The Simulation Research on Passive Heave Compensation System for Deep Sea Mining Jia Ni, Shaojun Liu, Mingfeng Wang, Xiaozhou Hu and Yu Dai College of Mechanical and Electrical Engineering Central South University Changsha, Hunan Province, China
[email protected] Abstract - A passive heave compensation system with accumulators is proposed according to the requirements of 6000m deep sea poly-metallic mining system. The principle of the heave compensation system is described, the main parameters of the system are calculated, a corresponding mathematical model of this system is built. The parameters which affect the performance of the system are simulated and analyzed by MATLAB. The simulation study of the passive heave compensation system is conducted. The results show that the satisfactory control effectiveness can be obtained under sea condition 4. The compensation rate of the system is higher than 80% under the influence of random wave. The results of modeling and simulation research offer theoretical basis and technical reference for the development of passive heave compensation system. Index Terms - Deep sea mining. Passive heave compensation. Accumulator. Modeling. Simulation.
I. INTRODUCTION Due to the influence of the marine environment, mining vessel will have significant heave movement during the operating process of deep sea hydraulic-lifting mining system. In the absence of heave compensation system, lifting pipes of several thousand meters will result in corresponding motion generated by the surface installations, which causes tremendous additional load and alternating stress to the system and affects the mining operations seriously. Therefore, heave compensation measures are adopted so as to guarantee the mining process going on smoothly. Heave compensation system (HCS) can be divided into active (AHCS) and passive (PHCS): AHCS has high compensation precision with extra power providing; while PHCS has comparatively lower compensation precision with little power consumption. American Global Marine Inc. [1][2], Driscoll [3], Kirstein [4] etc. have carried out a series of studies on HCS which is mainly used in semi-submersible platform and drilling vessels of offshore oil drilling and production currently, and mostly adopt AHCS for its high compensation precision. What’s more, HCS for deep sea mining is seldom studied and the existing research is only confined to AHCS [5]. However, in fact, as the compensation precision requirement of HCS for deep sea mining is comparatively low, it is reasonable to discuss PHCS which is not only simple but also energy-saving.
A PHCS with accumulator is proposed and a relevant mathematical model is established in this paper according to the requirements of 6000m deep sea poly-metallic mining system. The parameters which affect the performance of the system are simulated and analysed by MATLAB. The simulation result indicates that the PHCS is effective and feasible, which provides important theoretical basis and technical reference to the development and mining experiment of HCS. II. SYSTEM DESIGN A. Working Principle An accumulator type PHCS is proposed in this paper and the functional diagram is shown in Fig.1. The system consists of compensating cylinder, accumulator and air collectors. The compensating cylinder is used to bear the weigh of system load and the accumulator is used to store and release energy which is generated by the heave movement of the mining ship. When the mining ship rises, the cylinder housings follow the motion of the ship, while heave platform connected with the foot of the piston will maintain the trend of keeping staying at the equilibrium position for the inertia effect, at this moment, the oil of rod chamber is pressed into accumulator and the air of accumulator is compressed to compensate the increased displacement and store energy. When the mining ship falls, the cylinder housings descend following the motion of the heave platform which will maintain the trend of keeping staying at the equilibrium position for the inertia effect, meanwhile, the oil flows from accumulator to rod chamber and the air in accumulator expands to compensate decreased displacement and release energy, which makes heave compensation come true. It will be seen that the power of PHCS comes from sea waves, so it doesn’t need to provide extra power.
Fig. 1 Schematic diagram of PHCS
We acknowledged that this research is supported by the National Natural Science Foundation of China (Grant No. 50675226) .
