AN IMPROVED TECHNIQUE OF MEASUREMENT OF LIQUID LEVEL IN

A STORAGE TANK

Hiranmoy Mandal #1

#1Department of Applied Electronics and Instrumentation Engineering,

Academy of Technology, P.O.- Aedconagar, Hooghly -712121, India

#1hiranmoy_mandal@yahoo.co.in

Satish Chandra Bera*2

*2 Instrumentation Engineering Section, Department of Applied Physics,

University of Calcutta, 92, A.P.C. Road, Kolkata 700009, India

*2scbera_cal52@rediffmail.com

Abstract— The liquid level is measured by different techniques of which capacitance techniques has wide application in measurement of level of aqueous solution in a storage tank by using insulated metallic rod electrode immersed in a metallic tank or two such identical electrode immersed in a non metallic tank. This measurement may suffer from inductance effect. Hence, the system likes a coaxial cable which has both inductance and capacitance effect. In the present paper an improved capacitance probe is designed which has no inductance effect. The theory of operation of this sensor has been explained in the paper. The sensor has been designed and tested experimentally. The experimental results are described in the paper. A very good linearity has been observed. Keywords—Liquid level , Storage tank, capacitance , Inductance, Bridge network, Operational amplifiers.

I. INTRODUCTION

Liquid level in a storage tank is a very important process variable which has required to be measured and control in any process industry. The conventional techniques of liquid level measurement may be two type direct type and indirect type. The dip stick; gauge glass, float, displacer etc. are direct category and like capacitance type, pressure sensing type, ultrasonic type, radiation absorption type, electrical conductivity type etc. are indirect type. The capacitance technique [17-21] is widely used in measurement of level of aqueous solution in a storage tank. Since high value of dielectric constant of water provides high sensitivity of measurement using capacitance probe. In order to develop liquid level sensor with more accuracy reliability and simpler technique, various works are still being reported. K.A.P Menon et al [1] have utilized the liquid level as one boundary of a pneumatic capacitor and have designed fluid amplifier feedback oscillator whose frequency linearly varies with liquid level. R.M.A Azzam [2] has proposed a level detector which based on principle of light reflection. A non-contact capacitance type level transducer for a conductive liquid has been developed by S.C.Bera et al [3]. In this transducer , the liquid column of a conducting liquid has been considered as one plate of the sensing capacitor and a noninductively wound short circuited coil around a level sensing insulated cylinder has been considered as other, whereas insulation of the cylinder has been considered as dielectric. D.Xiaowei et al [4]

have proposed side-polished fiber Bragg grating (FBG) level sensor for detecting height variation of liquids of arbitrary refractive index. Q. Jiang et al [5] have proposed novel fiber optic sensor for the measurement of liquid level based on tilted fiber Bragg grating (TFBG). This technique offers goods sensitivity of over 0.6 dB/mm with good linearity. An optical fiber liquid level contact-type transducer has been proposed by G. Betta et al [6], [7]. This transducer generates optical pulses when the liquid level moves along the cladding and uncladding zones of the optical fiber. This transducer can be used with intrinsic safety in explosive or inflammable liquids. A digital fiber optic liquid level sensor has been proposed by J. A. Morris et al [11]. This sensor consists of a source wave guide and an array of digitally masked receiving wave guide and operates on selective coupling between the two. A. Hwili et al [12] have developed a single rod type level sensor for measurement of levels of multi interfaces among different materials. The sensor operates by using an A.C. current source. The differential optical absorption property of light in an optical fiber has been utilized by C.P.Yakymyshyn et al [13] to measure liquid level using LED source and multimode optical fiber. B.Yun et al [14] have proposed a highly sensitive liquid level sensor based on etched fiber Bragg grating. H.Zheng et al [15] have proposed an accurate level measuring technique for analysis and monitoring of ship stability. D.Royer et al [8] have utilized the absorption property of guided acoustic wave to design a level sensor.

