# Partial Least Squares Regression of Oil Sands Processing Variables within Discrete Event Simulation Digital Twin

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

^{3}), over 80% of which are concentrated in Canada, Venezuela and the United States [1]. Boasting the largest collection of these deposits globally with approximately 1.7 trillion barrels (270 billion m

^{3}) of in-place resources [1], Canada is strategically positioned as an important source of unconventional petroleum products. Of this total, roughly 165 billion barrels (26.3 billion m

^{3}) are considered technically recoverable and, thus, correspond to Canada’s estimated remaining established reserves [1]. Unlike traditional light oil well drilling, which will decline over time, forecasts show an overall 12% increase in unconventional petroleum production over the next 30 years, with peak rates reached in 2039 [2].

## 2. Background

#### 2.1. Oil Sands Geology and Petrochemical Processing

^{2}[7,21], the largest of which is the Athabasca region, containing ~75% of the provincial reserves [20,22].

#### 2.2. Multivariate Statistics and Partial Least Squares (PLS) Regression

**,**as:

#### 2.3. Digital Twins and Discrete Event Simulations

## 3. Incorporation of Quantitative Methods into Discrete Event Simulation

#### 3.1. Case Study: Predictive and System Process Modelling of Canada’s Oil Sands

#### 3.2. Sample Calculations

#### 3.2.1. Partial Least Squares (PLS) Regression

^{2}) quite low for the 1 component scenario (0.34), but root mean squared error (RMSE) and mean absolute residual values were also relatively high. Furthermore, the first component alone only accounts for ~88% of the total model variance, as determined by the sum of squares of the singular values. As a result, the behaviour of the PRESS statistic was tracked upon successive trials in order to identify an improved fit; ultimately, a total of 5 components was deemed appropriate for building the regression model in relation to the available dataset. This was based upon the fact that the PRESS value trended upwards over the first 4 components but dropped significantly upon addition of the fifth; this reversal also coincided with a much higher R

^{2}score of 0.72, improved (decreased) RMSE and residual values and an explained variance of 99.65%. Further addition of successive components (e.g., 10 components) did not greatly improve prediction accuracy or error metrics, resulted in poorer PRESS and ${\mathrm{Q}}^{2}$ statistics and would likely lead to severe overfitting to the present dataset. It is also noteworthy that residuals were consistently greater for marine samples, which indicates greater variability in the predicted set for this depositional type (as expected).

_{2}) plots opposite the other Ti-bearing phases. In the second dimension, the organic-related groups (bitumen, carbon and sulphur) clearly oppose the related silicate and oxide minerals; there is also a broad separation between silicates and carbonate + iron-bearing phases.

#### 3.2.2. Discrete Event Simulations

_{2A}) is 15% higher than that of the deposit (w

_{2D}). To account for the possibility of stockouts prior to a planned shutdown, contingency modes with adjusted configuration rates have been incorporated for each of Modes A and B.

_{1A,2A,1B,2B}) and throughput rates (r

_{A,B}) are assessed with respect to geological estimations (w

_{1D,2D}) using deterministic mass balancing, as follows [15,17]:

_{A}and t

_{B}denote the time elapsed under Modes A and B, respectively. Average throughput between the two modes, or similarly between each mode and its corresponding contingency configuration, can then be computed as follows [15,17]:

_{2D}of 45% less relative critical ore 2 throughput from 40–60 blending strategy). Similarly, the analysis indicates a minimum total target stockpile level (sum of ores 1 and 2) of 4.374 Mt, determined as the maximum rate of change between ore stockpiles 1 and 2 as a function of campaign duration (under either mode). However, the digital twin is subject to the geological uncertainty of the ore, which is not taken into account by Equations (7) and (8). Unexpected fluctuations in ore feed attributes can indeed cause either overages or shortfalls for a given ore type, potentially leading to stockout towards the end of a production campaign [15]. To mitigate this risk, an operational buffer can be introduced by raising the threshold for the critical (limiting) ore type; a similar control measure would be to raise the target total stockpile level.

## 4. Discussion and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Additional Comments

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## Appendix A

**Table A1.**Correlation matrix for all 46 variables (including 5 composites) used in PLS regression model. Coefficients greater than 0.75 are indicated by red text.

QTZ/ SIL | ILL | KAO | CHL | CAL | DOL | ANK | SID | PYR | ZIR | RUT | ANA | ILM | LEP | GYP | BAS | ANO | KSP | ALB | AFE | APA | CRI | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

