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An energy-saving oil drilling rig for recovering potential energy and decreasing motor power
Energy Conversion and Management 52 (2011) 359–365
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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
An energy-saving oil drilling rig for recovering potential energy and decreasing motor power Zhang Lujun School of Mechanical and Automotive Engineering, Yantai University, Yantai 264005, China
a r t i c l e
i n f o
Article history: Received 20 December 2008 Received in revised form 16 November 2009 Accepted 5 July 2010 Available online 31 July 2010 Keywords: Energy recovery Oil drilling rig Energy-saving Drill stem Lowering
a b s t r a c t An energy-saving oil drilling rig is researched. A large accumulator is adopted in this rig to store the energy of the motor during the auxiliary time of lifting the drill stem and the potential energy of the drill stem when lowered. The equipped power of this rig decreases remarkably compared with the conventional drilling rig, and this rig can also recover and reuse the potential energy of the drill stem. Therefore, this rig owns remarkable energy-saving effect compared with the conventional drilling rig, and the energy-saving effect of the energy-saving oil drilling rig is also verified by the field tests. The mathematical model of the energy-saving oil drilling rig lowering the drill stem was derived and simulation analysis was conducted. Through simulation the curves of the drill stem lowering velocity and lowering displacement with time were obtained, and some conclusions were reached: (1) the heavier the drill stem lowered, the higher the lowering velocity is, and the shorter the lowering time is; (2) the smaller the displacement of the variable pump-motor, the higher the lowering velocity is, and the shorter the lowering time is. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The drilling rig plays an important role in petroleum exploitation [1]. When the bit is dull, the drill stem is pulled out of the well. After replacing the dull bit with a new one, the drill stem is lowered into the well again. The operation of pulling the drill stem out of the well is an intermittent cycle process. In a cycle, the pure lifting time (the time of lifting the drill stem from the well) is only about one third of the time used, and here the motor works under a high power. The auxiliary time (the time of removing the stand from the drill stem and positioning the stand) is two-thirds, and here the motor works under a low power. The high power motor of the conventional drilling rig works mostly under low power, and therefore it is not economical [2,3]. The drill stem lifted up to the ground from the well deposits much potential energy, and when the drill stem is lowered down to the well, the deposited potential energy is released. The conventional drilling rig just wastes this energy by braking and this energy cannot be recovered. As mentioned above, the conventional drilling rig has an unreasonably large energy waste both in lifting and lowering the drill stem. Because energy is very precious, the problem of wasting energy must be resolved. Therefore, an energy-saving oil drilling rig is presented. The equipped power of this rig is only one third of a conventional drilling rig, and this rig can recover and reuse the
E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.07.009
potential energy which is released by the drill stem when lowered. This rig owns remarkable energy-saving effect. Because of the effects of the energy crisis and oil shortage, the researches on energy recovery and reuse are conducted in more and more fields, and the formerly wasted or detrimental energy is converted into other forms of energy to be stored and reused. Yang et al. [4] studied a hydraulic elevator which could recover the potential energy of the cabin during down-travel and reuse this energy during up-travel and showed this hydraulic elevator could achieve a significant energy-saving performance compared to the traditional elevators. Lin et al. [5] studied the system which could recover the arm potential energy in hybrid hydraulic excavators when the arm lowering. The recovery and reuse of the vehicle brake energy are the hot research fields these years. Jefferson and Ackerman [6] studied a flywheel variator energy storage system which could recover the vehicle brake energy and showed energy losses and consumption were minimized. Uzunoglu and Alam [7] studied fuel cell/ultra-capacitor hybrid vehicular power systems with the ultra-capacitor recovering the regenerative energy during braking. Suda and Shiiba [8] Studied an energy regenerative damper system which converts vibration energy of the vehicle into useful energy. The aforementioned researches are all about recovery and reuse of mechanical energy, and however, there are also many researches on regeneration of other forms of energy, such as recovery and reuse of waste gas energy. For example, the study of Beers and Biswas [9] demonstrated the significant potential to mitigate CO2 emissions through energy recovery from
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flue gases by applying technologies to convert the embedded energy into useful thermal and electric applications. However, there are no reports about the oil drilling rig which can recover and reuse the potential energy released by the drill stem when lowered. As a machine which exploits energy (oil), the drilling rig itself has energy waste, and it is a great pity. Therefore, an energy-saving oil drilling rig which can resolve this problem well is presented.
2. Basic structure As shown in Fig. 1, the energy-saving oil drilling rig consists of the frequency conversion motors 1 and 2, transmission cases 5 and 8, angle transmission case 9, variable pump-motor hydraulic system, drum 10, disk brake 11, blocks and hook 12, rotary table 14, and couplings and clutches connecting each part. The variable pump-motor hydraulic system is connected in parallel to the main system from the motor 1 to the drum 10 via the transmission case 5. The variable pump-motor hydraulic system consists of the variable pump-motor 15, two-position two way electromagnetic valve 16, accumulator, overflow valve 17, and oil tank 20. The accumulator is composed of oil-storing cylinder 18 and air vessel 19. The function of the transmission case 5 is to transfer the power of the motor 1 to the variable pump-motor 15 during the auxiliary time and transfer the power of the variable pump-motor 15 to the drum 10 when lifting the drill stem. The transmission case 5 includes two gears 53 and 54 which form a gearset. The shaft of the variable pump-motor 15 is attached to the shaft 52 of the transmission case 5 through the coupling 33 and clutch 44.The transmission case 5 attaches to the motor 1 through the clutch 41 and coupling 31, and attaches to the transmission case 8 and angle transmission case 9 through the clutch 43 and coupling 34. The angle transmission case 9 is attached to the drum 10 through the coupling 35. The motor 2 drives the rotary table 14 via the coupling 32, clutch 42, universal coupling 36 and 37, and transmission shaft 13. One sprocket of the chain transmission 6 is fitted on the shaft 51 loosely. Moving joint sleeves 7 left can realize the connection of the chain transmissions 6 with the shaft 51, and thereby realize the combination of the motors 1 and 2.
3. Working theory 3.1. Process of lifting the drill stem During the auxiliary time of lifting the drill stem, the clutch 43 is disengaged. The angle of the swash-plate of the variable pumpmotor 15 is adjusted in positive direction; that is, at this moment the direction of output torque of the variable pump-motor 15 under the action of the oil pressure is the same as that of the output torque of the motor 1. Then, the direction of the torque T1 which the motor 1 produces on the shaft of the variable pump-motor 15 via the coupling 31, engaged clutch 41, gearset 53 and 54, engaged clutch 44, and coupling 33 is contrary to that of the output torque T2 of the variable pump-motor 15 under the action of the oil pressure. Adjusting the displacement of the variable pump-motor 15 to make T1 larger than T2, the variable pump-motor 15 runs as a hydraulic pump and charges oil into the accumulator through the lower position of two-position two way electromagnetic valve 16. The overflow valve 17 functions as safeguard, and when the oil pressure of the accumulator surpasses the setting value, the overflow valve 17 opens to let the oil overflow. When lifting the drill stem, the clutch 43 is engaged, and the disk brake 11 is released. The angle of the swash-plate of the variable pump-motor 15 is adjusted in negative direction; that is, at this moment the direction of output torque of the variable pump-motor 15 under the action of the oil pressure is contrary to that of the output torque of the motor 1. The direction of the torque which the variable pump-motor 15 produces on the shaft 51 via the coupling 33, engaged clutch 44, and gearset 53 and 54 is the same as that of the output torque of the motor 1. At this moment, the variable pump-motor 15 runs as a hydraulic motor and combines with the motor 1 to provide power for the drum10 which rotates to lift the drill stem out of the well through blocks and hook 12. Therefore, the power of the motor 1 decreases greatly and is only about one third of the conventional drilling rig. For instance, for 3000 m drilling rig whose maximum drill stem weight is 900 kN, the equipped power of drawworks in the conventional drilling rig is 600 kW, and the power of drawworks in this new drilling rig is 209 kW. During lifting the drill stem, the weight of the drill stem is changeable and the drill stem gets lighter and lighter. Because
Fig. 1. Structure diagram of the energy-saving oil drilling rig.