During processing of compensation, there are corresponding changes in the working pressure when the air inside the accumulator is compressed or expanded, which lead to related changes of hydraulic driving force, meanwhile, certain heave displacement will occur for the lifting pipes can’t remain completely static state. The more the working pressure changes, the more the hydraulic driving force on the piston alters and it’s more difficult to stay at the equilibrium position. So, the choice of accumulator’s volume is closely related to system dynamic performance. B. Mainly Parameters Design In terms of the analysis above, the compensation cylinder whose lifting force is equal to the gross weight is used to bear the load and the working pressure of the system depends on the weight of the lifting pipe. Considering the static load of 6000m lifting system is about 560t, in order to prevent the size of compensation cylinder from being too large and the system pressure too high, two compensation cylinders are adopted in the system designing and the actual load of each is about 2776kN. According to the strength theory, the diameter of piston-rod is d ≥ 222.4mm , then round and take d = 250mm according to national standard. With comprehensive consideration of volume of the system and effects of the pressure, the inner diameter of cylinder is D = 450mm and system pressure is PE 0 = 25.31MPa . The length of housings is chosen as L = 2m based on wave height and responses of mining ship to wave motions in Chinese deep sea mining districts.
III. SYSTEM MODELING A. References The equation of vertical motion of cylinder’s piston is as follows:
Mxp = pE A2 − P1 A1 − Mg − c( x p − xh )
(1)
Where M is the total load of HCS; xp is the vertical displacement of piston, namely the vertical displacement of heave platform; xh is the vertical displacement of housing, namely the vertical displacement of ship-body. A1 is the area of non-rod chamber. A2 is the area of rod chamber, c is the viscosity damping coefficient of cylinder. P1 is atmospheric pressure which is taken as 0.1Mpa. pE is the instantaneous pressure of rod chamber. (1) is equivalently processed as: xp = −
c c A x p + xh + 2 ΔpE M M M
(2)
B. Flow Equation of Cylinder The relation between the pressure and volumetric flow of rod chamber can be written as: K [−qR − A2 ( x p − xh )] VE
C. Mathematical Model of Accumulator Suppose that (PG0 ,VG0) and (PG ,VG ) is the gas pressure and volume when accumulator is at its equilibrium position and at any moment, respectively. Thus the gas state equation can be written as: pGVGn = PG 0VGn0
(4)
Where n is adiabatic exponent of gas. (4) is equivalently processed as: pG = PG 0VGn0VG− n
VG =VG 0
− nPG 0VGn0VG− n −1 VG =VG 0 (VG − VG 0 )
Which reduces to: −(VG − VG 0 ) pG − PG 0 = nPG 0VG−01 dt dt p G = nPG 0VG−01qR
(5) (6)
Where q R = −(VG − VG 0 ) / dt (negative sign here is expressed as that volume variation of gas is in contrast with the volumetric flow). D. Flow Equation of Pipeline Cylinder and accumulator chamber are connected by pipeline, inside which the relationship between volumetric flow and pressure is: qR =
πd g 4 ( pE − pG ) 128μl
(7)
Where dg is the inside diameter of pipeline, l is the length of pipeline, μ is the dynamic viscosity of hydraulic oil. The pressure of rod chamber is equal to that inside the accumulator, that is PE 0 = PG 0 . pE − pG = ( pE − PE 0 ) − ( pG − PG 0 ) = ΔpE − ΔpG Thus (7) reduces to: qR = CqR (ΔpE − ΔpG )
(8)
Where CqR = πd g4 / 128μl . E. Mathematical Model of PHCS By arranging (2), (3), (6), (8), the dynamic differential equation of system can be expressed as follows :
Where ΔpE = pE − PE 0
p E =
Where, K is the bulk modulus of hydraulic oil. VE is the volume of rod chamber. qR is the volumetric flow out from cylinder, namely the volumetric flow into accumulate.