QTZ/SIL | 1.00 | |||||||||||||||||||||||

ILL | −0.89 | 1.00 | ||||||||||||||||||||||

KAO | −0.91 | 0.81 | 1.00 | |||||||||||||||||||||

CHL | −0.25 | 0.21 | 0.34 | 1.00 | ||||||||||||||||||||

CAL | −0.13 | 0.04 | −0.14 | −0.04 | 1.00 | |||||||||||||||||||

DOL | −0.57 | 0.53 | 0.26 | −0.08 | 0.57 | 1.00 | ||||||||||||||||||

ANK | −0.59 | 0.45 | 0.66 | 0.01 | −0.01 | −0.08 | 1.00 | |||||||||||||||||

SID | −0.30 | 0.19 | 0.26 | 0.06 | −0.05 | 0.10 | 0.20 | 1.00 | ||||||||||||||||

PYR | −0.06 | 0.20 | 0.01 | −0.15 | −0.06 | 0.29 | −0.08 | −0.23 | 1.00 | |||||||||||||||

ZIR | −0.22 | 0.28 | 0.30 | 0.12 | 0.00 | −0.04 | 0.13 | 0.04 | −0.16 | 1.00 | ||||||||||||||

RUT | 0.13 | −0.03 | −0.12 | 0.08 | −0.11 | −0.28 | −0.06 | 0.07 | 0.02 | 0.23 | 1.00 | |||||||||||||

ANA | −0.82 | 0.83 | 0.88 | 0.39 | −0.03 | 0.28 | 0.53 | 0.25 | −0.17 | 0.44 | −0.20 | 1.00 | ||||||||||||

ILM | 0.45 | −0.40 | −0.40 | −0.18 | −0.07 | −0.29 | −0.23 | −0.10 | 0.13 | −0.02 | 0.37 | −0.50 | 1.00 | |||||||||||

LEP | 0.38 | −0.33 | −0.33 | −0.15 | −0.18 | −0.33 | −0.20 | 0.00 | 0.11 | 0.01 | 0.45 | −0.45 | 0.75 | 1.00 | ||||||||||

GYP | 0.22 | −0.36 | −0.16 | 0.07 | 0.15 | −0.23 | −0.04 | 0.03 | −0.20 | −0.01 | 0.14 | −0.22 | 0.19 | 0.28 | 1.00 | |||||||||

BAS | 0.23 | −0.37 | −0.16 | 0.08 | 0.06 | −0.29 | −0.04 | 0.04 | −0.19 | −0.02 | 0.15 | −0.23 | 0.20 | 0.30 | 0.99 | 1.00 | ||||||||

ANO | 0.21 | −0.35 | −0.25 | 0.08 | 0.41 | −0.17 | −0.03 | 0.19 | −0.50 | 0.04 | 0.06 | −0.06 | 0.02 | −0.01 | 0.12 | 0.08 | 1.00 | |||||||

KSP | −0.19 | −0.05 | 0.27 | 0.51 | 0.00 | −0.06 | 0.03 | 0.17 | −0.45 | 0.01 | 0.02 | 0.28 | −0.13 | −0.06 | 0.19 | 0.18 | 0.45 | 1.00 | ||||||

ALB | −0.85 | 0.80 | 0.75 | 0.11 | 0.13 | 0.69 | 0.37 | 0.10 | 0.31 | 0.04 | −0.20 | 0.60 | −0.35 | −0.32 | −0.18 | −0.20 | −0.46 | 0.06 | 1.00 | |||||

AFE | −0.59 | 0.56 | 0.44 | 0.08 | 0.34 | 0.71 | 0.14 | −0.35 | 0.24 | 0.06 | −0.35 | 0.44 | −0.46 | −0.54 | −0.20 | −0.25 | −0.37 | −0.07 | 0.71 | 1.00 | ||||

APA | −0.60 | 0.61 | 0.40 | 0.07 | 0.31 | 0.71 | 0.07 | 0.11 | 0.35 | −0.05 | −0.18 | 0.38 | −0.21 | −0.19 | −0.47 | −0.48 | −0.10 | 0.01 | 0.65 | 0.45 | 1.00 | |||

CRI | 0.35 | −0.29 | −0.36 | −0.29 | 0.00 | −0.17 | −0.20 | −0.16 | 0.04 | −0.09 | −0.02 | −0.30 | 0.16 | 0.23 | 0.16 | 0.17 | 0.05 | −0.16 | −0.27 | −0.20 | −0.15 | 1.00 | ||

ORC | 0.63 | −0.76 | −0.67 | −0.32 | −0.15 | −0.46 | −0.22 | −0.17 | −0.11 | −0.27 | 0.13 | −0.76 | 0.35 | 0.34 | 0.20 | 0.23 | 0.08 | −0.18 | −0.64 | −0.45 | −0.53 | 0.33 | ||

ORS | 0.29 | −0.40 | −0.45 | −0.23 | 0.28 | 0.04 | −0.16 | −0.09 | −0.18 | −0.41 | 0.02 | −0.46 | −0.04 | −0.05 | 0.07 | 0.04 | 0.18 | −0.06 | −0.22 | 0.00 | −0.26 | 0.14 | ||

TOTAL CLAYS | −0.94 | 0.95 | 0.95 | 0.32 | −0.05 | 0.41 | 0.58 | 0.24 | 0.10 | 0.31 | −0.07 | 0.90 | −0.42 | −0.35 | −0.27 | −0.27 | −0.31 | 0.13 | 0.81 | 0.52 | 0.53 | −0.35 | ||

SID+AFE | −0.77 | 0.64 | 0.61 | 0.13 | 0.24 | 0.69 | 0.30 | 0.61 | −0.01 | 0.09 | −0.23 | 0.59 | −0.48 | −0.45 | −0.14 | −0.17 | −0.14 | 0.10 | 0.69 | 0.52 | 0.48 | −0.32 | ||