L. Zhang / Energy Conversion and Management 52 (2011) 359–365
the power of the motor 1 is only about one third of the conventional drilling rig, when lifting the drill stem whose weight is less than one third of the maximum drill stem weight, the motor 1 can lift the drill stem without the help of the variable pump-motor 15. At this moment, the clutch 44 is disengaged, and the variable pump-motor 15 does not work. Here, in order to prevent the variable pump-motor 15 from turning, two-position two way electromagnetic valve 16 is set at the upper position. That is to say, when lifting the drill stem whose weight is within this range, the energysaving oil drilling rig is the same as the ordinary frequency conversion electric drilling rig. When lifting the drill stem whose weight is larger than one third of the maximum drill stem weight, the motor 1 and the variable pump-motor 15 combine to work, and here the motor 1 runs under the rating constant torque. The load torque which surpasses the rating torque of the motor is afforded by the power of the variable pump-motor 15. The driller adjusts the displacement of the variable pump-motor 15 according to the weight indicator. When the drill stem to be lifted is heavier, the load torque which should be overcome by the variable pump-motor is larger. At this moment, the driller changes the displacement of the variable pump-motor 15 to be larger to increase the output torque of the variable pump-motor 15. On the contrary, when the drill stem to be lifted is lighter, the load torque which should be overcome by the variable pump-motor is smaller. At this moment, the driller changes the displacement of the variable pump-motor 15 to be smaller to decrease the output torque of the variable pump-motor 15. Generally the chain transmission 6 is not engaged, and the drum is driven by the motor 1, while the rotary table is driven by the motor 2. In special case, such as blockage during tripping, the chain transmission 6 is engaged, and the motor 1 together with the motor 2 drives the drum to improve the lifting ability of the drum. 3.2. Process of lowering the drill stem When lowering the drill stem, the motor 1 can be turned off and the clutch 41 is disengaged; that is, when lowering the drill stem, the motor 1 does not work. After the stand has been connected to the drill stem, the disk brake 11 is released, and the angle of the swash-plate of the variable pump-motor 15 is adjusted in negative direction. The direction of the torque T3 which the weight of the drill stem produces on the shaft of the variable pump-motor 15 through the drum 10, coupling 35, angle transmission case 9, transmission case 8, coupling 34, engaged clutch 43, gearset 53 and 54, engaged clutch 44, and coupling 33 is contrary to that of the output torque T2 of the variable pump-motor 15 under the action of the oil pressure. Adjusting the displacement of the variable pump-motor 15 to make T2 smaller than T3, the drill stem lowers into the well, and at the same time the variable pump-motor 15 runs as a hydraulic pump and charges oil into the accumulator through the lower position of two-position two way electromagnetic valve 16. That is to say, the potential energy of the drill stem is changed into the hydraulic energy to be stored in the accumulator, thus realizing the recovery of the potential energy of the drill stem. When the drill stem is lowered for a stand length, the volume Vra of the hydraulic oil recovered in the accumulator is
V ra ¼
10s iV ðm3 Þ 2pr
ð1Þ
where s is the length of a stand, r is the radius of the drum, i is the transmission ration from the variable pump-motor shaft to the drum shaft, V is the displacement of the variable pump-motor. During lowering the drill stem, the weight of the drill stem gets heavier and heavier. The driller timely adjusts the displace-
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ment of the variable pump-motor 15 according to the weight indicator. In the beginning, the drill stem lowered is lighter, thus the displacement of the variable pump-motor 15 is smaller, and from Eq. (1) we know that the amount of the recovered energy is smaller. Along with the increase of the drill stem weight, the driller timely enlarges the displacement V of the variable pump-motor 15, and the amount of the recovered energy becomes larger. This recovered energy can be reused to complete the auxiliary work, such as raising the elevator, driving the pipe tongs to make up pipe, driving the air compressor to offer the energy to operate the clutches and brakes. These works are completed by the power of the motor before, and now these works are completed by the recovered energy. Therefore lots of energy is saved.
4. Calculation of the motor power and the volume of the accumulator 4.1. Calculation of the motor power The maximum energy E for lifting the drill stem is
E¼
W max s
g1 g2
ð2Þ
where E is the energy, Wmax is the maximum weight of the drill stem, s is the length of a stand, g1 is the transmission efficiency from the variable pump-motor shaft to the drum shaft, g2 is the efficiency of the traveling system. In one cycle of lifting the drill stem, the ratio of the pure lifting time to the auxiliary time is 1:2. For the energy-saving oil drilling rig, in the auxiliary time the motor 1 supplies energy to the accumulator through the variable pump-motor 15, and in the pure lifting time, the accumulator through the variable pump-motor 15, together with the motor 1, outputs energy to lift the drill stem. That is to say, in the pure lifting time, one third of the total energy E is supplied by the motor 1, two-thirds of the total energy E is supplied by the accumulator. Therefore, the motor power Pe is
Pe ¼
E W max s ¼ 3t 3g1 g2 t
ð3Þ
where t is the time of lifting the drill stem. 4.2. Calculation of the volume of the accumulator The accumulator is piston accumulator and is composed of oilstoring cylinder and air vessel. Because the accumulator provides large amount of pressure oil for the system in a short time, the air in the accumulator varies according to the adiabatic process, and then [10].
p1 V 11:4 ¼ p0 ðV 1 þ DVÞ1:4
ð4Þ
where p1 is the highest pressure of the accumulator air, p0 is the accumulator air charging pressure, V1 is the volume of the air vessel, DV is the volume of the oil-storing cylinder. The volume DV of the oil-storing cylinder is determined by
DV ¼
10s iV max 2p r
ð5Þ
where s is the length of a stand, r is the radius of the drum, i is the transmission ration from the variable pump-motor shaft to the drum shaft, Vmax is the maximum displacement of the variable pump-motor for lifting the heaviest drill stem. From Eq. (4), we can obtain
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V1 ¼
DV
ð6Þ
1
ðp1 =p0 Þ1:4 1
As shown in Eq. (6), after DV and p1/p0 have been determined, the volume V1 of the air vessel cab be determined by Eq. (6).
From the kinematics,
xm ¼
10iv r
ð14Þ
where v is the drill stem lowering velocity. Substitution of Eq. (14) into Eq. (13) yields
5. Mathematical model of the energy-saving oil drilling rig lowering the drill stem
ðW þ W t Þr g1 g2 pV 10iJm ðW þ W t Þr dv ¼ þ 2pgm 10gi 10i r dt
5.1. Dynamics model of the variable pump-motor lowering part
Eq. (15) is dynamics model of the variable pump-motor lowering part.
