Sulfide Ore Flotation Study to Achieve 85% Gold Recovery as DECREE from Minister and Mineral Resources Indonesia 1827 K/30/MEM/2018

Fulfilling the provisions of the Ministry of Agriculture as a company under IUPK (special mining business license) is a must for mining companies in Indonesia. In KepMen 1827 K/30/MEM/2018, it is stated that the gold commodity under special mining business license (IUPK) minimum recovery is 85% for gold. This study wants to find the solution of how 85% gold recovery will be achieved by conducting statistical analyses on laboratory test results to simulate operating strategy in regard to increasing flotation performance. The research will require models on kinetic flotation laboratory test results. The combination of variables between grind size, reagent (primary collector and secondary collector), and flotation retention time will result in a response recovery in the flotation circuit.

Introduction

On 7 May 2018, Indonesia Minister of Energy and Mineral Resources (ESDM-energi dan sumber daya mineral), Mr. Ignasius Jonan (Minister of Energy and Mineral Resources of the Republic of Indonesia, 2018), made a decree with number 1827 K/30/MEM/2018 regarding implementing guidelines on good mining practices.

On page 349 (Fig. 1), it is stated that the gold commodity under a special mining business license (IUPK-izin usaha pertambangan khusus) minimum recovery is 85% for gold.

Fig. 1. Decree of minister of energy and mineral resources 1827 K/30/MEM/2018.

Fig. 2 shows the gold recovery for concentrators 1 and 2 (C1 & C2) that received DMLZ (deep mill level zone) ore has never achieved gold recovery at 85%.

Fig. 2. 2008–2023 plant gold recovery.

DMLZ is within the Ersberg Mining District in Papua, Indonesia, on the island of New Guinea. DMLZ has reserve at 0.89% Cu, 0.74 ppm Au and 4.4 ppm Ag.

In March 2022, the monthly composite samples from C1 and C2’s feed, concentrate, and tail were taken and analyzed for gold deportment (Fig. 3) at AMTEL laboratory, Canada.

Fig. 3. Gold deportment result (AMTEL report).

The feed head grade is 1.011 ppm Au. Free gold contributes 38.5% of the feed grade (0.407 g/t Au). Only 2% of the Au in this feed is carried by free gold grains greater than 75 μm, which could be readily recovered in a gravity (Knelson) circuit. This is a lower proportion than historically seen in the N/S feed. A further 7% of the Au in this feed is carried by free gold grains 40 μm to 75 μm in diameter, which could possibly have been recovered by a gravity circuit. In total, 32% of the Au is carried by free grains >7 μm, which are of readily floatable size. 6.5% of the feed grade is carried by free gold grains in the slimes (<7 μm), which are below the ideal size for conventional mechanical cells and may contribute to rougher losses. A total of 655 free gold grains were characterised from the microscopy study (from 2.07 kg of processed material). Observed free grains ranged from 1.6 μm to 100 μm in diameter, with a measured average diameter of 20.4 μm. The upper range of free gold is also lower than historically found for N/S feed. Gold grains had an analysed average composition of 90.6% Au. This is a consistent composition for all of the N/S flotation products and consistent for gold grains from previously studied Grasberg ores. Free sulphide particles are the principal contributor to this feed grade, accounting for 30%. This feed comprised an estimated 1.05% chalcopyrite, 1.13% bornite and 2.39% pyrite. Cu sulphides include an additional 0.1% digenite. A total of 110 gold grain attachments and 45 inclusions were observed with sulphide minerals. Observed attachments ranged from 1.3 μm to 70 μm in diameter (average 13.7 μm). Observed enclosed gold grains ranged from 1.7 μm to 22.5 μm (average 4.7 μm). Almost three-quarters of observed associated gold grains were hosted by Cu sulphide particles. Bornite was the most common observed host (accounting for 62% of the observed associated gold), with pyrite & chalcopyrite of secondary importance. Free sulphides in the slimes are not significant carriers of Au (1.5% of accounted feed grade). Sulphide–rock binary particles contribute 17% to this Feed grade. Gold may be carried by either sulphide or rock component. Au values decrease with decreasing particle size. The magnetic fraction has a significant mass in this feed (~11.5 wt.%) and is predominantly contributed by magnetite [unfloatable Fe oxide]. Gold associated with magnetic particles accounts for 12% of the gold grade (0.126 g/t Au). Gold associated with ‘clean’ rock particles (with less than 2.5% sulphide associations by mass) contributes only 2% to the Au balance (0.022 g/t Au). These are inherently not floatable and should report to the tails. Three gold grain attachments were seen with Fe oxide (1.9 μm–10.7 μm in size). Six gold grain attachments and three inclusions were observed with silicate gangue (2.2 μm to 19.2 μm in diameter).