RUT+ANA | −0.79 | 0.83 | 0.86 | 0.43 | −0.06 | 0.19 | 0.51 | 0.28 | −0.17 | 0.52 | 0.12 | 0.95 | −0.38 | −0.30 | −0.18 | −0.18 | −0.04 | 0.29 | 0.55 | 0.33 | 0.32 | −0.31 | ||

DOL+CAL+ANK | −0.56 | 0.49 | 0.24 | −0.08 | 0.72 | 0.97 | 0.01 | 0.09 | 0.22 | −0.03 | −0.27 | 0.27 | −0.28 | −0.34 | −0.16 | −0.23 | −0.05 | −0.05 | 0.64 | 0.70 | 0.68 | −0.16 | ||

ANO+KSP+ALB | −0.66 | 0.44 | 0.58 | 0.35 | 0.35 | 0.45 | 0.30 | 0.26 | −0.21 | 0.05 | −0.13 | 0.58 | −0.33 | −0.30 | −0.01 | −0.05 | 0.38 | 0.72 | 0.59 | 0.34 | 0.49 | −0.26 | ||

Na | −0.85 | 0.80 | 0.75 | 0.11 | 0.13 | 0.69 | 0.37 | 0.10 | 0.31 | 0.04 | −0.20 | 0.60 | −0.35 | −0.32 | −0.18 | −0.20 | −0.46 | 0.06 | 1.00 | 0.71 | 0.65 | −0.27 | ||

K | −0.92 | 0.96 | 0.86 | 0.35 | 0.04 | 0.50 | 0.45 | 0.23 | 0.07 | 0.28 | −0.02 | 0.88 | −0.42 | −0.33 | −0.30 | −0.31 | −0.22 | 0.23 | 0.79 | 0.53 | 0.60 | −0.33 | ||

Si | 0.96 | −0.79 | −0.80 | −0.15 | −0.23 | −0.62 | −0.58 | −0.32 | −0.05 | −0.15 | 0.15 | −0.69 | 0.43 | 0.37 | 0.18 | 0.20 | 0.19 | −0.11 | −0.80 | −0.59 | −0.58 | 0.32 | ||

Al | −0.96 | 0.93 | 0.96 | 0.33 | 0.01 | 0.43 | 0.59 | 0.26 | 0.05 | 0.30 | −0.08 | 0.92 | −0.43 | −0.36 | −0.25 | −0.26 | −0.21 | 0.22 | 0.81 | 0.51 | 0.55 | −0.35 | ||

Fe | −0.81 | 0.70 | 0.66 | 0.22 | 0.23 | 0.72 | 0.32 | 0.52 | 0.15 | 0.08 | −0.22 | 0.61 | −0.47 | −0.45 | −0.17 | −0.19 | −0.22 | 0.08 | 0.75 | 0.60 | 0.54 | −0.34 | ||

Mg | −0.62 | 0.58 | 0.33 | 0.08 | 0.56 | 0.99 | −0.05 | 0.11 | 0.27 | −0.02 | −0.27 | 0.35 | −0.33 | −0.36 | −0.22 | −0.28 | −0.16 | 0.02 | 0.72 | 0.73 | 0.73 | −0.22 | ||

Ca | −0.40 | 0.27 | 0.08 | −0.03 | 0.89 | 0.81 | −0.01 | 0.13 | 0.01 | −0.02 | −0.20 | 0.18 | −0.21 | −0.27 | 0.03 | −0.05 | 0.35 | 0.13 | 0.39 | 0.48 | 0.56 | −0.10 | ||

Ti | −0.79 | 0.83 | 0.85 | 0.43 | −0.07 | 0.18 | 0.51 | 0.28 | −0.17 | 0.53 | 0.13 | 0.94 | −0.37 | −0.29 | −0.17 | −0.18 | −0.04 | 0.29 | 0.54 | 0.32 | 0.32 | −0.31 | ||

Zr | −0.22 | 0.28 | 0.30 | 0.12 | 0.00 | −0.04 | 0.13 | 0.04 | −0.16 | 1.00 | 0.23 | 0.44 | −0.02 | 0.01 | −0.01 | −0.02 | 0.04 | 0.01 | 0.04 | 0.06 | −0.05 | −0.09 | ||

P | −0.60 | 0.61 | 0.40 | 0.07 | 0.31 | 0.71 | 0.07 | 0.11 | 0.35 | −0.05 | −0.18 | 0.38 | −0.21 | −0.19 | −0.47 | −0.48 | −0.10 | 0.01 | 0.65 | 0.45 | 1.00 | −0.15 | ||

C | 0.60 | −0.74 | −0.66 | −0.34 | −0.09 | −0.40 | −0.22 | −0.13 | −0.11 | −0.28 | 0.12 | −0.76 | 0.33 | 0.33 | 0.20 | 0.22 | 0.09 | −0.18 | −0.61 | −0.43 | −0.49 | 0.32 | ||

S | 0.30 | −0.37 | −0.47 | −0.27 | 0.27 | 0.11 | −0.20 | −0.18 | 0.22 | −0.46 | 0.06 | −0.56 | 0.06 | 0.06 | 0.18 | 0.16 | −0.02 | −0.22 | −0.11 | 0.06 | −0.20 | 0.18 | ||

