Figure 1.
Density, temperature and response variables
| Mixture | pH | Temperature (°C) | Density (g/cm3) | Viscosity v (mm2/s) | Viscosity μ (cp) | RAU (cicles) |
|---|---|---|---|---|---|---|
| 1 | 12.2 | 24.4 | 0.82 | 162.5 | 133.2 | 137 |
| 2 | 4.6 | 25 | 0.82 | 193.7 | 158.83 | 217 |
| 3 | 4.4 | 25.4 | 0.78 | 74.42 | 58.04 | 54 |
| 4 | 4.3 | 24.1 | 0.82 | 103.8 | 85.11 | 66 |
| 5 | 4.2 | 25.3 | 0.81 | 64.71 | 52.42 | 56 |
| 6 | 12 | 25.4 | 0.88 | 90.32 | 79.48 | 220 |
| 7 | 12 | 25 | 0.88 | 96.48 | 84.9 | 128 |
| 8 | 4.2 | 24.5 | 0.77 | 77.5 | 59.67 | 59 |
| 9 | 12 | 25 | 0.92 | 79.15 | 72.82 | 123 |
| 10 | 4.4 | 24.7 | 0.76 | 63.95 | 48.6 | 48 |
| 11 | 4.5 | 25.2 | 0.78 | 77.8 | 60.69 | 60 |
| 12 | 12 | 24.5 | 0.86 | 112.84 | 97.04 | 186 |
| 13 | 4.5 | 25.5 | 0.86 | 78.96 | 67.9 | 114 |
| 14 | 4.5 | 25.3 | 0.84 | 95.32 | 80.07 | 102 |
| 15 | 4.7 | 24.5 | 0.81 | 75.19 | 60.9 | 104 |
| 16 | 11.9 | 25 | 0.81 | 86.08 | 69.73 | 120 |
| 17 | 12 | 24 | 0.81 | 80.58 | 65.27 | 113 |
| 18 | 12 | 25 | 0.82 | 76.73 | 62.92 | 124 |
| 19 | 4.3 | 24 | 0.84 | 72.11 | 60.57 | 51 |
| 20 | 11.7 | 25.2 | 0.88 | 76.92 | 67.7 | 138 |
| 21 | 11.9 | 25 | 0.85 | 99.83 | 84.85 | 163 |
| 22 | 4.4 | 24.3 | 0.85 | 77.23 | 65.64 | 77 |
| 23 | 11.7 | 24.5 | 0.84 | 82.9 | 69.63 | 121 |
| 24 | 4.6 | 24 | 0.84 | 75.69 | 63.58 | 101 |
| 25 | 4.7 | 24 | 0.83 | 89.74 | 74.49 | 69 |
| 26 | 11.8 | 24 | 0.8 | 72.8 | 58.24 | 107 |
| 27 | 11.8 | 24 | 0.83 | 86.08 | 71.45 | 118 |
| 28 | 11.7 | 25.3 | 0.81 | 77.69 | 62.93 | 145 |
| 29 | 11.7 | 25 | 0.81 | 80.77 | 65.42 | 270 |
| 30 | 4.4 | 24.5 | 0.8 | 74.53 | 59.62 | 180 |
| 31 | 11.4 | 25.5 | 0.85 | 76.27 | 64.82 | 152 |
| 32 | 12.1 | 25.5 | 0.84 | 82.23 | 69.08 | 196 |
| 33 | 8.7 | 25.9 | 0.85 | 80.89 | 68.75 | 136 |
| 34 | 10.7 | 24.3 | 0.82 | 69.8 | 57.23 | 140 |
| 35 | 11.3 | 24.3 | 0.86 | 82.04 | 70.55 | 88 |
| 36 | 11.1 | 24.5 | 0.82 | 69.61 | 57.08 | 110 |
Minimum and maximum limits of each component in the mixture
| Proportion (%) | ||
|---|---|---|
| Component | Inferior | Superior |