The tail grade is 0.275 ppm Au. The mineralogically-accounted Au came to 0.231 g/t Au (84% of the average assayed value). There was a significant range in the assayed grades of this tails sample, ranging from 0.218 g/t Au to 0.348 g/t Au. This indicates the presence/absence of coarse gold in the sub-samples. The mineralogically accounted value is low compared to the assayed average, but the mineralogical value is well within the range (and is 97% of the average if the 0.348 g/t outlier is excluded). The primary carrier of Au is rock-sulphide composites (high-density rock particles), which contribute 38% to the grade. The grade of the composites in the tails is roughly two-thirds that of the corresponding composite particles in the rougher feed sample, indicating one-third of the value floated to the rougher con. The grade profile of the composite particles in the tails shows sequential liberation of Au with no particular benefit of finer grinding. Gold losses associated with rejected free sulphide particles amount to ~17.5% of the RT grade. These tails contain an estimated 1.02 wt% pyrite, 0.13 wt% chalcopyrite and 0.20 wt.% bornite [not all of which will be free particles]. 16% of the Au lost with free sulphides is associated with particles of readily floatable size (>7 μm).

The project aim of this flotation study is to study what combination of flotation parameters (reagent dosage for the primary and secondary collector, grind size, and flotation time) can increase the recovery of gold in flotation C1 & C2 (concentrator 1 and 2) to be able to achieve a minimum target of 85% recovery from the current performance that in range of 76%–80% recovery of gold.

Materials

Sampling campaign was conducted on 7 December 2023. The sample was handled in a metallurgy laboratory for drying, jaw crushing, double rolls crushing, sweco screen, and rotary splitting before conducting feed assay (Table I) by AAS (atomic absorption spectroscopy) and fire assay (FA) at the QC lab.

Table I. Sample Feed Assay

Variable	N	Mean	SE mean	StDev	Minimum	Q1	Median	Q3	Maximum
%Cu	70	0.66	0.00	0.02	0.57	0.64	0.66	0.67	0.69
Au (ppm)	70	0.49	0.01	0.12	0.25	0.41	0.46	0.53	0.95
AsCu	30	0.06	0.00	0.00	0.05	0.05	0.06	0.06	0.06
Fe	70	4.93	0.04	0.36	4.05	4.66	4.97	5.23	5.55
Ag	30	3.39	0.03	0.15	3.10	3.30	3.40	3.50	3.80
Pb	70	80.47	1.97	16.48	51.24	70.70	76.36	87.54	137.92
Zn	70	265.32	2.70	22.59	216.44	250.26	262.05	280.96	329.40
Insol	30	41.10	0.19	1.05	39.00	40.34	41.17	41.86	42.92

Sampling (Fig. 4) was conducted by a lab technician, and FRM (fatal risk management) was applied for this sampling campaign to put critical control on Falling Object Risk and Mobile Equipment Interaction Risk.

Fig. 4. Sampling campaign: (a) sampling campaign at MLA stockpile, and (b) sample bags stored at metallurgy laboratory.

Methods

In general, froth flotation performance is related to three major flotation systems: equipment, operation, and chemistry. (Willset al., 2006) In Cytec presentation, the collectors used in this test have a different targets of minerals due to the selectivity degree, which 7249 is more focused on chalcopyrite while six is more for all the sulfide minerals (Cytec Pty. Ltd., 2006).

Kinetic flotation test works were performed in 2.4-liter cell using Denver machine with 1400 g of dry solid, 42% solid, air injection 2 lpm (liter per minute) and agitator speed at 1200 rpm. There were four concentrates per kinetic test at minute-1, minute-4, minute-8 and minute-16. There was one dedicated lab technician to do float, and that person did not know about the sample condition (dosage of reagent and grind size) and another lab technician to prepare the sample in regard to grinding time to determine grind size and reagent dosage to the flotation cell. This is due to the recovery of froth is sensitive to operator technique (Willset al., 2006).