Bitumen | 0.73 | −0.80 | −0.75 | −0.30 | −0.18 | −0.47 | −0.38 | −0.20 | −0.11 | −0.32 | 0.14 | −0.82 | 0.38 | 0.36 | 0.23 | 0.25 | 0.05 | −0.16 | −0.67 | −0.48 | −0.54 | 0.37 | ||

Water | −0.69 | 0.73 | 0.72 | 0.33 | 0.04 | 0.36 | 0.38 | 0.10 | 0.28 | 0.22 | −0.10 | 0.70 | −0.31 | −0.25 | −0.18 | −0.18 | −0.18 | 0.14 | 0.68 | 0.43 | 0.56 | −0.21 | ||

Solids | −0.17 | 0.21 | 0.16 | 0.00 | 0.24 | 0.25 | 0.07 | 0.19 | −0.26 | 0.20 | −0.09 | 0.30 | −0.18 | −0.23 | −0.11 | −0.14 | 0.18 | 0.06 | 0.10 | 0.15 | 0.03 | −0.31 | ||

Fines | −0.86 | 0.86 | 0.85 | 0.41 | 0.06 | 0.41 | 0.47 | 0.27 | −0.07 | 0.31 | −0.15 | 0.91 | −0.50 | −0.45 | −0.22 | −0.23 | −0.09 | 0.27 | 0.69 | 0.46 | 0.52 | −0.37 | ||

Total Recovery | 0.49 | −0.46 | −0.50 | −0.17 | −0.20 | −0.33 | −0.27 | −0.11 | 0.08 | −0.33 | 0.13 | −0.56 | 0.03 | 0.13 | 0.09 | 0.12 | −0.12 | −0.24 | −0.41 | −0.28 | −0.37 | 0.28 | ||

ORC | ORS | TOTAL CLAYS | SID+AFE | RUT+ANA | DOL+CAL+ANK | ANO+KSP+ALB | Na | K | Si | Al | Fe | Mg | Ca | Ti | Zr | P | C | S | Bitumen | Water | Solids | Fines | Total Recovery | |

ORC | 1.00 | |||||||||||||||||||||||

ORS | 0.55 | 1.00 | ||||||||||||||||||||||

TOTAL CLAYS | −0.75 | −0.45 | 1.00 | |||||||||||||||||||||

SID+AFE | −0.54 | −0.09 | 0.66 | 1.00 | ||||||||||||||||||||

RUT+ANA | −0.73 | −0.46 | 0.89 | 0.53 | 1.00 | |||||||||||||||||||

DOL+CAL+ANK | −0.44 | 0.09 | 0.38 | 0.67 | 0.18 | 1.00 | ||||||||||||||||||

ANO+KSP+ALB | −0.56 | −0.10 | 0.54 | 0.53 | 0.55 | 0.48 | 1.00 | |||||||||||||||||

Na | −0.64 | −0.22 | 0.81 | 0.69 | 0.55 | 0.64 | 0.59 | 1.00 | ||||||||||||||||

K | −0.79 | −0.40 | 0.96 | 0.66 | 0.89 | 0.46 | 0.63 | 0.79 | 1.00 | |||||||||||||||

Si | 0.46 | 0.16 | −0.83 | −0.79 | −0.65 | −0.62 | −0.60 | −0.80 | −0.80 | 1.00 | ||||||||||||||

Al | −0.77 | −0.43 | 0.99 | 0.67 | 0.90 | 0.41 | 0.64 | 0.81 | 0.97 | −0.85 | 1.00 | |||||||||||||

Fe | −0.59 | −0.14 | 0.72 | 0.98 | 0.55 | 0.68 | 0.53 | 0.75 | 0.71 | −0.82 | 0.72 | 1.00 | ||||||||||||

Mg | −0.52 | 0.00 | 0.48 | 0.72 | 0.27 | 0.96 | 0.51 | 0.72 | 0.57 | −0.66 | 0.50 | 0.76 | 1.00 | |||||||||||

Ca | −0.35 | 0.16 | 0.18 | 0.53 | 0.12 | 0.91 | 0.58 | 0.39 | 0.30 | −0.48 | 0.25 | 0.51 | 0.81 | 1.00 | ||||||||||

Ti | −0.73 | −0.46 | 0.89 | 0.52 | 1.00 | 0.18 | 0.55 | 0.54 | 0.88 | −0.65 | 0.90 | 0.54 | 0.27 | 0.11 | 1.00 | |||||||||

Zr | −0.27 | −0.41 | 0.31 | 0.09 | 0.52 | −0.03 | 0.05 | 0.04 | 0.28 | −0.15 | 0.30 | 0.08 | −0.02 | −0.02 | 0.53 | 1.00 | ||||||||

P | −0.53 | −0.26 | 0.53 | 0.48 | 0.32 | 0.68 | 0.49 | 0.65 | 0.60 | −0.58 | 0.55 | 0.54 | 0.73 | 0.56 | 0.32 | −0.05 | 1.00 | |||||||

