A., & Tan, Y. H. (2023). Technical note: Measuring separation efficiency of flotation circuits using linear circuit analysis. Minerals Engineering, 204, Article 108418. https://doi.org/10.1016/j.mineng.2023.108418 β€” Applies Schulz (1970) SE to circuit-level analysis; validates SE as the appropriate metric for comparing single-stage vs. multi-stage gravity circuits.
F β€” Standards & Analytical Methods
[18]
ASTM International. (2021). ASTM D4422-21: Standard Test Method for Ash in Analysis of Petroleum Coke. ASTM International. β€” Provides standardised ash determination methodology; the ≀ 5% ash threshold in Step 4 is benchmarked against electrode-grade specifications based on this standard.
[19]
International Organization for Standardization. (2013). ISO 579:2013 β€” Coke: Determination of Total Moisture. ISO. β€” Referenced for moisture-corrected Fixed Carbon reporting, which affects apparent FC% measurement accuracy in feed grade characterisation.
[20]
British Standards Institution. (2006). BS EN ISO 1171: Solid Mineral Fuels β€” Determination of Ash. BSI. β€” Secondary ash determination standard applicable to natural graphite concentrates.
Citation Map β€” Algorithm Steps to Sources
Algorithm Step Parameter / Decision Primary Source(s) Supporting Source(s)
Stage 1 β€” Characterisation XRD, TGA, SEM-EDS methodology [3] Wills & Finch, 2016 [14] Zhang et al., 2022
Step 1 β€” CC Formula CC = (ρg βˆ’ ρf) / (ρm βˆ’ ρf) [1] Gaudin, 1939 [3] Wills & Finch, 2016 Table 10.1
Step 1 β€” CC Thresholds CC > 2.5 / 1.25–2.5 / < 1.25 [3] Wills & Finch, 2016 Ch. 10 [6] Simonsen & Potgieter, 2023
Step 2 β€” Coarse (> 4 mm) Dense Media Separation [3] Wills & Finch, 2016 [8] Falconer, 2003
Step 2 β€” Middlings (100 Β΅m–4 mm) Shaking Table / Jig [9] Patil et al., 1999 [5] Pattanaik & Venugopal, 2021
Step 2 β€” Fines (< 100 Β΅m) Centrifugal Concentrator [5] Pattanaik & Venugopal, 2021 [9] Patil et al., 1999; [11] Yerriswamy et al., 2002
Step 3 β€” Δρ Threshold Δρ > 0.3 g/cmΒ³ required [6] Simonsen & Potgieter, 2023 [1] Gaudin, 1939; [3] Wills & Finch, 2016
Step 4 β€” Electrode Grade FC β‰₯ 98%, Ash ≀ 5% [18] ASTM D4422; [12] Vasumathi et al., 2023 [10] Udaya Bhaskar et al., 2002
Step 4 β€” Multi-stage circuit Gravity + Thermal purification [13] Vasumathi et al., 2023 [10] Udaya Bhaskar et al., 2002
Step 5 β€” SE Formula SE = Rm βˆ’ Rg (derived from CC, feed grade, recovery) [2] Schulz, 1970 [17] Finch & Tan, 2023; [16] Irannajad & Mehdilo, 2018
Step 5 β€” SE thresholds β‰₯ 60% good; 40–60% acceptable; < 40% poor [2] Schulz, 1970 [3] Wills & Finch, 2016 Ch. 1
Step 6 β€” ER Formula ER = Ctarget / Cfeed [2] Schulz, 1970 [16] Irannajad & Mehdilo, 2018
Step 6 β€” ER β‰₯ 10 staging 3+ stages with regrind loops [13] Vasumathi et al., 2023 [14] Zhang et al., 2022
FC Calculator FC% = 100 βˆ’ M βˆ’ A βˆ’ VM [18] ASTM D3172; [19] ISO 17246 [3] Wills & Finch, 2016