Test works order was built using Minitab software with multilevel factorial design. Factors that are used and level (Table II) per factor are:

Table II. Run Order Setup Using Minitab

Factors:	3	Replicates:	3
Base runs:	36	Total runs:	108
Base blocks:	1	Total blocks:	3

• Primary collector (7249) with four levels: 0 gr/kg Cu, 2.5 gr/kg Cu, 4.5 gr/kg Cu, 6 gr/kg Cu

• Secondary collector (SIBX) with three levels: 0 g/T, 15 g/T, 30 g/T

• Grind size with three levels: 10%, 20%, 30% + 65 mesh (212 micron).

Multilevel Factorial Design–DMLZ Design Summary

The lab technician followed the run order from Table III, which was produced by Minitab software, and the total run order is 108 ea.

Table III. DoE of Kinetic Flotation Test

Standard order	Run order	Pt type	Blocks	7249	SIBX	% + 65M	Cu feed assay average (%)	Feed weight (grm)	Dossage 7249 (micro liter µL)	Dossage SIBX (mililiter mL)	Dossage OTX140 (micro liter µL)
26	1	1	1	4,5	30	20	0,66	1.400	37,0	6,0	30,8
9	2	1	1	1	30	30	0,66	1.400	8,2	6,0	30,8
7	3	1	1	1	30	10	0,66	1.400	8,2	6,0	30,8
4	4	1	1	1	15	10	0,66	1.400	8,2	3,0	30,8
22	5	1	1	4,5	15	10	0,66	1.400	37,0	3,0	30,8
20	6	1	1	4,5	1	20	0,66	1.400	37,0	0,2	30,8
17	7	1	1	2,5	30	20	0,66	1.400	20,5	6,0	30,8
13	8	1	1	2,5	15	10	0,66	1.400	20,5	3,0	30,8
12	9	1	1	2,5	1	30	0,66	1.400	20,5	0,2	30,8
10	10	1	1	2,5	1	10	0,66	1.400	20,5	0,2	30,8
18	11	1	1	2,5	30	30	0,66	1.400	20,5	6,0	30,8
32	12	1	1	6	15	20	0,66	1.400	49,3	3,0	30,8
35	13	1	1	6	30	20	0,66	1.400	49,3	6,0	30,8
2	14	1	1	1	1	20	0,66	1.400	8,2	0,2	30,8
15	15	1	1	2,5	15	30	0,66	1.400	20,5	3,0	30,8
3	16	1	1	1	1	30	0,66	1.400	8,2	0,2	30,8
21	17	1	1	4,5	1	30	0,66	1.400	37,0	0,2	30,8
23	18	1	1	4,5	15	20	0,66	1.400	37,0	3,0	30,8
27	19	1	1	4,5	30	30	0,66	1.400	37,0	6,0	30,8
14	20	1	1	2,5	15	20	0,66	1.400	20,5	3,0	30,8
19	21	1	1	4,5	1	10	0,66	1.400	37,0	0,2	30,8
5	22	1	1	1	15	20	0,66	1.400	8,2	3,0	30,8
24	23	1	1	4,5	15	30	0,66	1.400	37,0	3,0	30,8
8	24	1	1	1	30	20	0,66	1.400	8,2	6,0	30,8
11	25	1	1	2,5	1	20	0,66	1.400	20,5	0,2	30,8
30	26	1	1	6	1	30	0,66	1.400	49,3	0,2	30,8
28	27	1	1	6	1	10	0,66	1.400	49,3	0,2	30,8
25	28	1	1	4,5	30	10	0,66	1.400	37,0	6,0	30,8
16	29	1	1	2,5	30	10	0,66	1.400	20,5	6,0	30,8
31	30	1	1	6	15	10	0,66	1.400	49,3	3,0	30,8
36	31	1	1	6	30	30	0,66	1.400	49,3	6,0	30,8
1	32	1	1	1	1	10	0,66	1.400	8,2	0,2	30,8
34	33	1	1	6	30	10	0,66	1.400	49,3	6,0	30,8
33	34	1	1	6	15	30	0,66	1.400	49,3	3,0	30,8
29	35	1	1	6	1	20	0,66	1.400	49,3	0,2	30,8
6	36	1	1	1	15	30	0,66	1.400	8,2	3,0	30,8

Results

Flotation Recovery Model using Metso MetTools

The raw data is modelled with Klimpel model (1) to get the predicted recovery per flotation time. Then, iteration will determine the minimum sum square error between predicted recovery and actual recovery by modifying the R-infinity (recovery maximum) and k (flotation kinetic rate–min-1) (Fig. 5).