By Newton’s second law, when lowering the drill stem, the dynamics equation of the variable pump-motor shaft can be established as [11].
T de T re ¼ J
dxm dt
ð7Þ
where Tde is the equivalent driving torque on the variable pumpmotor shaft, Tre is the equivalent resisting torque on the variable pump-motor shaft, J is the total moment of inertia converted on the variable pump-motor shaft, xm is the angular velocity of the variable pump-motor shaft, t is the time. Because in lowering the drill stem, the weight of the drill stem is driving force, the equivalent driving torque Tde is the torque converted on the variable pump-motor shaft by the weight of the drill stem. Hence, by the principle of conservation of power, Tde can be expressed as [12]
T de
T d g1 ¼ i
ð8Þ
where Td is the driving torque on the drum produced by the weight of the drill stem, i is the transmission ration from the variable pump-motor shaft to the drum shaft, g1 is the transmission efficiency from the variable pump-motor shaft to the drum shaft. The 5 6 traveling system composed of the crown block, traveling block, and the wire line is adopted. The effective amount of the wire line of this traveling system is 10, and then
ðW þ W t Þr g2 Td ¼ 10
ð9Þ
where W is the weight of the drill stem, Wt is the weight of the traveling system, r is the radius of the drum, g2 is the efficiency of the traveling system. Substitution of Eq. (9) into Eq. (8) yields
T de ¼
ðW þ W t Þr g1 g2 10i
ð10Þ
The equivalent resisting torque Tre is also the input torque of the variable pump-motor, so Tre can be expressed as
T re ¼
pV
ð11Þ
2pgm
where p is the oil pressure of the variable pump-motor outlet, V is the displacement of the variable pump-motor, gm is the mechanical efficiency of the variable pump-motor. According to principle of conservation of kinetic energy, the expression of J is [13]
J ¼ Jm þ
ðW þ W t Þr2
ð12Þ
2
100gi
where Jm is the moment of inertia of the variable pump-motor shaft, g is acceleration of gravity. Substitution of Eqs. (10)–(12) into Eq. (7) yields
"
#
ðW þ W t Þrg1 g2 pV ðW þ W t Þr 2 dxm ¼ Jm þ 2 2pgm 10i dt 100gi
ð13Þ
ð15Þ
5.2. Energy equation for the variable pump-motor to the accumulator According to the Bernoulli energy equation, the oil pressure p of the variable pump-motor outlet is [14]
p ¼ pa þ Dp
ð16Þ
where pa is the oil pressure in the accumulator, Dp is the pressure loss of oil through the pipe and valve.
Dp ¼ nqv 21 =2
ð17Þ
where n is the coefficient of the pressure loss of oil through the pipe and valve, q is the oil density, v1 is the velocity of oil through the pipe and valve. The oil flow q through the pipe and valve is [15]
q ¼ v 1 A ¼ Vnm gV =60
ð18Þ
where A is the pipe path area, nm is the rotate speed of the variable pump-motor, gV is the volume efficiency of the variable pumpmotor. From the kinematics,
nm ¼
30xm
p
¼
300iv pr
ð19Þ
Combining Eqs.(17)–(19), we can obtain
Dp ¼ 12:5nq
2 iV gV v2 prA
ð20Þ
Substitution of Eq. (20) into Eq. (16) yields
2 iV gV p ¼ pa þ 12:5nq v2 prA
ð21Þ
5.3. Dynamics equation of the accumulator to the variable pumpmotor lowering part Substituting Eq. (21) into Eq. (15) and rearranging, the dynamics equation of the accumulator to the variable pump-motor lowering part can be written as
2 10iJm ðW þ W t Þr dv 25nqi V 3 g2V 2 p V v þ a þ þ 3 2 10gi 2pgm r dt 4p r A2 gm
ðW þ W t Þr g1 g2 ¼0 10i
ð22Þ
5.4. Flow continuous equation of the accumulator According to the flow continuous equation, the oil flow in the accumulator can be given as [14]
v a Aa ¼ Vnm gV =60
ð23Þ
where va is the flow velocity of oil in the accumulator and also the velocity of the oil-storing cylinder piston, Aa is the area of the oilstoring cylinder piston.
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L. Zhang / Energy Conversion and Management 52 (2011) 359–365
dv a 5iV gV dv ¼ dt prAa dt
Substitution of Eq. (19) into Eq. (23) yields
5iV gV v a Aa ¼ v pr
ð24Þ
Substituting Eq. (32) into Eq. (31) and rearranging, we obtain
Both sides of Eq. (24) product t, and we obtain
pa ¼
5iV gV A a xa ¼ x pr
ð25Þ
where xa is the displacement of the oil-storing cylinder piston, x is the displacement of the drill stem. 5.5. Dynamics equation of the accumulator As shown in Fig. 2, the air pressure acts on the top of the oilstoring cylinder piston and hydraulic pressure acts on the bottom. If the friction of the oil-storing cylinder piston is not considered, the dynamics equation of the oil-storing cylinder piston can be established as
ma
dv a ¼ pa Aa pi Aa Ga dt
ð26Þ
where ma is the mass of the oil-storing cylinder piston, Ga is the weight of the oil-storing cylinder piston, pi is the instantaneous pressure of air above the oil-storing cylinder piston. Because the air in the accumulator varies according to the adiabatic process, and then [10]
pi V 1:4 ¼ p0 ðV 1 þ DVÞ1:4 i
ð27Þ
where pi is the instantaneous pressure of the accumulator air, Vi is the instantaneous volume of the accumulator air, p0 is the accumulator air charging pressure, V1 is the volume of the air vessel, DV is the volume of the oil-storing cylinder. when t = 0, xa ¼ 0; v a ¼ 0; V i ¼ V 1 þ DV; pi ¼ p0 ; when time is a certain t, then
V i ¼ V 1 þ DV A a xa
ð28Þ
Substitution of Eq. (25) into Eq. (28) yields
5iV gV V i ¼ V 1 þ DV x pr
Substituting Eq. (29) into Eq. (27) and rearranging, we obtain
pi ¼
p0 ðV 1 þ DVÞ1:4
ð30Þ
ðV 1 þ DV 5iVprgV xÞ1:4
Substituting Eq. (30) into Eq. (26), dynamics equation of the accumulator can be given as
ma
dv a p0 ðV 1 þ DVÞ1:4 Aa Ga ¼ pa Aa dt ðV 1 þ DV 5iV gV xÞ1:4
ð31Þ
pr
5.6. Mathematical model of the energy-saving oil drilling rig lowering the drill stem Differentiation of Eq. (24) yields
p0 ðV 1 þ DV Þ1:4 ðV 1 þ DV 5iVprgV xÞ1:4
þ
5iVma gV dv Ga þ prA2a dt Aa
ð33Þ
Substituting Eq. (33) into Eq. (22) and rearranging, we obtain
" # 2 2 10iJm ðW þ W t Þr 5iV ma gV dv 25nqi V 3 g2V 2 þ v þ þ 2 10gi r 2p2 rAa gm dt 4p3 r2 A2 gm þ
Ga V p0 ðV 1 þ DVÞ1:4 V ðW þ W t Þr g1 g2 þ ¼0 2pgm Aa 2pgm ðV 1 þ DV 5iV gV xÞ1:4 10i pr
ð34Þ Eq. (34) is the mathematical model of the energy-saving oil drilling rig lowering the drill stem. The displacement V of the variable pump-motor in Eq. (34) is determined by
ðW þ W t Þr g1 g2 p V P h 2pgm 10i
ð35Þ
where ph is the maximum pressure in the accumulator when lowering the drill stem under the displacement V.When pi = ph ,
V i ¼ V 1 þ DV V ra
ð36Þ
where Vra is the volume of the hydraulic oil recovered in the accumulator when the drill stem is lowered for a stand length, it is determined by Eq. (1). Substitution of Eq. (1) into Eq. (36) yields
V i ¼ V 1 þ DV
10s im V 2pr
ð37Þ
Substitution of pi = ph and Eq. (37) into Eq. (27) yields
ph ¼ p0 ð29Þ
ð32Þ
V 1 þ DV V 1 þ DV 10siV=ð2prÞ
1:4 ð38Þ
Substitution of Eq. (38) into Eq. (35) yields
1:4 ðW þ W t Þr g1 g2 p V V 1 þ DV P 0 2pgm V 1 þ DV 10siV=ð2prÞ 10i
ð39Þ
That is to say, the displacement V of the variable pump-motor in Eq. (34) should satisfy Eq. (39). The maximum displacement Vmax for lowering the drill stem whose weight is W can be obtained by Eq. (39); that is, when V 6 Vmax, the drill stem whose weight is W can lower into the well. However, from Eq. (1), we know that the larger the displacement V, the more the energy recovered in the accumulator is. Therefore, in order to improve the rate of energy recovery, the displacement V of the variable pump-motor should be adjusted as large as possible under the condition that the drill stem can lower into the well. 6. Simulation analysis of the energy-saving oil drilling rig lowering the drill stem 6.1. Simulation results Ò
Fig. 2. Force on oil-storing cylinder piston.