C | 1.00 | 0.57 | −0.74 | −0.48 | −0.73 | −0.37 | −0.53 | −0.61 | −0.77 | 0.41 | −0.75 | −0.53 | −0.46 | −0.28 | −0.73 | −0.28 | −0.49 | 1.00 | ||||||

S | 0.52 | 0.90 | −0.44 | −0.12 | −0.55 | 0.14 | −0.20 | −0.11 | −0.42 | 0.17 | −0.44 | −0.11 | 0.06 | 0.16 | −0.56 | −0.46 | −0.20 | 0.55 | 1.00 | |||||

Bitumen | 0.95 | 0.50 | −0.81 | −0.58 | −0.78 | −0.47 | −0.59 | −0.67 | −0.82 | 0.58 | −0.83 | −0.64 | −0.53 | −0.38 | −0.78 | −0.32 | −0.54 | 0.94 | 0.49 | 1.00 | ||||

Water | −0.76 | −0.51 | 0.77 | 0.46 | 0.68 | 0.34 | 0.52 | 0.68 | 0.75 | −0.57 | 0.77 | 0.55 | 0.42 | 0.23 | 0.67 | 0.22 | 0.56 | −0.76 | −0.41 | −0.80 | 1.00 | |||

Solids | −0.41 | −0.05 | 0.19 | 0.30 | 0.27 | 0.27 | 0.21 | 0.10 | 0.22 | −0.12 | 0.22 | 0.24 | 0.25 | 0.29 | 0.27 | 0.20 | 0.03 | −0.40 | −0.18 | −0.44 | −0.18 | 1.00 | ||

Fines | −0.82 | −0.44 | 0.91 | 0.63 | 0.87 | 0.40 | 0.63 | 0.69 | 0.91 | −0.74 | 0.92 | 0.67 | 0.49 | 0.29 | 0.87 | 0.31 | 0.52 | −0.81 | −0.50 | −0.85 | 0.73 | 0.31 | 1.00 | |

Total Recovery | 0.55 | 0.37 | −0.50 | −0.34 | −0.52 | −0.35 | −0.51 | −0.41 | −0.51 | 0.41 | −0.54 | −0.35 | −0.36 | −0.35 | −0.53 | −0.33 | −0.37 | 0.54 | 0.41 | 0.57 | −0.53 | −0.15 | −0.53 | 1.00 |

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**Figure 1.**Location map of the Alberta Oil Sands Region (AOSR), showing the relative positions of the Peace River, Athabasca and Cold Lake oil sand deposit areas.

**Figure 3.**Simplified schematic comparison of multiple linear regression (MLR) and partial least squares (PLS) regression methods. (

**a**) MLR uses all original variables to directly form a linear combination via the normal equations; (

**b**) PLS first transforms the original variables by projecting to latent structures (linear combinations) that maximize covariance (orthogonality) between the new variables ($t$ and $u$ ) (modified after [50].

**Figure 4.**Generalized diagram showing the implementation of discrete event simulations (DES) in the formulation of blending control strategies and related operational modes.

**Figure 5.**Generalized flowsheet for the extraction of diluted bitumen (“dilbit”) from mined oil sands. Blending should occur during ore preparation (prior to processing) to improve hydrotransport along pipelines [73]. Red dotted ellipse indicates potential additional point of hydrotransport for remote extraction sites.

**Figure 6.**Stacked panel line chart for a variety of quality of prediction statistics tabulated for each of the 1, 2, 3, 4, 5 and 10 component scenarios. Abbreviation definitions: RMSE = root mean squared error; RES = mean absolute residual (all samples); VAR = percentage of model variance explained; R2 = coefficient of determination (×100); ${\mathrm{Q}}^{2}$ criterion (as in Equation (6)); PRESS statistic (as in Equation (5)); RESS statistic (as in Equation (4)).

**Figure 7.**Plot of predicted vs. observed recoveries from the 5-component regression model. Samples are sorted according to ascending observed values to better reflect residual distances; predictions clearly improve in the middle to upper recovery ranges.

**Figure 8.**Plot of the $X$ variable loadings (matrix $P$) for the first two components (dimensions 1 and 2).

**Figure 9.**Simulated operational dynamics of Canadian oil sands data in response to geological uncertainty, configured with a critical ore 2 level of 2.916 Mt (deterministic value) and total stockpile target levels of (

**a**) 4.374 Mt under Scenario 1; (

**b**) 8.748 Mt under Scenario 3. Contingency modes are depicted by the fine jagged saw-tooth pattern and result from short contingency segments of 1 day; note the abundance of these ore shortages in (

**a**) compared to (

**b**).

**Figure 10.**Simulated mining surge caused by high variability of Canadian oil sands data in response to geological uncertainty. Surges are indicated when the level of one of the ore types increases above the total stockpile target and are required to provide feed directly to the plant as recourse to a sustained stockout of the other ore type (e.g., ~1055–1065-day range).