(1) $$\begin{array}{r}R=R_{\mathrm{\infty }}\{1-[\frac{1}{kt}(1-\mathit{\text{exp}}(-kt))]\}\end{array}$$

where R is cumulative recovery after time t, R ∞ is maximum theoretical flotation recovery, k is rate constant (time^-1), t is flotation cumulative time (Klimpel, 2000). After getting the R-max and k-rate, the regression setup using MetTools software that is used in Excel add-ins generates coefficient, error, and p-value for each independent variable per dependent variable: copper kinetic rate (Cu-k), gold kinetic rate (Au-k), copper recovery maximum (Cu R∞), and gold recovery maximum (Au R∞).

Fig. 5. Optimum parameters using MetTools.

Gold kinetic rate mostly affected by independent combination variable between primary collector (7249) with secondary collector (sibx) with p-value of 0.000001. The other significant variable are secondary collector (sibx) and combination variable between grind size (% + 65mesh) with secondary collector (sibx).

Gold maximum recovery mostly affected by independent combination variable between grind size (% + 65mesh) with secondary collector (sibx) with p-value of 0.00000000000001. The other significant variables are primary collector (7249), grind size (% + 65mesh), combination variable between secondary collector (sibx) with primary collector (7249), combination variable between grind size (% + 65mesh) with primary collector (7249), quadratic of grind size (% + 65mesh).

Stepwise regression automates the introduction and removal of independent variables to regress them against a dependent variable. Variables are entered or removed based on the p-value of the corresponding parameter (excluded if the p-value is greater than the user-defined threshold).

Both forward (adding variables) and backward (removing variables) steps are supported. Forward only is achieved by setting backward alpha (threshold) to 1 and making sure that no independent variable is selected prior to running stepwise regression (MetTools Documentation, n.d.).

From the combination of the regression model that is shown in Tables IV and V, the kinetic prediction model can be established, as shown in Table VI. All the independent variables are included to predict k (gold kinetic rate) and R∞ (recovery max). To model the rougher kinetic test, the methodology proposed by Yianatoset al. (2006a, 2006b, 2010) was considered (Monteset al., n.d.)

Table IV. Regression for Gold Kinetic Rate Flotation

Linear			Linear interaction			Quadratic
Blank/Y/X/F/S	Variable number	Variable name	Blank/X/F/S	Variable number	Variable name	Blank/X/F/S	Variable number	Variable name
X	1	Ln(7249)	X	1*2	Ln(7249) * Ln(SIBX)	X	1*1	Ln(7249) * Ln(7249)
x	2	Ln(SIBX)		1*3	Ln(7249) * Ln(% + 65M)		2*2	Ln(SIBX) * Ln(SIBX)
F	3	Ln(% + 65M)	S	1*4	Ln(7249) * K - Cu		3*3	Ln(% + 65M) * Ln(% + 65M)
S	4	K - Cu	S	1*5	Ln(7249) * Rmax - Cu	S	4*4	K - Cu * K - Cu
S	5	Rmax - Cu	S	1*6	Ln(7249) * K - Au	S	5*5	Rmax - Cu * Rmax - Cu
Y	6	K - Au	S	1*7	Ln(7249) * Rmax - Au	S	6*6	K - Au * K - Au
S	7	Rmax - Au	x	2*3	Ln(SIBX) * Ln(%+65M)	S	7*7	Rmax - Au * Rmax - Au
			S	2*4	Ln(SIBX) * K - Cu
			S	2*5	Ln(SIBX) * Rmax - Cu
			S	2*6	Ln(SIBX) * K - Au
			S	2*7	Ln(SIBX) * Rmax - Au
			S	3*4	Ln(% + 65M) * K-Cu
			S	3*5	Ln(% + 65M) * Rmax - Cu
			S	3*6	Ln(% + 65M) * K - Au
			S	3*7	Ln(% + 65M) * Rmax - Au
			S	4*5	K - Cu * Rmax - Cu
			S	4*6	K - Cu * K - Au
			S	4*7	K - Cu * Rmax - Au
			S	5*6	Rmax - Cu * K - Au
			S	5*7	Rmax - Cu * Rmax - Au
			S	6*7	K - Au * Rmax - Au
	Dependent var	K - Au		df	29	SSR	13,54711
	R-squared	0,6847466		F	10,4982485	SSE	6,2370118
	Standard error	0,46375573		Prob. F	3,421E-06	Const	TRUE
	PRESS model	Coefficient	Standard error	t-stat	p-value	Lower 95%	Upper 95%
	Intercept	3,2281992	0,594318552	5,431766	0,000008	2,0126813	4,4437171
	Ln(7249)	−0,3413005	0,182570175	−1,869421	0,071693	−0,7146984	0,0320974
	Ln(SIBX)	0,21244168	0,086474186	2,456706	0,020245	0,0355821	0,3893012
	Ln(% + 65M)	−0,0197563	0,173092432	−0,114138	0,909915	−0,3737701	0,3342574
	Ln(7249) * Ln(SIBX)	−0,017789	0,002898292	−6,137738	0,000001	−0,0237166	−0,0118613
	Ln(SIBX) * Ln(% + 65M)	−0,0675598	0,029436233	−2,295123	0,029151	−0,1277636	−0,0073559
	Ln(7249) * Ln(7249)	−0,0475975	0,02347054	−2,027969	0,051838	−0,0956002	0,0004051