Based on the function ode45() of MATLAB [16], the program is written to conduct numerical simulation analysis for Eq. (34), in order to know the law of parameters affecting the tubing string lifting velocity. The function ode45() is based on the Runge–Kutta methods and uses adaptive variable step sizes in the numerical integration. Take the design of 3000 m drilling rig whose maximum drill stem weight is 900 kN as an example to conduct analysis. The
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known data are i = 24, Jm = 2 kg m2, r = 0.35 m, Wt = 80 kN, ma = 882 kg, Aa = 0.75m2, gm = 0.95, gV = 0.95, A = 0.0051m2, n = 16, q = 880 kg/m3, p0 = 18 MPa, V1 = 7.423m3, DV = 1.529m3, g1 = 0.92, g2 = 0.85, s = 28 m. Substituting these data into Eq. (34) and conducting numerical integration with Matlab, the simulation results for lowering the drill stem whose stand length is 28 m can be obtained. When lowering the drill stem of different weights W under their respective maximum displacements Vmax, the curves of the drill stem lowering velocity v and lowering displacement x with time t are shown in Figs. 3 and 4, respectively. As shown in Figs. 3 and 4, when lowering the drill stem for a stand length, the heavier the drill stem, the higher the lowering velocity is, and the shorter the lowering time is. The curves of the drill stem lowering velocity v and lowering displacement x with time t under different displacement V of the variable pump-motor are shown in Figs. 5 and 6, respectively. As shown in Figs. 5 and 6, when lowering the drill stem for a stand length, the smaller the displacement V of the variable pump-motor, the higher the lowering velocity is, and the shorter the lowering time is. Based on this characteristic, the energy-saving oil drilling
Fig. 3. Curve of the drill stem lowering velocity
v with time t.
Fig. 5. Curve of the drill stem lowering velocity
v with time t.
Fig. 6. Curve of the drill stem lowering displacement x with time t.
rig can change speed by changing the displacement of the variable pump-motor when lowering the drill stem. 6.2. Comparison of the simulation results with the actual measure results Unfortunately, the actual curves of the drill stem lowering velocity and displacement cannot be tested owing to the lack of necessary apparatus. A digital electrical stop watch was used to measure the actual lowering time of the drill stem. The simulation results and the actual measure results are shown in Table 1. As shown in Table 1, the actual measure value and the simulation value of the drill stem lowering time are basically the same,
Table 1 Drill stem lowering time of W = 600 kN.
Fig. 4. Curve of the drill stem lowering displacement x with time t.
Variable pump-motor displacement V/mL/r Actual measure value t/s Simulation value t/s
229
214
198
183
167
142
35.9 35.2
27.3 26.9
22.1 22.4
19.3 19.8
17.2 17.8
14.9 15.6
L. Zhang / Energy Conversion and Management 52 (2011) 359–365 Table 2 Results of field test. Number
1 2
Lifting
71 stands 93 stands
Lowering
71 stands 93 stands
Electricity consumption Energy-saving oil drilling rig
Conventional drilling rig
359 kW h
452 kW h
590 kW h
714 kW h
which proves the dynamic model and simulation results are basically right. 7. Field tests The contrast experiments between the energy-saving oil drilling rig and the conventional drilling rig were conducted twice. The field test results are shown in Table 2. As shown in Table 2, the electricity consumption of the energysaving oil drilling rig is less than that of the conventional drilling rig when lifting and lowering stands of same amount. These results show the efficiency and the energy-saving effect of the energy-saving oil drilling rig. 8. Conclusions The energy-saving oil drilling rig is an energy-saving machine. The accumulator energy-storing technology is adopted to store the energy of the motor at idle during lifting the drill stem and the potential energy released by the drill stem when lowered. The equipped power of this rig is decreased remarkably compared with the conventional drilling rig, and this rig can also recover and reuse the potential energy of the drill stem. Therefore, this rig owns remarkable energy-saving effect compared with the conventional drilling rig, and the energy-saving effect of the energy-saving oil drilling rig is
365
also verified by the field tests. The mathematical model of the new rig lowering the drill stem was derived and simulation analysis was conducted. Through simulation the laws of the drill stem weight and displacement of the variable pump-motor affecting the lowering velocity and lowering time of the drill stem were obtained. References [1] Cohen JH, Maurer WC, Westcott PA. High-power TSP bits. J Energy Res Technol 1994;116(3):33–7. [2] Zhou S, Hua J. Introduction to petroleum machinery. Beijing, China: Petroleum Industry Press; 2002. [3] Moak R. New hydraulic lift rig for drilling and workover. World Oil 1996;217(7):41–2. [4] Yang H, Sun W, Xu B. New investigation in energy regeneration of hydraulic elevators. IEEE/ASME Trans Mechatron 2007;12(5):519–26. [5] Lin X, Guan C, Pei L, Pan S. Research on the system of arm potential energy recovery in hybrid hydraulic excavators. Trans Chin Soc Agric Mach 2009;40(4):96–101. [6] Jefferson CM, Ackerman M. A flywheel variator energy storage system. Energy Convers Manage 1996;37(10):1481–91. [7] Uzunoglu M. Alam MS.Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications. Energy Convers Manage 2007;48(5):1544–53. [8] Suda Y, Shiiba T. New hybrid suspension system with active control and energy regeneration. Veh Syst Dynam 1996;25(Suppl.):641–54. [9] Beers D, Biswas WK. A regional synergy approach to energy recovery: The case of the Kwinana industrial area, Western Australia. Energy Convers Manage 2008;49(11):3051–62. [10] Mordas JB. Accumulators-The neglected components. Hydraul Pneumat 1994;47(7):41–3. [11] Boresi AP, Schmidt RJ. Engineering mechanics. Chongqing, China: Chongqing University Press; 2005. [12] Deng X. Mechanical and electrical transmission control. Wuhan, China: Huazhong University of Science and Technology Press; 2002. [13] Norton RL. Design of machinery: an introduction to the synthesis and analysis of mechanisms and machines. New York (US): McGraw-Hill; 2001. [14] Jin Z. Hydraulic hydromechanics. Beijing, China: National Defence Industry Press; 1994. [15] Jiang J, Song J, Gao C. Hydraulic and pneumatic transmission. Beijing, China: Higher Education Press; 2002. [16] Xu D, Chen Y. Simulating technology based on Matalab/Simulink. Beijing, China: Tsinghua University Press; 2002.