The capacitance technique is widely used for measurement of level of water or aqueous solution in a storage tank. Since water has a very high value of dielectric constant compared to that of any other liquid, so capacitance type liquid level sensor is found to have very good sensitivity in water or in aqueous solutions in a storage tank. This sensor generally consists of an insulated uniform metallic rod immersed in a metallic storage tank or two such identical rods immersed in a nonmetallic storage tank. The capacitance between metallic storage tank and the immersed metallic rod or the capacitance between two identical immersed metallic rods is found to vary almost linearly with liquid level. This capacitance is generally measured by an A.C bridge circuit. In this case, an A.C current is passed through the metallic rod. A metallic rod carrying an A.C current is associated with a varying magnetic flux. So, the metallic rod should have an

equivalent self inductance which is connected in series with the capacitance being measured. This self inductance [16] is nonlinearly related with frequency, current density etc. In the present paper, a modified capacitance type level sensor has been designed and tested. This level sensor is free from self inductance effect of a metallic rod electrode of conventional capacitance type level sensor. In this sensor, each electrode consists of uniformly wound short circuited non inductive coil on an insulating cylinder kept inside a shielding cylinder, made of insulating material. One such cylinder is placed inside a larger diameter cylinder, so that a cylindrical capacitance is formed between inner coil and outside coil which are not in contact with the liquid. The change in capacitance of a capacitor due to a change in level is generally very small. Hence, different attempts have been made by different researchers [9], [10] to accurately measure this change in capacitance. In the present work a modified capacitance bridge technique [3] has been used to measure the change of capacitance of the proposed level sensor free from any self inductance effect. The theoretical equations, explaining the performance of the sensor have been derived. The performance of the level transducer designed on the basis of the modified capacitance bridge is experimentally analyzed. The experimental results are reported in the paper. A very good linear characteristics and repeatability of the transducer is observed.

II. METHODOLOGY

The conventional capacitance type level sensor consists of an insulated metallic electrode immersed in the liquid of a metallic storage tank or two identical insulated metallic electrodes immersed in the liquid of non metallic storage tank as shown in Fig. 1(a) &1(b) respectively. The capacitance between metallic probe and metallic storage tank as shown in Fig. 1(a) or the capacitance between two metallic probes as shown in Fig. 1(b) is almost linearly related with liquid level. This Capacitance is measured by various techniques such as a.c bridge network technique, capacitance to frequency conversion technique etc [21].In these techniques, the self inductance effect between a metallic electrode & a metallic storage tank or between two metallic electrodes is not generally considered. We know that the capacitance (C) per unit length and the self inductance (L) per unit length between the central conductor & outer conductor of a coaxial cable [16] is given by

2

1

2

lnC

rr

πε=⎛ ⎞⎜ ⎟⎝ ⎠

(1)

0 2

1

ln2

rLr

μπ

⎛ ⎞= ⎜ ⎟

⎝ ⎠ (2)

Where, ε is the permittivity of the insulated medium between the two conductors and µ0 is the permeability of the insulated medium, r1 is the radius of inner conductor & r2 is the inner radius outer conductor of the coaxial cable. Now, an insulated metallic electrode immersed in the liquid of a metallic storage tank or two parallel insulated metallic electrodes immersed in

the liquid of non metallic storage tank may be assumed to behave like coaxial cable. So in a metallic storage tank, where inner radius (r2) of the tank is much larger than the radius (r1) of the metallic level sensing electrode, the inductance effect may be comparable with the capacitance effect. So measurement of level by using capacitance technique may be affected due to the self inductance effect. To overcome this probable defect of capacitance type level measurement, a modified capacitance type technique is developed in the present work as discussed below.

(a)

(b)

Fig. 1 Conventional capacitance probe. (a) Insulated metallic electrode immersed in the liquid of a metallic storage tank. (b)Two identical insulated metallic electrodes immersed in the liquid of non-metallic storage tank.

Let us consider two co-axial vertical cylinders made

of insulating material with a small gap between them. Each of these cylinders is wound with two layer uniform non-inductive winding with open end short circuited as shown in Fig. 2(a). Each of inner and outer cylinders is placed inside another coaxial seal cover cylinder so that there is little air gap between winding and cover cylinder and the coil may never come in contact with liquid. The inner most cylinder with coil and cover cylinder acts as inner sensing cylinder and the outer cylinder with coil and cover cylinder acts as outer sensing cylinder.