Table V. Regression for Gold Recovery Infinity Flotation

Linear			Linear interaction			Quadratic
Blank/Y/X/F/S	Variable number	Variable name	Blank/X/F/S	Variable number	Variable name	Blank/X/F/S	Variable number	Variable name
X	1	Ln(7249)	X	1*2	Ln(7249) * Ln(SIBX)		1*1	Ln(7249) * Ln(7249)
	2	Ln(SIBX)	x	1*3	Ln(7249) * Ln(% + 65M)		2*2	Ln(SIBX) * Ln(SIBX)
F	3	Ln(% + 65M)	S	1*4	Ln(7249) * K - Cu	x	3*3	Ln(% + 65M) * Ln(% + 65M)
S	4	K - Cu	S	1*5	Ln(7249) * Rmax - Cu	S	4*4	K - Cu * K - Cu
S	5	Rmax - Cu	S	1*6	Ln(7249) * K - Au	S	5*5	Rmax - Cu * Rmax - Cu
S	6	K - Au	S	1*7	Ln(7249) * Rmax - Au	S	6*6	K - Au * K - Au
Y	7	Rmax - Au	x	2*3	Ln(SIBX) * Ln(% + 65M)	S	7*7	Rmax - Au * Rmax - Au
			S	2*4	Ln(SIBX) * K - Cu
			S	2*5	Ln(SIBX) * Rmax - Cu
			S	2*6	Ln(SIBX) * K - Au
			S	2*7	Ln(SIBX) * Rmax - Au
			S	3*4	Ln(% + 65M) * K - Cu
			S	3*5	Ln(% + 65M) * Rmax - Cu
			S	3*6	Ln(% + 65M) * K - Au
			S	3*7	Ln(% + 65M) * Rmax - Au
			S	4*5	K - Cu * Rmax - Cu
			S	4*6	K - Cu * K - Au
			S	4*7	K - Cu * Rmax - Au
			S	5*6	Rmax - Cu * K - Au
			S	5*7	Rmax - Cu * Rmax - Au
			S	6*7	K - Au * Rmax - Au
	Dependent var	Rmax - Au		df	29	SSR	1,1146253
	R-squared	0,96086241		F	118,662605	SSE	0,0454006
	Standard error	0,03956689		Prob. F	4,6452E-19	Const	TRUE
	PRESS model	Coefficient	Standard error	t-stat	p-value	Lower 95%	Upper 95%
	Intercept	−0,096013	0,395066078	−0,24303	0,80969273221337	−0,9040139	0,7119878
	Ln(7249)	0,03209306	0,009265654	3,463658	0,00167700219865	0,0131427	0,0510434
	Ln(% + 65M)	0,73084326	0,285330103	2,561396	0,01588912568479	0,1472777	1,3144088
	Ln(7249) * Ln(SIBX)	−0,0033843	0,000247061	−13,69829	0,00000000000003	−0,0038896	−0,002879
	Ln(7249) * Ln(% + 65M)	−0,0065542	0,003155644	−2,076976	0,04676854308294	−0,0130082	−0,0001002
	Ln(SIBX) * Ln(% 5M)	0,00571817	0,000401801	14,23135	0,00000000000001	0,0048964	0,0065399
	Ln(% + 65M) * Ln(% + 65M)	−0,1455325	0,050340249	−2,890976	0,00720458470007	−0,2484898	−0,0425751