Contents lists available at ScienceDirect
Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman
An energy-saving oil drilling rig for recovering potential energy and decreasing motor power Zhang Lujun School of Mechanical and Automotive Engineering, Yantai University, Yantai 264005, China
a r t i c l e
i n f o
Article history: Received 20 December 2008 Received in revised form 16 November 2009 Accepted 5 July 2010 Available online 31 July 2010 Keywords: Energy recovery Oil drilling rig Energy-saving Drill stem Lowering
a b s t r a c t An energy-saving oil drilling rig is researched. A large accumulator is adopted in this rig to store the energy of the motor during the auxiliary time of lifting the drill stem and the potential energy of the drill stem when lowered. The equipped power of this rig decreases remarkably compared with the conventional drilling rig, and this rig can also recover and reuse the potential energy of the drill stem. Therefore, this rig owns remarkable energy-saving effect compared with the conventional drilling rig, and the energy-saving effect of the energy-saving oil drilling rig is also verified by the field tests. The mathematical model of the energy-saving oil drilling rig lowering the drill stem was derived and simulation analysis was conducted. Through simulation the curves of the drill stem lowering velocity and lowering displacement with time were obtained, and some conclusions were reached: (1) the heavier the drill stem lowered, the higher the lowering velocity is, and the shorter the lowering time is; (2) the smaller the displacement of the variable pump-motor, the higher the lowering velocity is, and the shorter the lowering time is. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction The drilling rig plays an important role in petroleum exploitation [1]. When the bit is dull, the drill stem is pulled out of the well. After replacing the dull bit with a new one, the drill stem is lowered into the well again. The operation of pulling the drill stem out of the well is an intermittent cycle process. In a cycle, the pure lifting time (the time of lifting the drill stem from the well) is only about one third of the time used, and here the motor works under a high power. The auxiliary time (the time of removing the stand from the drill stem and positioning the stand) is two-thirds, and here the motor works under a low power. The high power motor of the conventional drilling rig works mostly under low power, and therefore it is not economical [2,3]. The drill stem lifted up to the ground from the well deposits much potential energy, and when the drill stem is lowered down to the well, the deposited potential energy is released. The conventional drilling rig just wastes this energy by braking and this energy cannot be recovered. As mentioned above, the conventional drilling rig has an unreasonably large energy waste both in lifting and lowering the drill stem. Because energy is very precious, the problem of wasting energy must be resolved. Therefore, an energy-saving oil drilling rig is presented. The equipped power of this rig is only one third of a conventional drilling rig, and this rig can recover and reuse the
E-mail address: [email protected] 0196-8904/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.enconman.2010.07.009
potential energy which is released by the drill stem when lowered. This rig owns remarkable energy-saving effect. Because of the effects of the energy crisis and oil shortage, the researches on energy recovery and reuse are conducted in more and more fields, and the formerly wasted or detrimental energy is converted into other forms of energy to be stored and reused. Yang et al. [4] studied a hydraulic elevator which could recover the potential energy of the cabin during down-travel and reuse this energy during up-travel and showed this hydraulic elevator could achieve a significant energy-saving performance compared to the traditional elevators. Lin et al. [5] studied the system which could recover the arm potential energy in hybrid hydraulic excavators when the arm lowering. The recovery and reuse of the vehicle brake energy are the hot research fields these years. Jefferson and Ackerman [6] studied a flywheel variator energy storage system which could recover the vehicle brake energy and showed energy losses and consumption were minimized. Uzunoglu and Alam [7] studied fuel cell/ultra-capacitor hybrid vehicular power systems with the ultra-capacitor recovering the regenerative energy during braking. Suda and Shiiba [8] Studied an energy regenerative damper system which converts vibration energy of the vehicle into useful energy. The aforementioned researches are all about recovery and reuse of mechanical energy, and however, there are also many researches on regeneration of other forms of energy, such as recovery and reuse of waste gas energy. For example, the study of Beers and Biswas [9] demonstrated the significant potential to mitigate CO2 emissions through energy recovery from
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flue gases by applying technologies to convert the embedded energy into useful thermal and electric applications. However, there are no reports about the oil drilling rig which can recover and reuse the potential energy released by the drill stem when lowered. As a machine which exploits energy (oil), the drilling rig itself has energy waste, and it is a great pity. Therefore, an energy-saving oil drilling rig which can resolve this problem well is presented.
2. Basic structure As shown in Fig. 1, the energy-saving oil drilling rig consists of the frequency conversion motors 1 and 2, transmission cases 5 and 8, angle transmission case 9, variable pump-motor hydraulic system, drum 10, disk brake 11, blocks and hook 12, rotary table 14, and couplings and clutches connecting each part. The variable pump-motor hydraulic system is connected in parallel to the main system from the motor 1 to the drum 10 via the transmission case 5. The variable pump-motor hydraulic system consists of the variable pump-motor 15, two-position two way electromagnetic valve 16, accumulator, overflow valve 17, and oil tank 20. The accumulator is composed of oil-storing cylinder 18 and air vessel 19. The function of the transmission case 5 is to transfer the power of the motor 1 to the variable pump-motor 15 during the auxiliary time and transfer the power of the variable pump-motor 15 to the drum 10 when lifting the drill stem. The transmission case 5 includes two gears 53 and 54 which form a gearset. The shaft of the variable pump-motor 15 is attached to the shaft 52 of the transmission case 5 through the coupling 33 and clutch 44.The transmission case 5 attaches to the motor 1 through the clutch 41 and coupling 31, and attaches to the transmission case 8 and angle transmission case 9 through the clutch 43 and coupling 34. The angle transmission case 9 is attached to the drum 10 through the coupling 35. The motor 2 drives the rotary table 14 via the coupling 32, clutch 42, universal coupling 36 and 37, and transmission shaft 13. One sprocket of the chain transmission 6 is fitted on the shaft 51 loosely. Moving joint sleeves 7 left can realize the connection of the chain transmissions 6 with the shaft 51, and thereby realize the combination of the motors 1 and 2.