(3)
100 0 Compensatiocn Rate (%)
⎧ c A c ⎪xp = − x p + 2 Δp E + x h M M M ⎪ ⎪⎪ KCqR KCqR AK A2 K ΔpE + ΔpG + 2 x h x p − ⎨ p E = − V VE V V E E E ⎪ ⎪ nP C nP C ⎪ p G = G 0 qR ΔpE − G 0 qR ΔpG ⎪⎩ VG 0 VG 0
(9)
The state variable of system is selected as x = [ x p ΔpE ΔpG ]T ; while input is d = xh ; output is
-100 -200 -300 -400 -500 -600
y = x p . Thus the state equation of system can be expressed
-700
0
10
20
30
40
50
Accumulator Volume (m3)
as:
Fig. 2 The relationship between accumulator volume and compensation rate
(10)
Where
⎡ c ⎢ − ⎢ M ⎢ AK A = ⎢− 2 ⎢ VE ⎢ ⎢ 0 ⎣ ⎡c E=⎢ ⎣M
−
A2 M KCqR
VE nPG 0CqR
A2 K VE
VG 0 ⎤ 0⎥ ⎦
⎤ ⎥ ⎥ KCqR ⎥ ⎥ VE ⎥ nPG 0CqR ⎥ − VG 0 ⎥⎦ 0
T
C = [1 0 0] IV. MAIN INFLUENCING FACTORS AND PARAMETERS SELECTION Parameters in (10) which are related to cylinder, system load and working pressure have been designed in chapter 2.2, while the others such as the volume of accumulator and parameters of pipeline could not be determined yet, which will be studied in this chapter. A. Influence of Accumulator Volume As the main element of PHCS, accumulator is used to store and release the energy generated by the movement of ship. The size of its volume is closely related to compensation performance of PHCS. Supposing for a period of time, Axh and Axp are the maximum heave displacement differences of ship and compensation platform respectively. Thus compensation rate could be defined as η = 1 − Axp / Axh × 100% .
(
)
Simulation has been carried out by taking following data: pipe diameter 0.05m, pipe length 0.5m, wave period 5.8s and the relationship between volume of accumulator and compensation rate is shown as Fig.2. Fig.2 indicates that compensation rate is negative when VG0≤ 4m3, which means the vibration of ship is enlarged by
PHCS, on the other hand, PHCS behaves effectively only when VG0≥4m3. In this range, compensation rate increases as the accumulator volume enlarges, but the relationship is not linear. When accumulator volume grows from 4m3 to 20m3, the compensation rate could be greatly improved to 72.26% by enlarging 16m3, however, when accumulator grows from 20m3 to 50m3, the rate could only be increased 10.37% by enlarging 30m3, and the rate grows so slowly that it tends to be a certain value with the further increasing of volume. Evidently, no matter how large the volume is, the compensation rate can not achieve 100%. What needs to additional explained is that the simulation results above are obtained according to the typical sea state where the wave period is 5.8s. Though the result would be changed as the wave period varies, the general trend of curve which Fig.2 shows would not make difference. The analysis above shows that it is feasible to add accumulators to the system for heave compensation. The compensation effect of PHCS is impacted greatly by the volume of accumulator. The PHCS could be effective if the volume is selected reasonably. The system has been simulated and analysed to time domain response by selecting three volume values (5m3, 20m3 and 50m3) which can be effectively compensated and dg = 0.05m , l = 0.5m , T= 5.8s . Comparison of these three situations is shown as Fig.3. 0.04 0.03 0.02 Heave Displacment (m)
⎧ x = Ax + Ed ⎨ ⎩ y = Cx
0.01 0 -0.01 Ship Platform VG0=5m3 Platform VG0=20m3
-0.02 -0.03
Platform VG0=50m3 -0.04
0
10
20
30 time (s)
40
Fig. 3 Comparison of different volumes
50
60
B. Influence of pipeline The selection of the diameter and length of pipeline which connects accumulator and cylinder, directly affects the flow velocity of oil in compensation process and dynamic performance of the system. In the practical engineering application, though the arrangement and length of pipe are influenced by overall layout, considering the importance of pipeline in compensation, some unideal results could be avoided by selecting reasonable parameter before overall layout. Choosing accumulator volume as 20m3, wave period as 5.8s and according to the national standard, selecting diameter as 0.04m, 0.05m, 0.065m, 0.08m and length as 0.01m, 0.1m, 