The two cylinders are held together rigidly between two insulating plates with perforating holes in the region between the two sensing cylinders so that liquid may enter the space between the two cylinders freely. Two lead wires are brought out from the short circuited ends of two non- inductive coils. Thus inner sensing cylinder and outer sensing cylinder with bottom plate and cover plate act as a single unit with two lead wires. When this unit is placed inside the storage tank by suitable holders, the liquid of the tank enters into the space between two sensing cylinders through the perforating holes of the bottom plate. With increase of level above the datum level, the level of the liquid in the space between the two sensing cylinders also increases. Now the two non-inductively wound coils together act as an inductance free cylindrical capacitor with liquid and other materials between them as the dielectric. Since the two coils are non-inductively wound so the self inductance effect of the conventional capacitance type level sensor is not present in this modified technique.

(a)

(b)

Fig. 2: Proposed modified capacitance type level sensor. (a) Sectional view (b) Cross sectional view

Now a single turn coil with conductor radius r has conductor height 2r [3]. So, the capacitance between the two single turn coils of the two sensing cylinders is given by

1 2 2

1 1 2

3 3 3

2 3 3

8 82 2 2

16 8 8 81 0 22 2 2

2 2 2

3 2 12 2 2

1 1 14

1 1 1

d t r d D

d t r d t r d

d D Dt

D d D

dx dx dxC rx x x

dx dx dxx x x

πε ε ε

ε ε ε

+ +

+ + + +

+

⎡⎢= + + +⎢⎢⎣

⎤⎥+ + ⎥⎥⎦

∫ ∫ ∫

∫ ∫ ∫

(3)

1 32

10 1 1 3 1

2 3 3

2 2 3 3 2

( 8 8 )( 2 )1 14 ln ln( 8 8 ) ( 6 8 )

1 1ln ln

d t r D tdC r

d t r D d t r

D D dd d D

πε ε

ε ε

⎡ ⎛ ⎞⎛ ⎞ + + += + +⎢ ⎜ ⎟⎜ ⎟+ + + +⎢ ⎝ ⎠ ⎝ ⎠⎣

⎤⎛ ⎞ ⎛ ⎞+ ⎥⎜ ⎟ ⎜ ⎟

⎥⎝ ⎠⎝ ⎠ ⎦

(4)

where t is the thickness of insulation of super enameled copper wire, d1 is the diameter of inner solid insulating cylinder wound with inner sensing coil, d2 and D2 are inner and outer diameters of seal cover cylinder of inner sensing coil, d3 and D3 are inner and outer diameters of outer sensing cylinder wound with outer sensing coil, 0 1, 2 3, and ε ε ε ε are the permittivities of air, super enameled coating material of copper wire, insulating material of sensing cylinder & seal cover cylinder and process liquid in storage tank respectively. For level h above datum level, the capacitance between two sensing coils is given by

1 12( )h

hC C

r t=

+ (5)

Or,

1 1hC K h= (6)

11 = constant

2( )C

Kr t

=+

(7)

Here, 1hC indicates the capacitance between those turns of the coils which are embraced by the liquid over level h. Another capacitance 0C is the parallel combination of three

capacitances which are (a) Capacitance ( airC ) between the coils for the remaining number of turns which are not embraced by the liquid, (b) Capacitance ( 0C ′ ) between the coils for datum height ho and (c) parasitic or fringe capacitance ( parasiticC ) at the upper end and lower end of coils due to the presence of other conductors as well as due to leakage flux which is in parallel with 1hC . Thus,

1 0h hC C C= + (8) Where,

0 0 parasiticairC C C C′= + + (9)

If the total length of each coil above datum level be l then for level h, the length of each coil above liquid surface is (l – h). Hence,

2 3 1 3

0 2 1 1 3 1

2 3

2 2 3

( 8 8 )( 2 )1 12 ( ) ln ln( 8 8 ) ( 6 8 )

1 ln

aird d d t r D t

C l hD d t r D d t r

D Dd d

πε ε

ε

⎡ ⎛ ⎞⎛ ⎞ + + += − + +⎢ ⎜ ⎟⎜ ⎟+ + + +⎝ ⎠ ⎝ ⎠⎣

⎤⎛ ⎞⎥⎜ ⎟

⎝ ⎠⎦

(10)

