Technical sciences  / 5. Energy

 

Ph.D. Solntseva A.V., Ph.D. Borminsky S.A.

Samara State Aerospace University, Russia

System for remote monitoring of liquids stored in pools and tanks

 

Plants of oil-extracting, oil-processing, aircraft, medical and food industries need to organize remote control of liquids, stored or transported in pools and tanks. Main control parameters are level and density of liquids.

Picture 1 shows Tank 1 with liquid to be monitored. Wave Guide 2 is installed inside the tank. Acoustic Sensor 3 is set at an open end of the wave guide. It receives sounding impulses from Generator 4. Data collected from Acoustic Sensor 3 and from Generator 4 go to Data Collecting Unit 5. Data Collecting Unit 5, Analog-Digital Converter Unit 6, Spectrum Analysis Unit 7,  Level Calculating Unit 8 and Density Calculating Unit 9 are in series connection to process information received.

 

Picture 1 - Block diagram of system for remote monitoring of liquids' parameters

 

Tank 1 is filled with liquid to be monitored (Medium II), empty part of tank is filled with Medium I. Generator 4 sends a sounding pulse p(0,t) to Acoustic Sensor 3. This pulse is an energy bunch, that stimulates around vibration set of variable frequencies. Its spectral density is described by Fourier transformation:

                       .                       (1)

Pulse spreads in Medium I inside the Wave Guide 2 till medium boundary. Its form at medium boundary and at current level of liquid in tank is described by the following expression:

                       ,                       (2)

Its spectral density:

                                                               (3)

where Í – is distance to medium boundary,

       kI(jω) - is a wave vector of Medium I, in which the sounding pulse is being spread. It is described by the following expression:

                                                                                                                              (4)

where ñ - is phase acoustic velocity,

      r - medium density,

      b - dissipative coefficient.

The signal is reflected from medium boundary. Reflectance coefficient of acoustic signal at the boundary, at normal fall, absorption by medium not taken into consideration, is described by the following formula:

                               ,                                                                                              (5)

where cI, cII, ρI, ρÕ – acoustic velocities and densities of contacting mediums.

Acoustic velocity c in a medium is seen as a polynomial dependence from density, and in general is described by the following expression:

                                          .                                    (6)

For oil-products with relative density from 0,651 to 1,076 kg/m3 this analytical dependence is expressed as follows:

.     (7)

For any group of liquid products  a linear dependence can be found. It will bind acoustic velocity in the medium and its density. For example, for heavy oil-products with  relative density ranging from 0,8 – 0,95 kg/m3 dependence can be set as linear:

                                                                                       (8)

where ÊÑ =1654 [m4/s·kg]– is a coefficient of correlation between density and acoustic velocity.

Form of the signal, reflected from Medium II, at the moment when it returns to its radiation point, is described by the following expression:

                                   (9)

Reflected signal is received in Data Collecting Unit 5. It is converted into electric signal p(2Í,t). Also, sounding signal from Generator 4 is sent to the input of Data Collecting Unit 5. In Analog-Digital Converter Unit 6 the signals are converted correspondently. Digital signals are Fourier-transformed in Unit 7.

Spectrum densities of sounding signal and signal reflected from Medium II, that has passed 2Í distance (from its emission point to Medium II boundary and backwards), are bound by the following expression:

                                             (10)

Expression (8) states, that level and density are correlated with signals' spectral densities, taking into account  (7), by the following relations:

           ,           (11)

              .                   (12)

Spectrum densities of sounding and reflected signals are complex variables. In Spectrum Analysis Unit 7 they are decomposed into amplitude and phase components.

Equating relations  and , represented in exponential form and in form (10), we  will derive the following expression:

                    .                    (13)

Thus, data about amplitude and phase components ,,, is used to calculate level and density variables in Units 8 and 9. When measuring, from amplitude and phase  frequency range, we take the frequency, at which calculation is made (frequency selection ωi). Frequency i-selection means definite spectrum component values ,,,, taken at frequency ωi.

Distance Í from sensor to medium boundary is calculated in Unit 8. Forms (13) and (4) are used. Besides, the fact that complex numbers are equal, provided their real and imaginary components are equal, is taken into consideration. The following expression is used:

                   .                           (14)

The following formula calculates the level of Medium II in tank:

                                              HX=H0-H.                                         (15)

Medium II density is calculated in Unit 9 according to this expression:

                           .                                   (16)

There are  cases, when measurement matter allows to compose linear dependence between acoustic velocity and density as shown in (6), as for example for heavy oil-products in expression (8). Then density is calculated by the following expression:

                 ,                (17)

where d0, d1 - are polynomial coefficients (6) for Medium I,

a0, a1 - are polynomial coefficients (6) for Medium II.

As for accuracy of methods suggested, at tank Medium II level equal to 1m, level measurement absolute error is 1.5 sm, while density measurement relative reduced error is 4.5%.

 

Reference

 

1. Solntseva A.V., Borminsky S.A. Measurement method of tank infill based on spectrum analysis of acoustic impulse reflected from the controlled medium // Volga Region Scientific and technical Bulletin. – 2014. – ¹6. – P. 348-351.

2. Solntseva A.V., Borminsky S.A., Skvortsov B.V. Method Controlling  Density of Liquid Medium Based on Spectral Characteristics of Reflected Acoustic Impulses // Samara Scientific Center of RAS bulletin. – 2014. – V.16. - ¹6. – P.85-88.