0.5m, 1m, 1.5m, 2m, 2.5m for simulation. The compensation rates of different diameter and length are shown in Table I. Table I shows that the compensation rates are influenced significantly by lengths and diameters of pipeline in the condition that accumulator volume is the same, the maximum difference of which reaches to 36%. The optimum value of the diameter of pipe can be obtained with as pipe length increasing, however, the larger value is not always better, but displays parabola distribution in a certain range. The set of data whose pipe length is 0.5m is the optimal within the oil velocity allowable range. Table I also indicates that the compensation rate of the system is only 34.74% when the diameter is 0.04m, and length is 2.5m. When applying this set of pipe parameter at the condition of different accumulator volumes, the compensation rate of the system are shown in TableⅡ. Table Ⅱ shows that, the compensation rate only reaches 39.78%, even when the accumulator volume increases to 100m3, it is much worse than the result of the situation with the condition that pipe diameter is 0.05m, pipe length is 0.5m and accumulator volume is 20m3. It is shown that no matter how large the accumulator volume would be taken, better compensation can not be achieved unless reasonable pipe parameter has been chosen. TABLE I COMPARISON OF DIFFERENT DIAMETER AND LENGTH Diameter (m) Length (m) 0.04 0.05 0.065 0.08 0.01 70.28% 70.13% 70.06% 70.04% 0.1 71.83% 70.97% 70.39% 70.19% 0.5 69.19% 72.26% 71.49% 70.77% 1 59.44% 70.65% 72.16% 71.35% 1.5 50.53% 66.94% 72.25% 71.77% 2 42.80% 62.91% 71.90% 72.05% 2.5 36.26% 58.90% 71.25% 72.22%
TABLE Ⅱ COMPARISON OF COMPENSATION (DG=0.04M, L=2.5 M) Compensation Rate (%) Accumulate Volume (m3) 20 36.26 50 38.95 100 39.78
Therefore, while it is necessary to increase the length of pipeline, the diameter should be chosen properly to obtain an optimum compensation. It is suggested that the pipeline which connects accumulator and cylinder should not be longer than 2.5m; otherwise, the volume of the pipeline would be too huge and heavy. Ⅴ. EFFECT OF CONTROL
According to the discussion of the main influencing factors, a better set of data is applied where accumulator volume is 20m3, pipe diameter is 0.05m and pipe length is 0.5m is taken for simulation. The comparison of frequency response between two systems which are with and without PHCS is illustrated as Fig.4. The effective compensation frequency is defined as the one crossed at the dashed line −3 db by the amplitude-frequency curve. In Fig.4, the vertical lines represent the wave frequency range of sea condition 4 in Chinese mining area. The wave energy is mainly concentrated among the frequency (0.08~0.4) Hz, and reaches to maximum around 0.13 Hz, while it is rather small among the frequency (0.05~0.08) Hz and (0.4~0.5) Hz. Fig.4 shows that the amplitude ratio of the heave platform that is without HCS and ship is 1 in real wave frequency range where there is almost no action of compensation, while the PHCS proposed in the study shows excellent performance of compensation, in addition, the compensation effect of PHCS is much better when the wave frequency is higher. The amplitude is amplified when wave frequency is in (0.05~0.06) Hz and it reaches maximum when the wave frequency is 0.05 Hz namely the wave period is 20s. The controlling effect of PHCS with different volumes on wave frequency are studied by changing the accumulator volume. Choose accumulator volumes as 5m3,20m3 and 45m3 for simulation. The result is shown as Fig.5. Magnitude Response 60
40
20 Gain (db)
Fig.3 indicates that the compensation is unstable in the first few periods and the amplitude of platform is comparatively large, 40s later, the compensation will tend to be stable, and the amplitude will decrease. The certain lags, which decrease with the increase of volume, is always existing in compensation of different volumes. The response times of PHCS whose accumulator’s volumes are 5m3, 20m3 and 50 m3 are respectively 2.6s, 2.3 s and 1.8 s.
