Method for imaging multiphase flow using electrical capacitance tomography

• US 7,496,450 B2
• Filed: 08/22/2003
• Issued: 02/24/2009
• Est. Priority Date: 08/22/2003
• Status: Expired due to Fees

• Current Assignee: Instituto Mexicano Del Petrã³Leo (Gobierno Federal De Los Estados Unidos Mexicanos)
• Original Assignee: Instituto Mexicano Del Petrã³Leo (Gobierno Federal De Los Estados Unidos Mexicanos)
• Inventors: Martin, Roland, Ortiz Alemán, José Carlos, Gamio Roffé, José Carlos
• Primary Examiner(s): Raymond; Edward
• Application Number:
  US10/568,814
• Publication Number:
  US 20070133746A1
• Time in Patent Office: 2,013 Days
• Field of Search: 702/2, 702/6, 702/12, 702/13
• US Class Current: 702/6
• CPC Class Codes: G01F 1/64 by measuring electrical currents passing through the fluid flow; measuring electrical potential generated by the fluid flow, e.g. by electrochemical, contact or friction effects G01F1/58 takes precedence
• CPC Class Codes: G01F 1/74 Devices for measuring flow of a fluid or flow of a fluent solid material in suspension in another fluid
• CPC Class Codes: G01N 27/228 Circuits therefor measuring capacitance per se G01R27/26
• CPC Class Codes: G01N 33/2823 Raw oil, drilling fluid or polyphasic mixtures

Abstract

The invention relates to an image-reconstruction technique which is used to view multiphase flows using electrical capacitance tomography (ECT), which is based on non-linear heuristic global optimization methods involving simulated annealing and genetic algorithms. The inventive method consists in obtaining electrical capacitance data which are measured between electrodes positioned on the outer surface of pipeline, well or tank (electrically-insulating) containing fluids. The aforementioned data are dependent on the distribution of the fluids inside the pipeline, well or tank. Moreover, the data are processed in order to reconstruct an image of the spatial distribution of the relative electrical permittivity (also known as the dielectric constant) inside the tube, well or tank, which reflects the distribution of the different phases present in the flow.

Claims

1. An image reconstruction method from electrical capacitance tomography data comprising:

(a) obtaining the measurement electrical capacitance tomography data by using a recording sensor formed by an array of electrodes located on the perimeter of an oil-pipe, well or tank;

(b) processing said measurement data using the Method of Simulated Annealing for the estimation of an electrical permittivity distribution image; and

(c) displaying said processed image on a display device in order to visualize multiphase oil-flows through a cross section of a pipe, well or tank.

2. A method according to claim 1, wherein the measurement data are collected on the perimeter of a region such as the inside of an oil-pipeline, well or tank.

3. A method according to claim 2, wherein said are the electrical capacitance values recorded between the electrodes of a sensor, which is formed by a plurality of said electrodes placed around the perimeter of the region (pipeline, well, tank).

4. A method according to claim 3, wherein said sensor is formed by a pipe made of an electrically insulating material, on whose outer wall an array of rectangular metallic electrodes is placed.

5. A method according to claim 3, wherein the sensor contains a multiphase or multicomponent flow, and images that show the distribution of the phases or components, such as gases or/and liquids, are obtained in accordance to what is said in the background of the invention.

6. A method according to claim 2, wherein said permittivity image is formed by a finite number of sub-regions or pixels in the oil-flow viewing, which number depends on the desired resolution permittivity image resolution.

7. A method according to claim 1, wherein said estimated image represents the spatial distribution of the electrical permittivity in a cross sectional region of an oil-pipeline, well, or tank, which reflects the spatial distribution of the materials or substances, such as gases and/or liquids, that are flowing through this region (pipeline, well, tank).

8. A method according to claim 1, wherein a cost function associated to the energy of the system is iteratively minimized with respect to E (the vector of the permittivity values in each pixel of the image), said cost function being of the form:

$E_k=L_{2<br><br>\left(k\right)}=\frac{\underset{i=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[c_i^{\mathrm{meas}}-c_i^{\mathrm{calc}}<br><br>\left({\mathrm{\varepsilon <br><br>}}_k\right)\right]}^2}{\underset{i=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[c_i^{\mathrm{meas}}\right]}^2}<br><br><br><br>\left(i=1,\mathrm{\dots <br><br>}<br><br>,m\right)$

where c_i^meas are the m measured mutual capacitances and c_i^calc(∈

_k) are the ones calculated by solving the forward problem for a given permittivity distribution ∈

_k.

