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Table 8 Comparison of real observations and conditions with calculation results of scenarios 1–4. The critical flow velocity \({U_{critical = min.}}\) and the washout flow velocity \({U_{washout = max.}}\) were calculated by Eq. 12 considering also the parameter ranges. The ripple height and ripple length were calculated by Eqs. 4 and 5 considering also the parameter ranges. In the lower part of the table, ripple length and height predictions by the simple Eqs. 1–3 are indicated for comparison. Empty fields: unknown parameters, n.v. = equations not valid for the given input parameters (out of calibration)
Observed ripple geometries | Observed conditions during production | Observed conditions during maintenance | Scenario 1 (production \(22\, \mu \hbox {m}\) calcite) | Scenario 2 (production \(150\, \mu \hbox {m}\) flocc. calcite) | Scenario 3 (maintenance \(22 \, \mu \hbox {m}\) calcite) | Scenario 4 (maintenance \(92 \, \mu \hbox {m}\) coated oil) | |
|---|---|---|---|---|---|---|---|
T, \(^\circ \hbox {C}\) | 139 | 20 | 139 | 139 | 20 | 20 | |
\({\dot{V}}\) | 110 | \(5\, \pm \,2\) | 110 | 110 | \(5\, \pm \,2\) | \(5\, \pm \,2\) | |
\(\nu\), \(10^{-7}\cdot \, {\hbox {m}}^2/\hbox {s}\) | 2.19 | 9.81 | 2.19 | 2.19 | 9.81 | 9.81 | |
\(\rho _p\), \({\hbox {kg/m}}^3\) | \(2710\, \pm \,0.14\) | \(2710\, \pm \,0.14\) | \(2710\, \pm \,0.14\) | \(2710\, \pm \,0.14\) | \(2710\, \pm \,0.14\) | \(1073\,\pm \,28\) | |
\(\rho _l\), \({\hbox {kg/m}}^3\) | 927 | 927 | 927 | \(1020\, \pm \,10\) | \(1020\, \pm \,10\) | ||
\({\hbox {d}}_{50}\), \(\hbox {m} \cdot 10^{-6}\) | 22 (Q1: 18, Q3: 28) | 22 (Q1: 18, Q3: 28) | 150 | 22 (Q1: 18, Q3: 28) | 92 (Q1: 71, Q3: 117) | ||
D* | 1.35 – 2.00 | 11.00 | 0.44 – 0.73 | 0.38 - 1.4 | |||
\(\Theta _c\) | 0.09 - 12 | 0.03 | 0.16 - 0.20 | 0.12 - 0.21 | |||
\({U_{critical = min.}}\), m/s | 1.2 | 0 | 0.18 | 0.22 | 0.21 | 0.04 | |
\({U_{washout = max.}}\), m/s | 2.2 | 0.08 | 0.52 | 0.33 | 0.58 | 0.23 | |
\(\eta _{max}\), \(\hbox {m} \cdot 10^{-3}\) | 1.2 | 3.1 - 3.9 | 8 | n.v. | n.v. | ||
\(\lambda _{max}\), \(\hbox {m} \cdot 10^{-3}\) | 9.7 | 31 - 33 | 83 | n.v. | n.v. | ||
\(\eta _{max-flem.}\), \(\hbox {m} \cdot 10^{-3}\) | 1.2 | 1.2 - 1.9 | 10 | 1.2 - 1.9 | 4.8 - 7.9 | ||
\(\lambda _{max-colem.}\), \(\hbox {m} \cdot 10^{-3}\) | 9.7 | 8.6 - 12.0 | 42 | 8.6 - 12.0 | 24 - 35 | ||
\(\lambda _{max-yalin}\), \(\hbox {m} \cdot 10^{-3}\) | 9.7 | 18 - 28 | 150 | 18 - 28 | 71 - 117 |