Applied Mechanics and Materials Vols. 26-28 (2010) pp 416-421
Online available since 2010/Jun/30 at www.scientific.net
© (2010) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.26-28.416
Automatic Measurement System for Vertical tank Volume by
Electro-Optical Distance-Ranging Method
Jintao Wang1, a, Ziyong Liu1, b, Long Zhang1, c, Ligong Guo1, d, Xuesong Bao1, e,
and Lin Tong1, f
1
Division of Mechanics and Acoustics, National Institute of Metrology, Beijing, China, 100013
a
[email protected], [email protected], [email protected], [email protected] , [email protected]
, [email protected]
Keywords: Vertical tank, Volume measurement, Laser, Eletro-optical distance-ranging method,
Comparison experiment
Abstract. The precision measurement of vertical tank volume is one of key problems for the
international trade of liquefied petroleum products. One measurement system based on
Electro-Optical Distance-Ranging (EODR) principle was proposed. Laser ranging and
optic-encoding methods were applied to determine the location of each point on the tank shell. Based
on the coordinate computation, the space model of vertical tank was established. Regarded as
cylinder, the volume of tank can be calculated by using fitted radius of each course. Weighted
Average Method and Direct Iterative Method were used to carry out radius fitting. One comparison
experiment was designed, in which one 1000m3 vertical tank was used as test object, and Strapping
Method was regarded as reference according to OIML R71. The maximal radius errors of two
methods were 2.05mm and 1.48mm, and the absolute value of mean radius errors were 0.97mm and
0.63mm, which verified the system discussed.
Introduction
Vertical cylindrical tank is one type of tanks in general use throughout the world for the storage of
petroleum and petroleum products. Measurement of liquid levels and the use of the tank capacity table
permit the assessment of volume of the liquid held in store or transferred. In order to be accepted for
fiscal or custody transfer application, vertical cylindrical tanks shall be calibrated carefully to ensure
the accuracy of volume measurement of liquid contained [1,2].
There are mainly three volume calibration methods used for vertical tank, which are strapping
method, optical reference line method and optical triangulation method.
The strapping method involves measuring tank external circumference that is then converted into tank
internal diameter at each course by subtract the course thicknesses [3]. The method has been used for
more than half a century and is still regarded as the referee method for evaluation of all existing and
future emerging technologies. With the increase of tank diameter and height, determination of tank
circumferences at higher elevation (other than the bottom course generally) tends to be more and more
difficult and dangerous. Therefore, the strapping method is applied mostly as reference method.
For optical reference line method, one vertical reference line is established by using an optical device.
A magnetic trolley with ruler intersecting the optical reference line moves along the tank shell [4].
The circumference of bottom course is measured by strapping method, and the radial offsets of higher
courses are measured optically. By using the reference circumference and the radial offsets, diameter
at each course is computed mathematically. The main advantage of this method is the avoiding of
work at height.
The optical triangulation method also known as OTM is an extension of the optical reference line
method. With two theodolites at a known distance, the target points on tank shell are determined by
triangulation [5,6]. OTM is more easily adopted for internal application because the optical devices
can be located in one single location for the entire calibration, and provides capability to carry out
calibration from ground level without any manual strapping.
All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,
www.ttp.net. (ID: 130.203.136.75, Pennsylvania State University, University Park, United States of America-05/06/14,02:32:00)
Applied Mechanics and Materials Vols. 26-28
417
For the three calibration methods above, there is one common feature that they all are not automatic
measurement method and the working efficiency needs to be improved greatly.
In this paper, one automated measuring system for vertical tank volume was researched based on
EODR method. Distance measurement by laser ranging technology and angular measurement by
optic-encoding principle was applied to acquire coordinate values of points in each course. Two
fitting algorithms based on Weighted Average Method and Direct Iterative Method were used to
process measured data and deduce equivalent radius of each course. One comparison experiment was
designed to validate the method discussed.
Measurement System for Coordinate of Points on Vertical Tank Shell
The measurement system for coordinates of points in tank shell is shown as Fig. 1. The EODR
instrument was installed firmly on the bottom of vertical tank, and adjusted to horizontal level.
Z
P
X
zp
rp
yp
αp
βp
xp
Y
O
Fig. 1 The measurement system for coordinated of points in tank shell
Fig. 2 The coordinate system for measurement system
During measurement, the laser is transmitted from the instrument to the surface of tank shell.
According to the phase-shift principle, the distance rp between point P and instrument can be
achieved by Eq. 1
rp = [λ (m + ε )] / 2 .
(1)
Where rp is measured distance; λ=λ0/n is wavelength of laser and n is the refractive index; m is the
integral order of interference fringes；ε is the partial order of interference fringes. Vertical angle βp
and horizontal angle αp for each point are acquired by optic-encoding devices[7,8,9]. Therefore, with
the center o of the instrument as original of coordinate and plumb-line as vertical axis, one rectangular
coordinate was established as shown in Fig. 2.
The coordinate value (xp,yp,zp) of point P in tank shell could be deduce by Eq. 2 based on the three
parameters rp , βp and αp.
x p = rp cos β p cos α p 