**Figure 11.**Time-averaged distribution of operational modes in response to geological uncertainty in the context of Canada’s oil sands, for (

**a**) naïve framework using the deterministic critical ore 2 threshold of 2.916 Mt and target total stockpile level of 4.374 Mt; (

**b**) enhanced configuration using a critical value of 7.290 Mt (2.5×) and target total stockpile level of 14.580 Mt.

**Table 1.**Summary of descriptive statistics for mineral phases analyzed by X-ray diffraction (XRD) in 60 samples.

Mineral Phase Concentrations (wt.%) | ||||||
---|---|---|---|---|---|---|

Mineral | Max | Min * | Median | Mean | Standard Deviation | Variance |

Quartz + silica | 87.94 | 33.30 | 77.43 | 74.96 | 11.22 | 125.82 |

Illite | 25.63 | 0.01 | 5.31 | 5.89 | 5.20 | 27.06 |

Kaolinite | 24.09 | −1.49 | 2.18 | 3.90 | 5.15 | 26.48 |

Chlorite | 1.42 | −1.09 | 0.01 | 0.10 | 0.37 | 0.14 |

Calcite | 3.15 | −1.06 | 0.01 | 0.09 | 0.50 | 0.25 |

Dolomite | 8.21 | −0.03 | 0.12 | 0.83 | 1.69 | 2.85 |

Ankerite | 0.98 | −0.03 | 0.01 | 0.05 | 0.16 | 0.03 |

Siderite | 5.09 | 0.00 | 0.61 | 1.04 | 1.15 | 1.33 |

Pyrite | 1.05 | −0.05 | 0.04 | 0.16 | 0.23 | 0.05 |

Zircon | 0.44 | 0.00 | 0.06 | 0.09 | 0.08 | 0.01 |

Rutile | 0.62 | 0.03 | 0.13 | 0.15 | 0.09 | 0.01 |

Anatase | 1.13 | 0.00 | 0.11 | 0.26 | 0.29 | 0.09 |

Ilmenite | 0.05 | 0.00 | 0.01 | 0.02 | 0.01 | 0.00 |

Lepidolite | 0.05 | 0.00 | 0.01 | 0.02 | 0.01 | 0.00 |

Gypsum | 0.29 | −0.85 | 0.01 | 0.01 | 0.13 | 0.02 |

Bassanite | 0.30 | −0.90 | 0.01 | 0.01 | 0.14 | 0.02 |

Anorthite | 3.65 | −7.14 | 0.12 | 0.22 | 1.22 | 1.49 |

K-feldspar | 4.16 | −0.35 | 1.06 | 1.19 | 0.86 | 0.74 |

Albite | 11.38 | 0.00 | 0.34 | 0.96 | 1.75 | 3.08 |

Iron oxide + hydroxide | 5.25 | −1.75 | 0.10 | 0.19 | 1.07 | 1.15 |

Apatite | 0.49 | 0.00 | 0.05 | 0.10 | 0.09 | 0.01 |

Cristobalite | 0.10 | 0.00 | 0.01 | 0.01 | 0.02 | 0.00 |

Organic carbon | 13.15 | 0.58 | 8.24 | 7.63 | 3.18 | 10.09 |

Organic sulphur | 1.03 | −0.17 | 0.39 | 0.38 | 0.27 | 0.07 |

**Table 2.**Summary of descriptive statistics for elemental and ore compositions analyzed by X-ray fluorescence (XRF) and Soxhlet-Dean and Stark extraction (respectively) in 60 samples.

Elemental Compositions (wt.%) | ||||||

Element | Max | Min | Median | Mean | Standard Deviation | Variance |

Na | 1.00 | 0.00 | 0.03 | 0.08 | 0.15 | 0.02 |

K | 2.00 | 0.09 | 0.55 | 0.64 | 0.43 | 0.18 |

Si | 42.01 | 26.75 | 38.42 | 37.98 | 2.77 | 7.69 |

Al | 9.09 | 0.00 | 1.56 | 2.22 | 2.09 | 4.36 |

Fe | 3.21 | 0.00 | 0.54 | 0.72 | 0.66 | 0.44 |

Mg | 1.09 | 0.00 | 0.05 | 0.12 | 0.22 | 0.05 |

Ca | 3.49 | 0.03 | 0.16 | 0.30 | 0.56 | 0.31 |

Ti | 0.72 | 0.02 | 0.20 | 0.25 | 0.17 | 0.03 |

Zr | 0.22 | 0.00 | 0.03 | 0.04 | 0.04 | 0.00 |

P | 0.09 | 0.00 | 0.01 | 0.02 | 0.02 | 0.00 |

C | 13.29 | 1.08 | 8.38 | 7.86 | 3.05 | 9.32 |

S | 1.31 | 0.05 | 0.47 | 0.47 | 0.28 | 0.08 |

Ore Compositions (wt.%) | ||||||

Phase | Max | Min | Median | Mean | Standard Deviation | Variance |

Bitumen | 16.28 | 0.00 | 9.53 | 9.16 | 4.48 | 20.04 |

Water | 19.57 | 0.41 | 5.63 | 6.65 | 4.37 | 19.06 |

Solids | 91.25 | 76.79 | 83.97 | 84.42 | 2.86 | 8.16 |

Fines | 99.46 | 1.36 | 24.80 | 34.22 | 27.01 | 729.80 |

**Table 3.**Comparison of summary statistics for observed and predicted bitumen recoveries from PLS regression model (5 components).