0
-20
-40
System without HCS PHCS
-60 -4 10
-3
10
-2
-1
10 10 Frequency (Hz)
Fig. 4 Frequency response of PHCS
0
10
1
10
to be comparatively smooth under the control of the PHCS, then the compensation rate of the system could reach 83.17%. As the wave surface slopes more badly, which means more dramatic change in waves, the effect of PHCS performs better and the heave frequency of the platform becomes lower than that of the ship, which could reduce influence on the lifting system caused by the alternating load.
Magnitude Response 40
Gain (db)
20
0
-20
Ⅶ EXPERIMENT
VG0=5m3
-40
VG0=20m
3
VG0=45m3 -60 -4 10
-3
-2
10
-1
10 10 Frequency (Hz)
0
1
10
10
Fig. 5 The frequency response comparison of PHCS with different volume
Fig.5 indicates that the frequency response curves of different accumulator volumes are similar. When the volume increases, peak frequency, peak value and effective compensation frequency become smaller, Frequency response curves tend to be coincided in the high frequency range. When accumulator volume is 5m3, PHCS works only when the frequency is higher than 0.14Hz and the compensation effects badly. When accumulator volume is 45m3, PHCS works when the frequency is higher than 0.05 Hz, namely the PHCS could compensate all of frequency in sea condition 4. Ⅵ. RESPONSE OF RANDOM WAVE
The significant wave height of sea condition 4 in Chinese deep sea mining area is 2.4m. The distribution of the wave energy, which is relative to frequency under sea condition 4, is obtained by spectrum analysis method [6]. The simulated diagram of a certain point of wave can be gained by using MATLAB to do numerical simulation [7]. The heave displacement of the mining ship is proportional to the wave height, and the heave period of the ship is the same as that of the wave. Affected by random wave of sea condition 4, the response of the PHCS inside which the accumulator volume is 20m3, the pipe diameter is 0.05m and the pipe length is 0.5m is as Fig.6. It is known in Fig.6 that PHCS shows excellent performance of compensation when it is influenced by random wave and the movement of the compensation platform seems
Heave Displacement (m)
0.6 Ship Platform
0.4
0.2
Ⅷ. CONCLUSIONS
According to the requirements of 6000m deep sea polymetallic mining system, a PHCS with accumulator is proposed and a relevant mathematical model is established in this paper. The compensation rate of PHCS operates effectively while the accumulator volume enlarges, but the relationship is not linear, and no matter how large the volume is, the compensation rate can not achieve 100%. Unless reasonable pipe parameter has been chosen, no matter how large the accumulator volume would be taken, better compensation can not be achieved. Therefore, it is necessary to consider the length and diameter of pipe, which will impact the system during pipeline layout. The compensation effect of PHCS to the high wave frequency is much better than that to low wave frequency. Under the sea condition 4 in Chinese deep sea mining area, the wave, among whose energy frequency is concentrated, can be effectively compensated by the PHCS, of which the accumulator volume is 20m3, pipe diameter is 0.05m and pipe length is 0.5m, and it shows excellent performance of compensation when it is impacted by random wave. In case it needs to compensate waves of all parts of frequency, the accumulator volume will be enlarged for it. In addition, it is suggested to adopt AHCS when the period of wave is more than 14s. ACKNOWLEDGMENT
0
We acknowledged that this research is supported by the National Natural Science Foundation of China (Grant No. 50675226) .
-0.2
-0.4
For the HCS of deep see mining is still on the step of researching, it can not be verified experimentally yet, however, the effects of the accumulator on the HCS are certainly proved by the experiment: as to a single-freedom hydraulic experimental platform, when the motion frequency of the cylinder is 3Hz, the pressure variation of nonaccumulator system is about 4.5 MPa, while that of the system with an accumulator is only about 0.4 MPa; when the motion frequency is 0.1 Hz, it is almost the same whether there is an accumulator or not, and the pressure variation is about 0.7 MPa, so it is comparatively to see that the accumulator makes an effective effort to the pressure variation generated by the high-frequency motion.
0
10
20
30 40 Time (s)
50
60
Fig. 6 Response of HPCS under the influence of random wave
70
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