Electrical network analysis of a multiphase system

1. A system for determining characteristics of a multi-material object comprising:

a measurement unit to obtain a measured electrical signal set from electrodes surrounding the multi-material object; and

a processing circuitry configured to perform steps of:

determining an electric element matrix representing the multi-material object based on the measured electrical signal set;

pre-multiplying the electric element matrix with a first mathematical transformation matrix to obtain a first transformed electric element matrix;

post-multiplying the first transformed electric element matrix with a second mathematical transformation matrix to obtain a second transformed electric element matrix; and

determining the characteristics of the multi-material object based on the second transformed electric element matrix,

wherein the characteristics of the multi-material object comprise compositions and distributions of different materials within the multi-material object.

2. The system of claim 1 , wherein the electric element matrix comprises an impedance matrix or an admittance matrix.

3. The system of claim 1 , wherein the first mathematical transformation matrix and the second mathematical transformation matrix transform a coordinate system of the electric element matrix.

4. The system of claim 1 , wherein the first mathematical transformation matrix comprises a discrete Fourier transform matrix and the second mathematical transformation matrix comprises an inverse of the discrete Fourier transform matrix.

5. The system of claim 1 , wherein the first mathematical transformation matrix comprises an identity matrix.

6. The system of claim 1 , wherein the second mathematical transformation matrix comprises an identity matrix.

7. The system of claim 1 , wherein determining the characteristics of the multi-material object comprises determining a spatial symmetry in the distribution of the materials within the multi-material object based on the elements along a diagonal of the second transformed impedance matrix and determining an asymmetry in the distribution of materials within the multi-material object based on the elements that do not lie along the diagonal of the second transformed impedance matrix.

8. The system of claim 1 , wherein determining the characteristics of the multi-material object comprises determining a presence of current paths other than current paths through energized electrodes surrounding the multi-material object based on elements in the first row and the first column of the second transformed electric element matrix.

9. The system of claim 1 , wherein determining the characteristics of the multi-material object comprises utilizing the information of the electric element matrix obtained from numerical simulations of randomly generated flow regimes and material distributions.

10. The system of claim 1 , wherein determining the characteristics of the multi-material object comprises utilizing the information on the electric element matrix based on prior experimental results.

11. The system of claim 1 , wherein elements not lying on a diagonal of the electric element matrix comprise zeros for a spatially symmetric flow regime.

12. The system of claim 11 , wherein the spatially symmetric flow regime comprises at least one of a churn flow regime or an annular flow regime.

13. The system of claim 1 , wherein elements not lying on a diagonal of the electric element matrix comprise non-zero values for an asymmetric flow regime.

14. The system of claim 13 , wherein the asymmetric flow regime comprises a bubbly flow regime.

15. The system of claim 1 , wherein determining the characteristics of the multi-material object comprises determining flow regimes, volumetric fraction, density and velocity of the materials within the multi-material object.

16. The system of claim 1 , wherein the processing circuitry is further configured for determining an equivalent visual representation of the material distribution within the multi-material object.

17. The system of claim 16 , wherein determining the characteristics of the multi-material object comprises determining flow regimes, volumetric fraction, density and velocity of the materials within the multi-material object based on the equivalent visual representation.

18. The system of claim 16 , wherein determining the equivalent visual representation of the material distribution within the multi-material object comprises combining various distributed areas of the secondary phase into a single area.

19. A multi-material sensing system comprising:

a power supply to provide an applied electrical signal set to electrodes surrounding a multi-material object;

a measurement unit to obtain a measured electrical signal set from the electrodes; and

processing circuitry to determine an electric element matrix based on the applied and measured electrical signal sets, to pre-multiply the electric element matrix with a first mathematical transformation matrix to obtain a first transformed electric element matrix, to post-multiply the first transformed electric element matrix with a second mathematical transformation matrix to obtain a second transformed electric element matrix and to determine the characteristics of the multi-material object based on the second transformed electric element matrix,

wherein the characteristics of the multi-material object comprise compositions and distributions of different materials within the multi-material object.

20. The system of claim 19 , wherein the power supply comprises a voltage source or a current source.

21. The system of claim 19 , wherein the measurement unit comprises a voltmeter or a current meter.

22. The system of claim 19 , wherein the multi-material object comprises oil, water, and gas.

23. A non-transitory computer-readable medium comprising computer-readable instructions of a computer program that, when executed by a processor, cause the processor to perform a method of determining characteristics of a multi-material object comprising:

providing an applied electrical signal set to the electrodes surrounding the multi-material object;

obtaining a measured electrical signal set of measured electrical signals from the electrodes;

pre-multiplying the measured electrical signal set with a first mathematical transformation matrix to obtain a first transformed measured electrical signal set;

post-multiplying the first transformed measured electrical signal set with a second mathematical transformation matrix to obtain a second transformed measured electrical signal set; and

determining the characteristics of the multi-material object based on the second transformed measured electrical signal set,

wherein the characteristics of the multi-material object comprise compositions and distributions of different materials within the multi-material object.

24. A system for determining characteristics of a multi-material object comprising:

a measurement unit to obtain a measured electrical signal set from electrodes surrounding the multi-material object; and

a processing circuitry configured to perform steps of:

determining an electric element matrix representing the multi-material object based on the measured electrical signal set;

pre-multiplying the electric element matrix with a first mathematical transformation matrix to obtain a first transformed electric element matrix;

post-multiplying the first transformed electric element matrix with a second mathematical transformation matrix to obtain a second transformed electric element matrix; and

determining the characteristics of the multi-material object based on the second transformed electric element matrix,

wherein the characteristics of the multi-material object comprise flow regimes, volumetric fraction, density and velocity of the materials within the multi-material object.