3. Working theory 3.1. Process of lifting the drill stem During the auxiliary time of lifting the drill stem, the clutch 43 is disengaged. The angle of the swash-plate of the variable pumpmotor 15 is adjusted in positive direction; that is, at this moment the direction of output torque of the variable pump-motor 15 under the action of the oil pressure is the same as that of the output torque of the motor 1. Then, the direction of the torque T1 which the motor 1 produces on the shaft of the variable pump-motor 15 via the coupling 31, engaged clutch 41, gearset 53 and 54, engaged clutch 44, and coupling 33 is contrary to that of the output torque T2 of the variable pump-motor 15 under the action of the oil pressure. Adjusting the displacement of the variable pump-motor 15 to make T1 larger than T2, the variable pump-motor 15 runs as a hydraulic pump and charges oil into the accumulator through the lower position of two-position two way electromagnetic valve 16. The overflow valve 17 functions as safeguard, and when the oil pressure of the accumulator surpasses the setting value, the overflow valve 17 opens to let the oil overflow. When lifting the drill stem, the clutch 43 is engaged, and the disk brake 11 is released. The angle of the swash-plate of the variable pump-motor 15 is adjusted in negative direction; that is, at this moment the direction of output torque of the variable pump-motor 15 under the action of the oil pressure is contrary to that of the output torque of the motor 1. The direction of the torque which the variable pump-motor 15 produces on the shaft 51 via the coupling 33, engaged clutch 44, and gearset 53 and 54 is the same as that of the output torque of the motor 1. At this moment, the variable pump-motor 15 runs as a hydraulic motor and combines with the motor 1 to provide power for the drum10 which rotates to lift the drill stem out of the well through blocks and hook 12. Therefore, the power of the motor 1 decreases greatly and is only about one third of the conventional drilling rig. For instance, for 3000 m drilling rig whose maximum drill stem weight is 900 kN, the equipped power of drawworks in the conventional drilling rig is 600 kW, and the power of drawworks in this new drilling rig is 209 kW. During lifting the drill stem, the weight of the drill stem is changeable and the drill stem gets lighter and lighter. Because
Fig. 1. Structure diagram of the energy-saving oil drilling rig.
L. Zhang / Energy Conversion and Management 52 (2011) 359–365
the power of the motor 1 is only about one third of the conventional drilling rig, when lifting the drill stem whose weight is less than one third of the maximum drill stem weight, the motor 1 can lift the drill stem without the help of the variable pump-motor 15. At this moment, the clutch 44 is disengaged, and the variable pump-motor 15 does not work. Here, in order to prevent the variable pump-motor 15 from turning, two-position two way electromagnetic valve 16 is set at the upper position. That is to say, when lifting the drill stem whose weight is within this range, the energysaving oil drilling rig is the same as the ordinary frequency conversion electric drilling rig. When lifting the drill stem whose weight is larger than one third of the maximum drill stem weight, the motor 1 and the variable pump-motor 15 combine to work, and here the motor 1 runs under the rating constant torque. The load torque which surpasses the rating torque of the motor is afforded by the power of the variable pump-motor 15. The driller adjusts the displacement of the variable pump-motor 15 according to the weight indicator. When the drill stem to be lifted is heavier, the load torque which should be overcome by the variable pump-motor is larger. At this moment, the driller changes the displacement of the variable pump-motor 15 to be larger to increase the output torque of the variable pump-motor 15. On the contrary, when the drill stem to be lifted is lighter, the load torque which should be overcome by the variable pump-motor is smaller. At this moment, the driller changes the displacement of the variable pump-motor 15 to be smaller to decrease the output torque of the variable pump-motor 15. Generally the chain transmission 6 is not engaged, and the drum is driven by the motor 1, while the rotary table is driven by the motor 2. In special case, such as blockage during tripping, the chain transmission 6 is engaged, and the motor 1 together with the motor 2 drives the drum to improve the lifting ability of the drum. 3.2. Process of lowering the drill stem When lowering the drill stem, the motor 1 can be turned off and the clutch 41 is disengaged; that is, when lowering the drill stem, the motor 1 does not work. After the stand has been connected to the drill stem, the disk brake 11 is released, and the angle of the swash-plate of the variable pump-motor 15 is adjusted in negative direction. The direction of the torque T3 which the weight of the drill stem produces on the shaft of the variable pump-motor 15 through the drum 10, coupling 35, angle transmission case 9, transmission case 8, coupling 34, engaged clutch 43, gearset 53 and 54, engaged clutch 44, and coupling 33 is contrary to that of the output torque T2 of the variable pump-motor 15 under the action of the oil pressure. Adjusting the displacement of the variable pump-motor 15 to make T2 smaller than T3, the drill stem lowers into the well, and at the same time the variable pump-motor 15 runs as a hydraulic pump and charges oil into the accumulator through the lower position of two-position two way electromagnetic valve 16. That is to say, the potential energy of the drill stem is changed into the hydraulic energy to be stored in the accumulator, thus realizing the recovery of the potential energy of the drill stem. When the drill stem is lowered for a stand length, the volume Vra of the hydraulic oil recovered in the accumulator is
V ra ¼
10s iV ðm3 Þ 2pr
ð1Þ
where s is the length of a stand, r is the radius of the drum, i is the transmission ration from the variable pump-motor shaft to the drum shaft, V is the displacement of the variable pump-motor. During lowering the drill stem, the weight of the drill stem gets heavier and heavier. The driller timely adjusts the displace-
361
ment of the variable pump-motor 15 according to the weight indicator. In the beginning, the drill stem lowered is lighter, thus the displacement of the variable pump-motor 15 is smaller, and from Eq. (1) we know that the amount of the recovered energy is smaller. Along with the increase of the drill stem weight, the driller timely enlarges the displacement V of the variable pump-motor 15, and the amount of the recovered energy becomes larger. This recovered energy can be reused to complete the auxiliary work, such as raising the elevator, driving the pipe tongs to make up pipe, driving the air compressor to offer the energy to operate the clutches and brakes. These works are completed by the power of the motor before, and now these works are completed by the recovered energy. Therefore lots of energy is saved.
4. Calculation of the motor power and the volume of the accumulator 4.1. Calculation of the motor power The maximum energy E for lifting the drill stem is
E¼
W max s
g1 g2
ð2Þ
where E is the energy, Wmax is the maximum weight of the drill stem, s is the length of a stand, g1 is the transmission efficiency from the variable pump-motor shaft to the drum shaft, g2 is the efficiency of the traveling system. In one cycle of lifting the drill stem, the ratio of the pure lifting time to the auxiliary time is 1:2. For the energy-saving oil drilling rig, in the auxiliary time the motor 1 supplies energy to the accumulator through the variable pump-motor 15, and in the pure lifting time, the accumulator through the variable pump-motor 15, together with the motor 1, outputs energy to lift the drill stem. That is to say, in the pure lifting time, one third of the total energy E is supplied by the motor 1, two-thirds of the total energy E is supplied by the accumulator. Therefore, the motor power Pe is
Pe ¼
E W max s ¼ 3t 3g1 g2 t
ð3Þ
where t is the time of lifting the drill stem. 4.2. Calculation of the volume of the accumulator The accumulator is piston accumulator and is composed of oilstoring cylinder and air vessel. Because the accumulator provides large amount of pressure oil for the system in a short time, the air in the accumulator varies according to the adiabatic process, and then [10].
p1 V 11:4 ¼ p0 ðV 1 þ DVÞ1:4
ð4Þ
where p1 is the highest pressure of the accumulator air, p0 is the accumulator air charging pressure, V1 is the volume of the air vessel, DV is the volume of the oil-storing cylinder. The volume DV of the oil-storing cylinder is determined by
DV ¼
10s iV max 2p r
ð5Þ
where s is the length of a stand, r is the radius of the drum, i is the transmission ration from the variable pump-motor shaft to the drum shaft, Vmax is the maximum displacement of the variable pump-motor for lifting the heaviest drill stem. From Eq. (4), we can obtain
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L. Zhang / Energy Conversion and Management 52 (2011) 359–365
V1 ¼
DV
ð6Þ
1
ðp1 =p0 Þ1:4 1
As shown in Eq. (6), after DV and p1/p0 have been determined, the volume V1 of the air vessel cab be determined by Eq. (6).