Metric | Observed Values (Y) | Predicted Values (Ŷ) |
---|---|---|

Max (%) | 98.29 | 100.00 |

Min (%) | 1.55 | 0.00 |

Median (%) | 78.80 | 61.27 |

Mean (%) | 64.91 | 65.17 |

Standard Deviation (%) | 31.14 | 26.91 |

Variance (%^{2}) | 969.95 | 724.18 |

Independent (Explanatory) Variables | ||||||
---|---|---|---|---|---|---|

Variable | No. of Observations | Mean (wt.%) | Standard Deviation (wt.%) | Bootstrap Ratio | Lower CI (95%) | Upper CI (95%) |

Sample type | 60,000 | 0.57 | 0.22 | 2.54 | 0.20 | 1.00 |

Na * | 60,000 | 0.08 | 0.05 | 1.57 | 0.03 | 0.21 |

K | 60,000 | 0.64 | 0.13 | 5.12 | 0.45 | 0.95 |

Si | 60,000 | 37.97 | 0.96 | 39.70 | 35.30 | 39.42 |

Al | 60,000 | 2.22 | 0.64 | 3.48 | 1.34 | 3.99 |

Fe | 60,000 | 0.72 | 0.24 | 2.98 | 0.35 | 1.42 |

Mg * | 60,000 | 0.12 | 0.10 | 1.19 | 0.02 | 0.48 |

Ca * | 60,000 | 0.30 | 0.31 | 0.99 | −0.02 | 1.53 |

Ti | 60,000 | 0.25 | 0.06 | 3.95 | 0.15 | 0.38 |

Zr | 60,000 | 0.04 | 0.02 | 2.41 | 0.01 | 0.08 |

P | 60,000 | 0.02 | 0.01 | 2.40 | 0.01 | 0.04 |

C | 60,000 | 7.87 | 1.00 | 7.90 | 5.88 | 9.67 |

S | 60,000 | 0.47 | 0.13 | 3.64 | 0.25 | 0.76 |

Bitumen | 60,000 | 8.79 | 1.36 | 6.46 | 6.06 | 11.16 |

Water | 60,000 | 6.64 | 1.42 | 4.69 | 4.25 | 9.97 |

Solids | 60,000 | 84.42 | 1.11 | 76.29 | 82.27 | 86.83 |

Fines | 60,000 | 34.27 | 7.91 | 4.33 | 22.22 | 52.30 |

Quartz + silica | 60,000 | 74.94 | 3.46 | 21.64 | 64.62 | 79.82 |

Illite | 60,000 | 5.89 | 1.66 | 3.55 | 3.43 | 10.21 |

Kaolinite | 60,000 | 3.90 | 1.83 | 2.13 | 1.08 | 8.58 |

Chlorite * | 60,000 | 0.10 | 0.14 | 0.73 | −0.16 | 0.41 |

Calcite (Cal) * | 60,000 | 0.09 | 0.28 | 0.33 | −0.24 | 1.07 |

Dolomite (Dol) * | 60,000 | 0.84 | 0.82 | 1.01 | −0.03 | 3.67 |

Ankerite (Ank) * | 60,000 | 0.06 | 0.07 | 0.85 | −0.05 | 0.21 |

Siderite (Sid) | 60,000 | 1.04 | 0.50 | 2.07 | 0.10 | 2.19 |

Pyrite * | 60,000 | 0.16 | 0.11 | 1.40 | −0.02 | 0.46 |

Zircon | 60,000 | 0.09 | 0.04 | 2.41 | 0.02 | 0.17 |

Rutile (Rut) | 60,000 | 0.15 | 0.04 | 3.73 | 0.07 | 0.22 |

Anatase (Ana) | 60,000 | 0.26 | 0.10 | 2.64 | 0.12 | 0.49 |

Ilmenite | 60,000 | 0.02 | 0.00 | 3.74 | 0.01 | 0.03 |

Lepidolite | 60,000 | 0.02 | 0.00 | 3.72 | 0.01 | 0.03 |

Gypsum * | 60,000 | 0.01 | 0.06 | 0.19 | −0.12 | 0.11 |

Bassanite * | 60,000 | 0.01 | 0.06 | 0.16 | −0.13 | 0.10 |

Anorthite (Ano) * | 60,000 | 0.22 | 0.61 | 0.36 | −0.92 | 1.77 |

K-feldspar (Ksp) | 60,000 | 1.20 | 0.38 | 3.17 | 0.39 | 1.96 |

Albite (Alb) * | 60,000 | 0.96 | 0.61 | 1.57 | 0.29 | 2.36 |

Iron oxide/hydroxide (AFE) * | 60,000 | 0.19 | 0.44 | 0.42 | −0.46 | 1.55 |

Apatite | 60,000 | 0.09 | 0.04 | 2.34 | 0.04 | 0.22 |

Cristobalite | 60,000 | 0.01 | 0.00 | 2.70 | 0.00 | 0.02 |

Organic carbon | 60,000 | 7.63 | 1.00 | 7.63 | 5.61 | 9.41 |

Organic sulphur | 60,000 | 0.39 | 0.13 | 2.96 | 0.14 | 0.67 |

Total clays | 60,000 | 9.89 | 3.24 | 3.05 | 5.13 | 19.00 |

Sid + AFE | 60,000 | 1.22 | 0.49 | 2.48 | 0.45 | 2.52 |

Rut + Ana | 60,000 | 0.40 | 0.11 | 3.82 | 0.24 | 0.63 |

Cal + Dol + Ank * | 60,000 | 0.98 | 1.01 | 0.97 | −0.05 | 4.39 |

Ano + Ksp + Alb | 60,000 | 2.37 | 0.82 | 2.91 | 1.09 | 4.76 |

