Figures 
6 
Tables 
8 
Nomenclature 
8 
1 
Background and Introduction 
11 

1.1 
Overview and Motivation 
11 
1.2 
Measurement Techniques 
12 
1.3 
Summary of Previous Work 
14 
2 
Theory 
14 

2.1 
ElectricalImpedance Tomography (EIT) 
14 
2.2 
GammaDensitometry Tomography (GDT) 
19 
2.3 
Combined EIT and GDT for ThreePhase Measurements 
21 
3 
Diagnostic Systems 
24 

3.1 
EIT Apparatus 
24 
3.2 
GDT Apparatus 
26 
4 
Experiments 
27 

4.1 
Benchtop Validation Test 
27 
4.2 
Sandia's Slurry BubbleColumn Reactor (SBCR) Facility 
29 
4.3 
Experimental Procedure for Measurement in Sandia's SBCR 
32 
4.4 
Experimental Material Properties 
34 
4.5 
Sources of Uncertainty 
35 
5 
Experimental Results and Discussion 
36 

5.1 
Benchtop Validation Measurements 
36 
5.2 
TwoPhase Measurements 
37 
5.3 
ThreePhase Measurements 
45 
6 
Conclusions and Future Recommendations 
52 
References 
53 
Appendix 
56 

LIST OF FIGURES 
Figure 1 
Schematic of an EIT system applied to an electrically insulating
(nonconducting) vessel 
16 
Figure 2 
Schematic of an EIT system applied to an electrically conducting
vessel 
17 
Figure 3 
Photograph of verification experiment showing the EIT
electronics, the electrode rod with seven copper ring electrodes
(the top eight ring shown is a plastic seal), and the standpipe 
25 
Figure 4 
Photographs of the circuit boards inside the EIT electronics box 
26 
Figure 5 
A schematic of the GDT system in the horizontal plane 
27 
Figure 6 
Schematic of verification experiment consisting of an electrode
rod inserted coaxially in an electrically conducting standpipe
filled with nonconducting solid polystyrene particles and liquid 
28 
Figure 7 
Photograph of the Sandia slurry bubblecolumn reactor facility.
Also shown is the vault for the gamma source mounted on the twoaxis
automated traverse 
29 
Figure 8 
Photograph of a cross sparger similar to that used in this study
to inject air into the bottom of the bubble column 
30 
Figure 9 
Schematic of EIT system applied to Sandia's slurry bubblecolumn
reactor (SBCR). Shown on the right is a photograph of the SBCR
(0.48mID). The bottom left shows predictions of voltage contours in
a crosssection of the SBCR for two cases, one of constant
conductivity in the top half, and one of variable conductivity in
the bottom half 
31 
Figure 10 
(a) Computational mesh corresponding to onequarter of the
interior of the SBCR with the EIT rod inserted along a diameter. (b)
Voltage contours computed for a uniform electrical conductivity
throughout the domain with current injection from electrode 4 
33 
Figure 11 
Plot of the EIT reconstructed particlebed height versus the
measured particlebed height in the steel standpipe 
36 
Figure 12 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 103 kPa and a
superficial gas velocity = _{g}u 10 cm/s 
39 
Figure 13 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 103 kPa and a
superficial gas velocity = _{g}u 15 cm/s 
39 
Figure 14 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 103 kPa and a
superficial gas velocity = _{g}u 20 cm/s 
40 
Figure 15 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 103 kPa and a
superficial gas velocity = _{g}u 25 cm/s 
40 
Figure 16 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 207 kPa and a
superficial gas velocity = _{g}u 10 cm/s 
41 
Figure 17 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 207 kPa and a
superficial gas velocity = _{g}u 15 cm/s 
41 
Figure 18 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 207 kPa and a
superficial gas velocity = _{g}u 20 cm/s 
42 
Figure 19 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 207 kPa and a
superficial gas velocity = _{g}u 25 cm/s 
42 
Figure 20 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 310 kPa and a
superficial gas velocity = _{g}u 10 cm/s 
43 
Figure 21 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 310 kPa and a
superficial gas velocity = _{g}u 15 cm/s 
43 
Figure 22 
Comparison of symmetric radial gas volume fraction profiles from
EIT and GDT for a column pressure _{colp} = 310 kPa and a
superficial gas velocity = _{g}u 20 cm/s 
44 
Figure 23 
Plot of the bulkaveraged gas fraction as a function of
superficial gas velocity and column pressure, from GDT measurements 
44 
Figure 24 
Plot of the bulkaveraged gas fraction as a function of
superficial gas velocity and column pressure, from EIT measurements 
45 
Figure 25 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 0%, with a column
pressure _{colp }= 103 kPa and a superficial gas
velocity nom= _{g}u
10 cm/s. 
47 
Figure 26 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 0%, with a column
pressure _{colp }= 207 kPa and a superficial gas
velocity nom= _{g}u
10 cm/s. 
48 
Figure 27 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 4%,
with a column pressure _{colp }= 103 kPa and a
superficial gas velocity nom= _{g}u
10 cm/s. 
48 
Figure 28 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 4%,
with a column pressure _{colp }= 207 kPa and a
superficial gas velocity nom= _{g}u
10 cm/s. 
49 
Figure 29 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 8%,
with a column pressure _{colp }= 103 kPa and a
superficial gas velocity nom= _{g}u
10 cm/s. 
49 
Figure 30 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 8%,
with a column pressure _{colp }= 207 kPa and a
superficial gas velocity nom= _{g}u
10 cm/s. 
50 
Figure 31 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 4%, with a column
pressure _{colp }= 103 kPa and a superficial gas
velocity = _{g}u
10 cm/s, and calculated
with a conductivity ratio
~
41.1
~ r )( ~
l
~ = 
50 
Figure 32 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 4%, with a column
pressure _{colp }= 207 kPa and a superficial gas
velocity = _{g}u
10 cm/s, and calculated
with a conductivity ratio
~
41.1
~ r )( ~
l
~ = 
51 
Figure 33 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 8%,
with a column pressure _{colp }= 103 kPa and a
superficial gas velocity = _{g}u
10 cm/s, and calculated
with a conductivity ratio
~
94.0
~ r
)( ~ l
~ = 
51 
Figure 34 
Radial material phasevolumefraction profiles for a nominal
slurry concentration
• 8%,
with a column pressure _{colp }= 207 kPa and a
superficial gas velocity = _{g}u
10 cm/s, and calculated
with a conductivity ratio
~
94.0
~ r )( ~
l
~ = 
52 

LIST OF TABLES 
Table 1 
Various industrial application that would benefit from improved
capability to measure spatial volumetric phase fractions 
12 
Table 2 
Some noninvasive diagnostic techniques reported in the
literature used to measure spatial volumetric phase fractions 
13 
Table 3 
Operating conditions for the two and threephase tests in the
SBCR 
32 
Table 4 
Properties of the phase materials used for the material
distribution reconstructions 
35 
Table 5 
Measured and predicted particlebed heights for 6 different
tests, 3 with copper electrodes and 3 with stainless steel
electrodes 
37 
Table 6 
Comparison of EIT and averaged GDT measurements of gas volume
fractions for the 11 different twophase operating conditions listed
in Table 4 
38 
Table 7 
Predicted bulkaveraged phase volume fractions for the 6
threephase cases measured and listed in Table 4 
46 
Table 8 
Predicted bulkaveraged volumetric phasefractions for the cases
of 4% and 8% nominal solids loading, using a scaled conductivity
ratio 
47 