y p = rp cos β p sin α p 

z p = rp sin β p

.
(2)
The method can be automated to measure the tank both horizontally and vertically. It is obvious that
the EODR method is more advanced than previous calibration methods.
The Algorithm of Radius Fitting for Measured Points of Each Course
According to technical requirement of OIML R71 [10], there is one hypothesis that the shape of
vertical tank is strictly one cylinder. Therefore, the main task of vertical tank volume calibration is the
418
Advanced Mechanical Engineering
computation for radius R of each course, based on the fitting of circle curve ( x − xc ) 2 + ( y − y c )2 = R 2 ,
where x and y are the acquired coordinates of points on the tank shell. Two algorithms based on
Weighted Average method and Direct Iterative Method were applied to carry out the research on
fitting of R.
Algorithm Based on Weighted Average Method (WAM). Under the assumption that the point set
P(xi,yi), i=1,2,…,n is distributed uniformly along the direction of circle, the following equation about
center of circle (xc,yc) can be deduced
n
n
i =1
i =1
xc = ∑ xi n, yc = ∑ yi n
(3)
Then the radius is the distance from P to the center of circle. However, the distribution of measured
points on the tank shell is not uniform, and the horizontal section curve of tank is not one strict circle.
Therefore, the computed center of circle based on Eq. 3 will move to the zone which contains more
points, and then the radius can not be calculated correctly. WAM algorithm was used to resolve this
non-uniform problem. The sum of distance between each two adjacent points is defined as l, and the
distance sum between point P(xi,yi) and its two adjacent ones is li. The weight of point P(xi,yi) can be
l
defined as ki = i , and then the Eq.3 can be rewritten as following
2l
n
n
i =1
i =1
x c = ∑ xi k i , y c = ∑ y i k i
(4)
The radius is
n
n
∑R ∑
i
( xi − xc ) 2 + ( yi − y c )
2
= i =1
(5)
n
n
The weight value of each point can also be calculated by using the arc length between two adjacent
points[8].
R=
i =1
Algorithms Based on Direct Iterative Method (DIM). The fitting of circle curve of data measured
from vertical tank is one problem of minimization of nonlinear objective function with multi variables
in nature, to which calculation by iteration is one of the most effective solutions [11,12]. For this
algorithm, there is no requirement for derivation of function, and it can be used whether the objective
function is continuous and differentiable or not.
Firstly, the center of fitting curve (xc0, yc0) is initialized and set to (0, 0) generally, and then the
objective function fobj is defined as Eq. 6
f obj = Rm − Rm −1 .
(6)
Where Rm is the estimated value of radius when iterative step is m. The iteration algorithm is as Eq. 7


ri
i =1
i =1

n
n y − x

i
c ( m −1)
 .
y cm = ∑ y i / n − ( R m / n)∑
ri
i =1
i =1


2
2
ri = ( x i − x c ( m −1) ) + ( y i − y c ( m −1) )