Table VI. Independent Variable and Coefficient Number

Term	Coefficient	Standard error coefficient	T-value	P-value
Constant	0.7710	0.0686	11.25	0.000
LN(7249)	0.11518	0.00424	27.14	0.000
LN(SIBX)	0.16788	0.00421	39.83	0.000
LN(% + 65M)	−0.04148	0.00448	−9.26	0.000
LN(retention time minutes)	0.12382	0.00420	29.47	0.000
LN(7249)*LN(7249)	−0.1019	0.0455	−2.24	0.026
LN(SIBX)*LN(SIBX)	−0.0980	0.0544	−1.80	0.072
LN(% + 65M)*LN(% + 65M)	−0.03744	0.00715	−5.23	0.000
LN(retention time minutes)*LN(retention time minutes)	−0.05244	0.00695	−7.55	0.000
LN(7249)*LN(SIBX)	−0.11632	0.00392	−29.64	0.000
LN(7249)*LN(% + 65M)	−0.01868	0.00440	−4.25	0.000
LN(SIBX)*LN(% + 65M)	0.01146	0.00403	2.85	0.005
Term	VIF
Constant
LN(7249)	1.36
LN(SIBX)	1.60
LN(% + 65M)	1.44
LN(retention time minutes)	1.01
LN(7249)*LN(7249)	1.24
LN(SIBX)*LN(SIBX)	1.29
LN(% + 65M)*LN(% + 65M)	1.02
LN(retention time minutes)*LN(retention time minutes)	1.01
LN(7249)*LN(SIBX)	1.42
LN(7249)*LN(% + 65M)	1.32
LN(SIBX)*LN(% + 65M)	1.12

(2) $$\begin{array}{r}Rc\left(\tau \right)=R_{\mathrm{\infty }}.\{1-\left[\frac{1-{(1+kt.\tau )}^{1-N}}{kt.\tau .(N-1)}\right]\}.CF\end{array}$$

where $\tau$ represents the retention time in a single flotation cell; N is the number of cells in a flotation line; CF is a cleaner efficiency factor; RC is the recovery at time t0; KMAX represents the Klimpel maximum kinetic constant from a uniform distribution; RMAX is recovery at infinite time. After getting the k and Rmax, using (2) that includes the equipment in the flotation circuit, which considers N quantity cells per line (per bank flotation) and Tau τ. Tau is number that calculates line or bank quantity, volume per cell flotation, feed %solid, effective volume per cell, dry throughout (tpoh).

Referring to Table VII after running manually iterating over several variables value, it appears minimum primary collector and maximum secondary collector that produce higher gold recovery which recommend operating strategy of cut off 7249 gr/T and run 30 gr/T sibx to get 78.59% recovery of gold.

Table VII. R-Square of Gold Recovery Response Surface

S	R-sq	R-sq (adj)	R-sq (pred)
0.0640939	90.10%	89.84%	89.51%

Flotation Recovery Model using Minitab

Response surface with response optimizer (Fig. 6) using Minitab software analyzes flotation data from 108 tests in the Metallurgy laboratory.

Fig. 6. Response optimization for Au Rec and Cu Conc grade.

The recovery model was built using response surface methodology used to find the optimum point for the primary collector, secondary collector, and grind size dosage. For existing models, a surface plot is created for recovery with independent variables used to form the recovery model.

Analyze Response Surface Design to model curvature (Allen, 2006) in this data test work and identify factor settings that optimize the response. By using response surface design after conducting a factorial experiment, we have identified the most important factors to get Au recovery and Cu conc grade for these analyses (Minitab Response Surface Design, n.d.).

The value of R² or coefficient of determination is produced in the Minitab response surface regression. R² represents the percentage of variation that can be explained by the regression equation (model). Higher number of R² means higher percentage of variation that can be explained by regression equation. The total variation of a regression equation is the sum of the variation that the regression equation can explain and the variation that cannot be explained.