Or,

2 ( ) airC K l h= − (11)

Where, 2 3 1 3

20 2 1 1 3 1

2 3

2 2 3

( 8 8 )( 2 )1 12 ln ln( 8 8 ) ( 6 8 )

1 ln

d d d t r D tKD d t r D d t r

D Dd d

πε ε

ε

⎡ ⎛ ⎞⎛ ⎞ + + += + +⎢ ⎜ ⎟⎜ ⎟+ + + +⎝ ⎠ ⎝ ⎠⎣⎤⎛ ⎞⎥⎜ ⎟

⎝ ⎠⎦ (12)

From equation (4),

0 1 0C K h′ = (13) Therefore,

1 0

1 0 parasitic

1 2 2 1 0 parasitic( )

h

air

C K h CK h C C C

K K h K l K h C

= +′= + + +

= − + + +

(14)

Thus Ch is linearly related with liquid level ‘h’ since K1, K2, l, h0 and Cparasitic are constants. Let

0 2 1 0 parasiticC K l K h C′′ = + + . (15) Hence change of capacitance due to level h is given by ( )0 1 2hC C C K K h′′Δ = − = − (16)

Or, 0 0 1 2( )hC C C C K K h′′ ′′= + Δ = + − (17)

Where, 0C′′ is the capacitance of the probe for the datum level of liquid.

III. MEASURING CIRCUIT A modified De’Sauty bridge circuit [3] using op-amp

is designed as shown in Fig.3 for measuring capacitance of the modified level transducer. Following the same procedure as in [3], the bridge output V0 is given by,

[ ]0f

h

j RV CP QC V

Qω

= − (18)

From equations (17) and (18), we have,

[ ]

[ ]

0 0

0 1 2

( )

{ ( ) }

f

f

j RV CP Q C C V

Qj R

CP Q C K K h VQ

ω

ω

′′= − + Δ

′′= − + − (19)

Now if the bridge be balanced at datum level then CP = Q 0C′′ and the bridge output may be given by

( )0 1 2f fV j R V C j R V K K hω ω= − Δ = − − (20) Thus, the bridge output is linearly related with the change in level (h) above datum level.

Fig.3: Modified De’Sauty bridge circuit for capacitance measurement.

IV. DESIGN

The materials used in the design of the proposed level sensor were super enamelled copper winding wire, acrylic rod and acrylic tubes and thick acrylic sheet. The sensor consists of two non-inductive two layer windings on two coaxial cylinders. The inner winding was made on an acrylic solid rod of diameter 6mm by using super enamelled copper wire of 40 SWG. This rod with winding was then placed inside another hollow acrylic tube of inner diameter 8 mm which is slightly larger than the inner rod so that there is little air gap between the winding & the outer cylinder. The second two layer non inductive winding of 40 SWG super enamelled copper wire was made on a second acrylic cylinder of inner diameter 18 mm which is greater than the outer diameter of the cover cylinder of the previous coil. This second cylinder with coil was placed inside a third acrylic cylinder of inner diameter 20mm which is slightly greater than the outer diameter of the second cylinder so that there is very little air gap between the second winding & the third cylinder. Each cylinder was of thickness 2 mm. The acrylic rod with first coil & the cover cylinder was placed inside the second cylinder so that there is sufficient air gap between the cover cylinder & second cylinder. The whole system was kept fixed in position between two end plates made of acrylic sheets by means of araldite. The space between the inner cover cylinder of inner coil & the cylinder of second coil was perforated on both sides so that when whole system was inserted into a liquid, this space between the cylinders can be easily filled with the liquid with equal level at inside & outside of the system. The free ends of each of non-inductively wound coils are short

circuited. From the upper short circuited end of each coil, a lead wire is drawn & is passed through suitable holes of the upper cover plate of the whole system. When the whole unit is inserted into a liquid, the liquid enters into the space between the two sealed coils and the capacitance between the coils changes with liquid level. The capacitance of this cylindrical capacitor is measured by a bridge network as shown in Fig.3.The bridge network is designed by using op-amps (OP-07).