From the kinematics,
xm ¼
10iv r
ð14Þ
where v is the drill stem lowering velocity. Substitution of Eq. (14) into Eq. (13) yields
5. Mathematical model of the energy-saving oil drilling rig lowering the drill stem
ðW þ W t Þr g1 g2 pV 10iJm ðW þ W t Þr dv ¼ þ 2pgm 10gi 10i r dt
5.1. Dynamics model of the variable pump-motor lowering part
Eq. (15) is dynamics model of the variable pump-motor lowering part.
By Newton’s second law, when lowering the drill stem, the dynamics equation of the variable pump-motor shaft can be established as [11].
T de T re ¼ J
dxm dt
ð7Þ
where Tde is the equivalent driving torque on the variable pumpmotor shaft, Tre is the equivalent resisting torque on the variable pump-motor shaft, J is the total moment of inertia converted on the variable pump-motor shaft, xm is the angular velocity of the variable pump-motor shaft, t is the time. Because in lowering the drill stem, the weight of the drill stem is driving force, the equivalent driving torque Tde is the torque converted on the variable pump-motor shaft by the weight of the drill stem. Hence, by the principle of conservation of power, Tde can be expressed as [12]
T de
T d g1 ¼ i
ð8Þ
where Td is the driving torque on the drum produced by the weight of the drill stem, i is the transmission ration from the variable pump-motor shaft to the drum shaft, g1 is the transmission efficiency from the variable pump-motor shaft to the drum shaft. The 5 6 traveling system composed of the crown block, traveling block, and the wire line is adopted. The effective amount of the wire line of this traveling system is 10, and then
ðW þ W t Þr g2 Td ¼ 10
ð9Þ
where W is the weight of the drill stem, Wt is the weight of the traveling system, r is the radius of the drum, g2 is the efficiency of the traveling system. Substitution of Eq. (9) into Eq. (8) yields
T de ¼
ðW þ W t Þr g1 g2 10i
ð10Þ
The equivalent resisting torque Tre is also the input torque of the variable pump-motor, so Tre can be expressed as
T re ¼
pV
ð11Þ
2pgm
where p is the oil pressure of the variable pump-motor outlet, V is the displacement of the variable pump-motor, gm is the mechanical efficiency of the variable pump-motor. According to principle of conservation of kinetic energy, the expression of J is [13]
J ¼ Jm þ
ðW þ W t Þr2
ð12Þ
2
100gi
where Jm is the moment of inertia of the variable pump-motor shaft, g is acceleration of gravity. Substitution of Eqs. (10)–(12) into Eq. (7) yields
"
#
ðW þ W t Þrg1 g2 pV ðW þ W t Þr 2 dxm ¼ Jm þ 2 2pgm 10i dt 100gi
ð13Þ
ð15Þ
5.2. Energy equation for the variable pump-motor to the accumulator According to the Bernoulli energy equation, the oil pressure p of the variable pump-motor outlet is [14]
p ¼ pa þ Dp
ð16Þ
where pa is the oil pressure in the accumulator, Dp is the pressure loss of oil through the pipe and valve.
Dp ¼ nqv 21 =2
ð17Þ
where n is the coefficient of the pressure loss of oil through the pipe and valve, q is the oil density, v1 is the velocity of oil through the pipe and valve. The oil flow q through the pipe and valve is [15]
q ¼ v 1 A ¼ Vnm gV =60
ð18Þ
where A is the pipe path area, nm is the rotate speed of the variable pump-motor, gV is the volume efficiency of the variable pumpmotor. From the kinematics,
nm ¼
30xm
p
¼
300iv pr
ð19Þ
Combining Eqs.(17)–(19), we can obtain
Dp ¼ 12:5nq
2 iV gV v2 prA
ð20Þ
Substitution of Eq. (20) into Eq. (16) yields
2 iV gV p ¼ pa þ 12:5nq v2 prA
ð21Þ
5.3. Dynamics equation of the accumulator to the variable pumpmotor lowering part Substituting Eq. (21) into Eq. (15) and rearranging, the dynamics equation of the accumulator to the variable pump-motor lowering part can be written as
2 10iJm ðW þ W t Þr dv 25nqi V 3 g2V 2 p V v þ a þ þ 3 2 10gi 2pgm r dt 4p r A2 gm
ðW þ W t Þr g1 g2 ¼0 10i
ð22Þ
5.4. Flow continuous equation of the accumulator According to the flow continuous equation, the oil flow in the accumulator can be given as [14]
v a Aa ¼ Vnm gV =60
ð23Þ
where va is the flow velocity of oil in the accumulator and also the velocity of the oil-storing cylinder piston, Aa is the area of the oilstoring cylinder piston.