R² (adj) is a coefficient of determination that has been modified considering the number of predictors or factors in the regression equation. Higher independent variables that are included in the regression that are not important will produce lower R² (adj). R² (pred) is the ability of the equation to predict a data scenario. Fig. 11 shows relatively high R², R² (adj), and R² (pred).

Regression equation in uncoded units is:

(3) $$\begin{array}{rcl}& & Aurec\left(\mathrm{\%}\right)=-0.371-0.00300LN\left(7249\right)-0.01150\\ & & LN\left(SIBX\right)+0.616LN(\mathrm{\%}+65M)+0.2324\\ & & LN\left(RetentionTimeminutes\right)-0.001271\\ & & LN\left(7249\right)\ast LN\left(7249\right)-0.001029\\ & & LN\left(SIBX\right)\ast LN\left(SIBX\right)-0.1238\\ & & LN(\mathrm{\%}+65M)\ast LN(\mathrm{\%}+65M)-0.02714\\ & & LN\left(RetentionTimeminutes\right)\\ & & \ast LN\left(RetentionTimeminutes\right)-0.001331\\ & & LN\left(7249\right)\ast LN\left(SIBX\right)-0.003792LN\left(7249\right)\\ & & \ast LN(\mathrm{\%}+65M)+0.002134LN\left(SIBX\right)\\ & & \ast LN(\mathrm{\%}+65M)\end{array}$$

Using the (3), the response optimizer can run scenarios in this particular study to maximize gold recovery with a target of copper concentrate grade in the condition of incumbent plant capacity based on the long-term forecast.

This graph in Fig. 6 visualizes the existence of certain variable ranges that produce gold recovery values best. Response surface optimization is one of the tools that has the ability to handle a variety of design factors and responses efficiently. (Myerset al., n.d.)

Referring to Fig. 6, after setting the objective of the response variable at Minitab response optimization over several variable values, it appears that the minimum primary collector and maximum secondary collector produce higher gold recovery, which recommends an operating strategy of cut-off 7249 and run 30 gr/T six to get 81.06% recovery of gold.

From response optimization, each parameter shows each correlation to the gold recovery. 7249 behaves as an “inverted u-shape” or curvilinear, six behaves as an inverse exponential graph, grind size behaves as a negative exponential trend, and retention behaves almost like a positive linear.

Fig. 7 shows an illustration of parameter effects (Brestet al., 2021) on the gold recovery. The parameters significance level is indicated by the dashed vertical line, the baseline. The factor that exceeds the baseline is significant, with a confidence interval of 95%. The effect of parameters on the gold recovery is shown in the Pareto diagram (Fig. 7), where 4 of 4 studied variables had a statistical effect on the gold recovery.

Fig. 7. Pareto chart for Au Rec.

It can be observed that SIBX as secondary collector is the most significant parameter to gold recovery. The response optimizer also shows the effect of high 7249 and high sibx is negative to gold recover. Based on one of the mineral processing books written by a flotation process expert, namely Mular, giving too much collector can reduce the flotation kinetics which in turn reduces the metal recovery rate (Mular, 2001).

Conclusions

In this study, a multilevel factorial design method was used to make DoE test work in the metallurgy laboratory and run 108 kinetic test work from DMLZ ore that was sent to the MLA stockpile. This study aims to find the optimum operating parameter to reach 85% gold recovery as required by a mining company in Indonesia set in KepMen 1827 K/30/MEM/2018.

With current Concentrator 1 and 2, based on the long-term forecast plan is process 383 tpoh per ball mill, and total ball mill per concentrator is four ball mills, four rougher banks with each bank having 7 cells with 42 m³ per cell, 33% solid, retention time is 17.37 minutes, grind size is 26.89.

Both MetTools regression and Minitab response surface show minimum primary collector (7249) and maximum secondary collector (sibx), without sacrifice throughput rate that relates with retention time and grind size, will produce maximum Au rec and acceptable copper concentrate grade (minimum 10%Cu at ro conc), but still, the Au Rec is only 78.5%–81.06%Au, and this is below the minimum requirement of 85%Au.

Further study is recommended to produce finer grind size without sacrificing throughput, find reagents that increase kinetic rate, and upgrade current mechanical cell flotation to more advanced technology.