V. EXPERIMENT The experiment was performed in three steps. In the

first step the self inductance effect between two metallic rod electrodes of the conventional capacitance type level sensor was studied. In this study two bare brass electrodes each of diameter 10 mm. was immersed in a plastic tank at a distance of 20 mm. from each other. The tap water level in the tank was increased and self inductance between the electrodes was measured by digital LCR meter (MIC4070D).A nonlinear variation of self inductance with level was observed as shown in Fig.4.

Fig.4 Variation of self inductance with level between two metallic electrodes of conventional capacitance type level sensor.

In the second step, the static characteristic of the

proposed level sensor was determined with experimental arrangement as shown in Fig.5 .In this step, the self inductance between the short circuited coils was measured by the same LCR meter (MIC4070D) and was found to be zero at all levels. Now to find the static characteristic of the sensor, the liquid level in the storage tank was increased by adding water and capacitance between the two lead wires of the sensor was measured by the same LCR meter (MIC4070D) and level was measured from gauge glass. The static characteristic curve of the level sensor was then drawn by plotting capacitance against level. The characteristic curves for three increasing and three decreasing modes are shown in Fig.6. The percentage deviation curves from ideal linearity for these experimental data are shown in Fig.7 and the corresponding standard deviation curve is shown in Fig.8.

Fig. 5: Block diagram of proposed level sensor.

Fig.6: Static characteristic curves of the proposed level sensor

Fig.7: Percentage deviation curves from linearity of the

proposed level sensor

Fig.8: Standard deviation curve of the proposed level sensor

In the third step of the experiment the characteristic of the modified De’ Sauty bridge type level transducer was determined by connecting the sensor terminals with the bridge arm as shown in Fig.3. The level in the storage tank was increased in steps and at each step bridge circuit output was measured by a four and half digit digital multimeter. Static characteristic of the transducer was then drawn by plotting bridge output against level. The static characteristic curves of the transducer in three increasing and three decreasing modes are shown in Fig.9. The corresponding percentage deviation curves from linearity are shown in Fig.10 and the standard deviation curve is shown in Fig.11.

Fig.9: Static characteristic curves of the proposed level

transducer.

Fig. 10: Percentage deviation curves from linearity of the

level transducer

Fig.11: Standard deviation curve of the level transducer

VI. DISCUSSIONS From the experimental graph as shown in Fig.4 it is

observed that there exists a self inductance effect between the metallic electrodes of a conventional two electrode capacitance type level sensor. This self inductance varies nonlinearly with level and may affect the linear performance of the level transducer. So a modified non inductive capacitance type level sensor has been proposed in the present work. From Fig.6 it is observed that the proposed level sensor has a very good linearity and the maximum percentage deviation from linearity is also within tolerable limit as shown in Fig.7. In the standard deviation curve shown in Fig.8 a good repeatability of this sensor has been observed. From Fig.9 it is observed that the proposed level transducer has also a good linearity with small percentage deviation from ideal linearity as shown in Fig.10. From the standard deviation curve shown in Fig.11, a good repeatability of this transducer has been observed. The noninductive coils of the proposed sensor remove the self inductance effect of the conventional capacitance type level sensor. Since these coils have no contact with the process liquid the life period of the sensor will be much more than the conventional capacitive sensor. The sensing dielectric materials including the process liquid between the two coils are only responsible for the capacitance of the proposed sensor. The outermost cover cylinder has no effect on the performance of the sensor. The proposed sensor may be used for both conductive and nonconductive liquid in a metallic or non metallic storage tank but in case of conventional sensor two identical electrodes are needed for measurement of liquid level in a nonmetallic storage tank. In the conventional capacitive sensor the sensing electrode is coated with insulated material like teflon, PVC etc. and the performance of the sensor is highly affected by the non uniformity of thickness of coating material since uniformity of thickness is difficult to be obtained. This does not arise in the proposed sensor since insulating cylinders with uniform thickness and copper wire with uniform enameled coating are easily available. Hence the design of the proposed sensor may be easier than that of the conventional sensor. So the cost of the proposed sensor with insulating cylinders and copper coils may be less than the conventional capacitance sensor. Moreover, the same sensor may be used in all types of liquid for both metallic and non-metallic tanks, which is not possible with the conventional sensor.

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