Dependent (response) variables | ||||||

Variable | No. of observations | Mean (wt.%) | Standard deviation (wt.%) | Bootstrap ratio | Lower CI (95%) | Upper CI (95%) |

Total Recovery | 60,000 | 64.84 | 28.86 | 2.25 | 1.52 | 109.53 |

Throughput (t/h) | Ore 1 in Feed (%) | Ore 2 in Feed (%) | ||
---|---|---|---|---|

Algebraic Notation: | r_{A,ACont,B,BCont} | w_{1A,1ACont,1B,1BCont} | w_{2A,2ACont,2B,2BCont} | |

Mode A | Regular | 30,000 | 40 | 60 |

Contingency | 19,500 | 100 | 0 | |

Mode B | Regular | 27,000 | 80 | 20 |

Contingency | 13,500 | 0 | 100 | |

Deposit | - | 55 | 45 |

Segment Type | Duration (Days) |
---|---|

Production campaign | 27 |

Planned shutdown | 1 |

Contingency modes | 1 |

Regular modes | Indeterminate |

Scenario: | 1 | 2 | 3 | 4 | 5 | ||
---|---|---|---|---|---|---|---|

Replications: | 1 | 1 | 1 | 100 | 1 | 1 | |

Critical Ore 2 Level (Mt): | 2.916 | 2.916 | 2.916 | 2.916 | 2.916 | 2.916 | |

Target Total Stockpile Level (Mt): | 4.374 (1×) | 6.561 (1.5×) | 8.748 (2×) | 8.748 (2×) | 13.122 (3×) | 21.870 (5×) | |

Portion of time (%) | |||||||

Mode A | Regular | 45.6 | 54.8 | 59.7 | 60.1 | 58.4 | 59.4 |

Contingency | 4.9 | 0.2 | 1.6 | 1.4 | 0.6 | 0.6 | |

Mode B | Regular | 34.8 | 37.3 | 35 | 34.5 | 37.4 | 36.4 |

Contingency | 11.1 | 4.2 | 0.1 | 0.4 | 0 | 0 | |

Shutdown | 3.6 | 3.5 | 3.6 | 3.6 | 3.6 | 3.6 | |

Throughput (kt/h) | 26.5 | 28.1 | 28.7 | 28.7 | 28.8 | 28.8 | |

Replications with stockouts | - | - | - | 82 | - | - |

Scenario: | 6 | 7 | 8 | ||||
---|---|---|---|---|---|---|---|

Replications: | 1 | 100 | 1 | 100 | 1 | 100 | |

Critical Ore 2 Level (Mt): | 5.832 (2×) | 5.832 (2×) | 7.290 (2.5×) | 7.290 (2.5×) | 8.748 (3×) | 8.748 (3×) | |

Target Total Stockpile Level (Mt): | 11.664 | 11.664 | 14.580 | 14.580 | 17.496 | 17.496 | |

Mode A | Regular | 58.7 | 59.6 | 58.6 | 60.0 | 58.6 | 60 |

Contingency | 0 | 0.1 | 0 | 0.05 | 0 | 0 | |

Mode B | Regular | 37.3 | 36.3 | 37.8 | 36.3 | 37.8 | 36.4 |

Contingency | 0.4 | 0.4 | 0 | 0.05 | 0 | 0 | |

Shutdown | 3.6 | 3.6 | 3.6 | 3.6 | 3.6 | 3.6 | |

Throughput (kt/h) | 28.8 | 28.8 | 28.8 | 28.9 | 28.8 | 28.9 | |

Replications with stockouts | - | 62 | - | 5 | - | 0 |

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## Share and Cite

**MDPI and ACS Style**

Wilson, R.; Mercier, P.H.J.; Patarachao, B.; Navarra, A.
Partial Least Squares Regression of Oil Sands Processing Variables within Discrete Event Simulation Digital Twin. *Minerals* **2021**, *11*, 689.
https://doi.org/10.3390/min11070689

**AMA Style**

Wilson R, Mercier PHJ, Patarachao B, Navarra A.
Partial Least Squares Regression of Oil Sands Processing Variables within Discrete Event Simulation Digital Twin. *Minerals*. 2021; 11(7):689.
https://doi.org/10.3390/min11070689

**Chicago/Turabian Style**

Wilson, Ryan, Patrick H. J. Mercier, Bussaraporn Patarachao, and Alessandro Navarra.
2021. "Partial Least Squares Regression of Oil Sands Processing Variables within Discrete Event Simulation Digital Twin" *Minerals* 11, no. 7: 689.
https://doi.org/10.3390/min11070689