9. A method according to claim 8, wherein the Metropolis criterion is used to do the minimization.

10. A method according to claim 9, wherein in the minimization process it is used, as the initial guess for the permittivity distribution, E, both a homogeneous distribution and the distribution that results from applying the linear back-projection (LBP) method to the measurement data.

11. A method according to claim 8, wherein the computation of the calculated capacitances c_i^calc (∈

_k) known as the forward problem, is carried out by means of the finite-volume method.

12. A method according to claim 11, wherein for the solution of the system of equations that results from solving the forward problem c_i^calc (∈

_k), iterative methods that rapidly converge are used, by employing as initial estimation of the electrostatic potential the result of the forward problem solution obtained in the previous iteration of the inverse problem.

13. A method according to claim 1, wherein the method of genetic algorithms is used as an alternative electrical permittivity image estimation method.

14. A method according to claim 13, wherein, starting from an initial population of Q permittivity models ∈

_k(o) (k=1, . . . , Q), evolutionary mechanisms such as selection, crossover and mutation are applied in order to obtain new populations.

15. A method according to claim 14, wherein individuals ∈

_k are characterized by having a small cost (or misfit) function, which is given by

$E_k=L_{2<br><br>\left(k\right)}=\frac{\underset{i=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[c_i^{\mathrm{meas}}-c_i^{\mathrm{calc}}<br><br>\left({\mathrm{\varepsilon <br><br>}}_k\right)\right]}^2}{\underset{i=1}{\overset{m}{\sum <br><br>}}<br><br>{\left[c_i^{\mathrm{meas}}\right]}^2}<br><br><br><br>\left(i=1,\mathrm{\dots <br><br>}<br><br>,m\right)$

where c_i^meas are the m measured mutual capacitances and c_i^calc(∈

_k) are the calculated ones by solving the forward problem for a given model or permittivity distribution ∈

_k.

16. A method according to claim 14, wherein the accumulated probability of selection for a particular model ∈

_k is given by

$P<br><br>\left({\mathrm{\varepsilon <br><br>}}_k\right)=P<br><br>\left({\mathrm{\varepsilon <br><br>}}_{k-1}\right)+\frac{E_{\max }-E<br><br>\left({\mathrm{\varepsilon <br><br>}}_k\right)}{Q<br><br>\left(E_{\max }-E_{\mathrm{avr}}\right)}$

where E_max, and E_avr are maximum and average cost functions of the generation, respectively, and Q is the number of individuals in the population.

17. A method according to claim 16, wherein a biased roulette procedure can be used to decide which models are selected on each iteration of the method.

18. A method according to claim 17, wherein crossover and mutation of models are carried out randomly according to the probabilities of crossover and mutation, P_c y P_m.

19. A method according to claim 18, wherein the probability of mutation P_m is determined using the average variation coefficient γ

, given by

$\mathrm{\gamma <br><br>}=\frac{1}{p}<br><br>\underset{i=1}{\overset{p}{\sum <br><br>}}<br><br>\left(\frac{{\mathrm{\sigma <br><br>}}_i}{{\mathrm{\varepsilon <br><br>}}_i}\right)$

where p is the number of parameters, ∈

_i is the average of the i-th parameter, and σ

_i is the standard deviation.

20. A method according to claim 18, wherein P_m is defined as a function of γ

, that is;

$P_m=\{\begin{array}{ccc}{P}_{\mathrm{ini}}& \mathrm{para}& \mathrm{\gamma <br><br>}><br><br>0.1\\ 0.1& \mathrm{para}& 0.02<<br><br>\mathrm{\gamma <br><br>}<<br><br>0.1\\ 0.2& \mathrm{para}& \mathrm{\gamma <br><br>}<<br><br>0.02\end{array}$

where P_ini is the initial probability of mutation.

21. A method according to claim 14, wherein the calculation of c_i^calc (∈

_k), known as the forward problem, is performed by means of the finite-volume method.