n
Rm = ∑ ( x i − x c ( m −1) ) 2 + ( y i − y c ( m −1) ) 2 / n

i =1
n
n
x cm = ∑ xi / n − ( Rm / n)∑
xi − x c ( m −1)
(7)
Applied Mechanics and Materials Vols. 26-28
419
Where (xi,yi)，i=1,2,…,n are the n points obtained from measurement. Calculate xcm, ycm, ri and Rm
until the new value of Rm differs from old one by less than δ, as shown in Eq. 8
f obj < δ
.
(8)
Where δ is the calculation threshold, and usually set to 0.1mm. If the iterative computation is
finished, the latest values of (xcm, ycm) and Rm are regarded as the best fits of center and radius for
sampled points on tank shell.
Comparison Experiment and Data Analysis
To verify the measuring method discussed above, a comparison experiment system was designed, in
which one 1000m3 vertical tank with top roof and 8 courses was used as test object. The height and
diameter of this tank is 8.9m and 12.0m respectively. Two series of radius in each course at different
height (about 1/4 and 3/4 of course height) were measured by strapping method complying with the
requirement of OIML R71. It took about 10 days to complete the strapping work. The calculated
radius value obtained from strapping method is named as Rst, which is regarded as reference value.
The EODR system was installed near the middle of tank bottom, and limited error of ranging and
angle measurement is 2mm and 2″ respectively. The space distributions of measured points by EODR
method was shown in Fig. 3.
7
6
5
z(m)
4
3
2
1
0
6
6
3
y(m)
3
-3
-3
-6
-6
x(m)
Fig. 3 the space distributions of measured points from strapping method
The coordinates of measured points were processed by using two algorithms discussed to achieve the
fitting value of radius at each course, which are expressed as RWAM and RDIM. The experimental results
between strapping method and EODR method were shown in Fig.4.
420
Advanced Mechanical Engineering
5985
5980
Radius/mm
5975
Reference
WMA Algorithm
DIM Algorithm
5970
5965
5960
5955
5950
1
2
3
4
5
Tank Height/m
6
7
8
9
Fig.4 The experimental result comparision between EODR method and reference
Based on the comparison experiment, it can be concluded that the radius value obtained from EODR
method is well consistent with reference value achieved by manual strapping method, and the
maximal deviation is 2.05mm. It took less than one hour for the whole calibration in situ, so the work
efficiency can be improved greatly by the new method. On the other hand, DIM algorithm is more
accurate than WAM algorithm to calculate the radius of each course. The maximal radius error of
these two methods was 2.05mm and 1.48mm, and the absolute value of mean radius errors were
0.97mm and 0.63mm. Algorithm based on DIM has the advantages of a simple use, but weakness of
slow computation due to iterative procedure. On the contrary, algorithm based on WMA is with the
merit of fast computation, but low accuracy.
Summary
According to the technical requirements of international legal metrology recommendations R71, one
measurement method based on Electro-Optical Distance-Ranging (EODR) principle was proposed.
Laser ranging and optic-encoding methods were applied to determine the location of each point on the
tank shell. Based on the coordinate computation, the space model of vertical tank was established.
The radius value obtained from EODR method is well consistent with reference value achieved by
manual strapping method, and the maximal deviation is 2.05mm. Two algorithms based on WMA
and DIM were studied for the computation of course radius from the measured data. DIM algorithm
is more accurate than WAM algorithm to calculate the radius of each course. By using the method
discussed, the calibration efficiency of vertical tank volume can be improved greatly.
References
[1] Y.Y. Lian: Volume Metrology Technology (Beijing Metrology Press, China 2006).
[2] S. G. Makushkin, S. A. Kuzmin, G. G. Kalashnik: Tank Deformation and Accuracy in Measuring
Oil Product Mass. Chemical and Petroleum Engineering. Vol. 37(2001) , p. 278
[3] ISO7507-1. Petroleum and liquid petroleum products-volumetic calibration of vertical
cylindrical tanks (2003).
[4] ISO7507-2. Petroleum and liquid petroleum products volumetric calibration of vertical
cylindrical tanks part2 :optical reference line method (2005).
Applied Mechanics and Materials Vols. 26-28
421
[5] ISO7505-3 2006. Petroleum and liquid prtroleum products volumetric calibration of vertical
cylindrical tanks part3: optical triangulation method (2006).
[6] Calibration Of Upright Cylindrical Tanks - OTM, Optical Triangulation Method. API MPMS Ch.
2.2C (2008).
[7] Y.Y. Lian, Z.Y. Liu, L He, L Zhang: A New Method For Vertical Cylinder Tanks. ACTA
ME'IROLOCICA SINICA. Vol.9(1988), p.241
[8] Q. Y. Zhao: 3D Laser Scanner Data Acquisition System Developed. Xi’an University of
Technology Master Dissertation (Xi’an, China 2008).
[9] T. Nguyen, A. Stojcevski, R. Veljanovski, J. Chandran: Measurement Of The Volumetric
Temperature Distribution In Bulk Liquid Tanks. 13th Abu Dhabi International Petroleum
Exhibition and Conference (2008).
[10] Information on http:// www.oiml.org/publications/R
[11] M.S. Richard: Calibration of storage tanks. Proceedings of the International School of
Hydrocarbon Measurement (1985).
[12] Z.H. Xu, L.J. Zhang, J.X. Wei: The Columanar Tank Calibration System Based On Leica TCR
Series Total Station. Journal of Geo-matics. Vol 27(2002), p.1
Advanced Mechanical Engineering
10.4028/www.scientific.net/AMM.26-28
Automatic Measurement System for Vertical Tank Volume by Electro-Optical Distance-Ranging
Method
10.4028/www.scientific.net/AMM.26-28.416