| X | 0.03 | 0.2 |
| Y | 0.20 | 0.37 |
| Z | 0.30 | 0.47 |
| W | 0.30 | 0.47 |
| S | 0 | 0.17 |
Regression equations for the response variables viscosity, pH, and RAU
| Response variable | Regression equation | R2 |
|---|---|---|
| Viscosity | ŷ = 152.57X + 57.56Y + 84.86Z + 52.58W + 130.57S - 147.2XY - 127.7XZ - 132.3XW - 181.9XS - 93.4YS-94.1ZS | 93.28% |
| pH | ŷ = 4.14X +4.35Y +4.36Z +4.24W + 10.63S + 22.16XS + 23.06YS + 23.69ZS + 23.71WS | 87.34% |
| RAU | ŷ = 197.6X + 47.9Y + 49.3Z + 59.3W + 141.0S + 338.0WS | 60.40% |
Mixtures generated by Minitab 20_4 software
| Mixture | X | Y | Z | W | S |
|---|---|---|---|---|---|
| 1 | 0.03 | 0.2 | 0.3 | 0.3 | 0.17 |
| 2 | 0.2 | 0.2 | 0.3 | 0.3 | 0 |
| 3 | 0.03 | 0.37 | 0.3 | 0.3 | 0 |
| 4 | 0.03 | 0.2 | 0.47 | 0.3 | 0 |
| 5 | 0.03 | 0.2 | 0.3 | 0.47 | 0 |
| 6 | 0.03 | 0.2 | 0.3 | 0.39 | 0.09 |
| 7 | 0.03 | 0.2 | 0.39 | 0.3 | 0.09 |
| 8 | 0.03 | 0.2 | 0.39 | 0.39 | 0 |
| 9 | 0.03 | 0.29 | 0.3 | 0.3 | 0.09 |
| 10 | 0.03 | 0.29 | 0.3 | 0.39 | 0 |
| 11 | 0.03 | 0.29 | 0.39 | 0.3 | 0 |
| 12 | 0.12 | 0.2 | 0.3 | 0.3 | 0.09 |
| 13 | 0.12 | 0.2 | 0.3 | 0.39 | 0 |
| 14 | 0.12 | 0.2 | 0.39 | 0.3 | 0 |
| 15 | 0.12 | 0.29 | 0.3 | 0.3 | 0 |
| 16 | 0.03 | 0.2 | 0.36 | 0.36 | 0.06 |
| 17 | 0.03 | 0.26 | 0.3 | 0.36 | 0.06 |
| 18 | 0.03 | 0.26 | 0.36 | 0.3 | 0.06 |
| 19 | 0.03 | 0,26 | 0.36 | 0.36 | 0 |
| 20 | 0.09 | 0.2 | 0.3 | 0.36 | 0.06 |
| 21 | 0.09 | 0.2 | 0.36 | 0.3 | 0.06 |
| 22 | 0.09 | 0.2 | 0.36 | 0.36 | 0 |
| 23 | 0.09 | 0.26 | 0.3 | 0.3 | 0.06 |
| 24 | 0.09 | 0.26 | 0.3 | 0.36 | 0 |
| 25 | 0.09 | 0.26 | 0.36 | 0.3 | 0 |
| 26 | 0.03 | 0.24 | 0.34 | 0.34 | 0.04 |
| 27 | 0.07 | 0.2 | 0.34 | 0.34 | 0.04 |
| 28 | 0.07 | 0.24 | 0.3 | 0.34 | 0.04 |
| 29 | 0.07 | 0.24 | 0.34 | 0.3 | 0.04 |
| 30 | 0.07 | 0.24 | 0.34 | 0.34 | 0 |
| 31 | 0.06 | 0.23 | 0.33 | 0.33 | 0.03 |
| 32 | 0.05 | 0.22 | 0.32 | 0.32 | 0.1 |
| 33 | 0.13 | 0.22 | 0.32 | 0.32 | 0.02 |
| 34 | 0.05 | 0.3 | 0.32 | 0.32 | 0.02 |
| 35 | 0.05 | 0.22 | 0.4 | 0.32 | 0.02 |
| 36 | 0.05 | 0.22 | 0.32 | 0.4 | 0.02 |