Multivariate recurrence network analysis for characterizing horizontal oil-water two-phase flow

Characterizing complex patterns arising from horizontal oil-water two-phase flows is a contemporary and challenging problem of paramount importance. We design a new multisector conductance sensor and systematically carry out horizontal oil-water two-phase flow experiments for measuring multivariate signals of different flow patterns. We then infer multivariate recurrence networks from these experimental data and investigate local cross-network properties for each constructed network. Our results demonstrate that a cross-clustering coefficient from a multivariate recurrence network is very sensitive to transitions among different flow patterns and recovers quantitative insights into the flow behavior underlying horizontal oil-water flows. These properties render multivariate recurrence networks particularly powerful for investigating a horizontal oil-water two-phase flow system and its complex interacting components from a network perspective.

Figure 1

Structure of the four-sector conductance sensor.

Figure 2

Experimental flow loop facility.

Figure 3

Scheme of the sensor system installed in the 20-mm-ID pipe.

Figure 4

Experimentally observed horizontal oil-water flow patterns.

Figure 5

The signals from the four-sector conductance sensor for different horizontal oil-water flow patterns. (a) ST flow ($U_{\text{sw}}=0.1105$ m/s, $U_{\text{so}}=0.1326$ m/s). (b) ST and MI flow ($U_{\text{sw}}=0.2210$ m/s, $U_{\text{so}}=0.1945$ m/s). (c) D O-in-W and W flow ($U_{\text{sw}}=0.7368$ m/s, $U_{\text{so}}=0.1945$ m/s). (d) D W-in-O and D O-in-W flow ($U_{\text{sw}}=0.7368$ m/s, $U_{\text{so}}=0.7368$ m/s). (e) D O-in-W flow ($U_{\text{sw}}=1.6579$ m/s, $U_{\text{so}}=0.7368$ m/s).

Figure 6

Global cross-clustering coefficients for the horizontal oil-water ST flow. (a) Cross-clustering coefficients of all pairs of subnetworks for the flow condition $U_{\text{so}}=0.1326$ m/s, $U_{\text{sw}}=0.1105$ m/s. (b) Distributions of $C_{\text{global}}^{CA}$, $C_{\text{global}}^{CB}$, and $C_{\text{global}}^{CD}$ for different flow conditions, where the means and the standard deviations are presented.

Figure 7

Global cross-clustering coefficients for the horizontal oil-water ST and MI flow. (a) Cross-clustering coefficients of all pairs of subnetworks for the flow condition $U_{\text{so}}=0.1326$ m/s, $U_{\text{sw}}=0.2210$ m/s. (b) Distributions of $C_{\text{global}}^{CA}$, $C_{\text{global}}^{CB}$, and $C_{\text{global}}^{CD}$ for different flow conditions, where the means and the standard deviations are presented.

Figure 8

Global cross-clustering coefficients for the horizontal oil-water D O-in-W and W flow. (a) Cross-clustering coefficients of all pairs of subnetworks for the flow condition $U_{\text{sw}}=0.7368$ m/s, $U_{\text{so}}=0.1945$ m/s. (b) Distributions of $C_{\text{global}}^{CA}$, $C_{\text{global}}^{CB}$, and $C_{\text{global}}^{CD}$ for different flow conditions, where the means and the standard deviations are presented.

Figure 9

Pearson correlation coefficient for the signals from the horizontal oil-water D O-in-W and W flow. (a) For the flow condition $U_{\text{sw}}=0.7368$ m/s, $U_{\text{so}}=0.1945$ m/s. (b) For the flow condition $U_{\text{sw}}=0.7368$ m/s, $U_{\text{so}}=0.4421$ m/s.

Figure 10

Global cross-clustering coefficients for the horizontal oil-water D W-in-O and D O-in-W flow. (a) Cross-clustering coefficients of all pairs of subnetworks for the flow condition $U_{\text{sw}}=1.1052$ m/s, $U_{\text{so}}=1.1052$ m/s. (b) Distributions of $C_{\text{global}}^{CA}$, $C_{\text{global}}^{CB}$, and $C_{\text{global}}^{CD}$ for different flow conditions, where the means and the standard deviations are presented.

Figure 11

Global cross-clustering coefficients for the horizontal oil-water D O-in-W flow. (a) Cross-clustering coefficients of all pairs of subnetworks for the flow condition $U_{\text{sw}}=1.6579$ m/s, $U_{\text{so}}=0.1945$ m/s. (b) Distributions of $C_{\text{global}}^{CA}$, $C_{\text{global}}^{CB}$, and $C_{\text{global}}^{CD}$ for different flow conditions, where the means and the standard deviations are presented.

Figure 12

Joint distribution of $C_{\text{global}}^{DA}$, $C_{\text{global}}^{DB}$, and $C_{\text{global}}^{DC}$ for different flow patterns.

Figure 13

Joint distribution of $S_{\text{dev}}^2$ and $S_{\text{dev}}^{\text{all}}$ for D W-in-O and D O-in-W and D O-in-W flow pattern. $S_{\text{dev}}^2$ is the standard deviation of the cross-clustering coefficients $C_{\text{global}}^{DB}$ and $C_{\text{global}}^{DC}$; $S_{\text{dev}}^{\text{all}}$ is the standard deviation of the cross-clustering coefficients for all pairs of subnetworks.

Figure 14

Distributions of global cross-clustering coefficients for the horizontal oil-water ST flow.

Figure 15

Distributions of global cross-clustering coefficients for the horizontal oil-water ST and MI flow.

Figure 16

Distributions of global cross-clustering coefficients for the horizontal oil-water D O-in-W and W flow.

Figure 17

Distributions of global cross-clustering coefficients for the horizontal oil-water D W-in-O and D O-in-W flow.

Figure 18

Distributions of global cross-clustering coefficients for the horizontal oil-water D O-in-W flow.