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L. Zhang / Energy Conversion and Management 52 (2011) 359–365
dv a 5iV gV dv ¼ dt prAa dt
Substitution of Eq. (19) into Eq. (23) yields
5iV gV v a Aa ¼ v pr
ð24Þ
Substituting Eq. (32) into Eq. (31) and rearranging, we obtain
Both sides of Eq. (24) product t, and we obtain
pa ¼
5iV gV A a xa ¼ x pr
ð25Þ
where xa is the displacement of the oil-storing cylinder piston, x is the displacement of the drill stem. 5.5. Dynamics equation of the accumulator As shown in Fig. 2, the air pressure acts on the top of the oilstoring cylinder piston and hydraulic pressure acts on the bottom. If the friction of the oil-storing cylinder piston is not considered, the dynamics equation of the oil-storing cylinder piston can be established as
ma
dv a ¼ pa Aa pi Aa Ga dt
ð26Þ
where ma is the mass of the oil-storing cylinder piston, Ga is the weight of the oil-storing cylinder piston, pi is the instantaneous pressure of air above the oil-storing cylinder piston. Because the air in the accumulator varies according to the adiabatic process, and then [10]
pi V 1:4 ¼ p0 ðV 1 þ DVÞ1:4 i
ð27Þ
where pi is the instantaneous pressure of the accumulator air, Vi is the instantaneous volume of the accumulator air, p0 is the accumulator air charging pressure, V1 is the volume of the air vessel, DV is the volume of the oil-storing cylinder. when t = 0, xa ¼ 0; v a ¼ 0; V i ¼ V 1 þ DV; pi ¼ p0 ; when time is a certain t, then
V i ¼ V 1 þ DV A a xa
ð28Þ
Substitution of Eq. (25) into Eq. (28) yields
5iV gV V i ¼ V 1 þ DV x pr
Substituting Eq. (29) into Eq. (27) and rearranging, we obtain
pi ¼
p0 ðV 1 þ DVÞ1:4
ð30Þ
ðV 1 þ DV 5iVprgV xÞ1:4
Substituting Eq. (30) into Eq. (26), dynamics equation of the accumulator can be given as
ma
dv a p0 ðV 1 þ DVÞ1:4 Aa Ga ¼ pa Aa dt ðV 1 þ DV 5iV gV xÞ1:4
ð31Þ
pr
5.6. Mathematical model of the energy-saving oil drilling rig lowering the drill stem Differentiation of Eq. (24) yields
p0 ðV 1 þ DV Þ1:4 ðV 1 þ DV 5iVprgV xÞ1:4
þ
5iVma gV dv Ga þ prA2a dt Aa
ð33Þ
Substituting Eq. (33) into Eq. (22) and rearranging, we obtain
" # 2 2 10iJm ðW þ W t Þr 5iV ma gV dv 25nqi V 3 g2V 2 þ v þ þ 2 10gi r 2p2 rAa gm dt 4p3 r2 A2 gm þ
Ga V p0 ðV 1 þ DVÞ1:4 V ðW þ W t Þr g1 g2 þ ¼0 2pgm Aa 2pgm ðV 1 þ DV 5iV gV xÞ1:4 10i pr
ð34Þ Eq. (34) is the mathematical model of the energy-saving oil drilling rig lowering the drill stem. The displacement V of the variable pump-motor in Eq. (34) is determined by
ðW þ W t Þr g1 g2 p V P h 2pgm 10i
ð35Þ
where ph is the maximum pressure in the accumulator when lowering the drill stem under the displacement V.When pi = ph ,
V i ¼ V 1 þ DV V ra
ð36Þ
where Vra is the volume of the hydraulic oil recovered in the accumulator when the drill stem is lowered for a stand length, it is determined by Eq. (1). Substitution of Eq. (1) into Eq. (36) yields
V i ¼ V 1 þ DV
10s im V 2pr
ð37Þ
Substitution of pi = ph and Eq. (37) into Eq. (27) yields
ph ¼ p0 ð29Þ
ð32Þ
V 1 þ DV V 1 þ DV 10siV=ð2prÞ
1:4 ð38Þ
Substitution of Eq. (38) into Eq. (35) yields
1:4 ðW þ W t Þr g1 g2 p V V 1 þ DV P 0 2pgm V 1 þ DV 10siV=ð2prÞ 10i
ð39Þ
That is to say, the displacement V of the variable pump-motor in Eq. (34) should satisfy Eq. (39). The maximum displacement Vmax for lowering the drill stem whose weight is W can be obtained by Eq. (39); that is, when V 6 Vmax, the drill stem whose weight is W can lower into the well. However, from Eq. (1), we know that the larger the displacement V, the more the energy recovered in the accumulator is. Therefore, in order to improve the rate of energy recovery, the displacement V of the variable pump-motor should be adjusted as large as possible under the condition that the drill stem can lower into the well. 6. Simulation analysis of the energy-saving oil drilling rig lowering the drill stem 6.1. Simulation results Ò
Fig. 2. Force on oil-storing cylinder piston.
Based on the function ode45() of MATLAB [16], the program is written to conduct numerical simulation analysis for Eq. (34), in order to know the law of parameters affecting the tubing string lifting velocity. The function ode45() is based on the Runge–Kutta methods and uses adaptive variable step sizes in the numerical integration. Take the design of 3000 m drilling rig whose maximum drill stem weight is 900 kN as an example to conduct analysis. The
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L. Zhang / Energy Conversion and Management 52 (2011) 359–365
known data are i = 24, Jm = 2 kg m2, r = 0.35 m, Wt = 80 kN, ma = 882 kg, Aa = 0.75m2, gm = 0.95, gV = 0.95, A = 0.0051m2, n = 16, q = 880 kg/m3, p0 = 18 MPa, V1 = 7.423m3, DV = 1.529m3, g1 = 0.92, g2 = 0.85, s = 28 m. Substituting these data into Eq. (34) and conducting numerical integration with Matlab, the simulation results for lowering the drill stem whose stand length is 28 m can be obtained. When lowering the drill stem of different weights W under their respective maximum displacements Vmax, the curves of the drill stem lowering velocity v and lowering displacement x with time t are shown in Figs. 3 and 4, respectively. As shown in Figs. 3 and 4, when lowering the drill stem for a stand length, the heavier the drill stem, the higher the lowering velocity is, and the shorter the lowering time is. The curves of the drill stem lowering velocity v and lowering displacement x with time t under different displacement V of the variable pump-motor are shown in Figs. 5 and 6, respectively. As shown in Figs. 5 and 6, when lowering the drill stem for a stand length, the smaller the displacement V of the variable pump-motor, the higher the lowering velocity is, and the shorter the lowering time is. Based on this characteristic, the energy-saving oil drilling
Fig. 3. Curve of the drill stem lowering velocity
v with time t.
Fig. 5. Curve of the drill stem lowering velocity
v with time t.
Fig. 6. Curve of the drill stem lowering displacement x with time t.
rig can change speed by changing the displacement of the variable pump-motor when lowering the drill stem. 6.2. Comparison of the simulation results with the actual measure results Unfortunately, the actual curves of the drill stem lowering velocity and displacement cannot be tested owing to the lack of necessary apparatus. A digital electrical stop watch was used to measure the actual lowering time of the drill stem. The simulation results and the actual measure results are shown in Table 1. As shown in Table 1, the actual measure value and the simulation value of the drill stem lowering time are basically the same,
Table 1 Drill stem lowering time of W = 600 kN.
Fig. 4. Curve of the drill stem lowering displacement x with time t.
Variable pump-motor displacement V/mL/r Actual measure value t/s Simulation value t/s
229
214
198
183
167
142
35.9 35.2
27.3 26.9
22.1 22.4
19.3 19.8
17.2 17.8
14.9 15.6
L. Zhang / Energy Conversion and Management 52 (2011) 359–365 Table 2 Results of field test. Number
1 2
Lifting
71 stands 93 stands
Lowering
71 stands 93 stands
Electricity consumption Energy-saving oil drilling rig
Conventional drilling rig
359 kW h
452 kW h
590 kW h
714 kW h
which proves the dynamic model and simulation results are basically right. 7. Field tests The contrast experiments between the energy-saving oil drilling rig and the conventional drilling rig were conducted twice. The field test results are shown in Table 2. As shown in Table 2, the electricity consumption of the energysaving oil drilling rig is less than that of the conventional drilling rig when lifting and lowering stands of same amount. These results show the efficiency and the energy-saving effect of the energy-saving oil drilling rig. 8. Conclusions The energy-saving oil drilling rig is an energy-saving machine. The accumulator energy-storing technology is adopted to store the energy of the motor at idle during lifting the drill stem and the potential energy released by the drill stem when lowered. The equipped power of this rig is decreased remarkably compared with the conventional drilling rig, and this rig can also recover and reuse the potential energy of the drill stem. Therefore, this rig owns remarkable energy-saving effect compared with the conventional drilling rig, and the energy-saving effect of the energy-saving oil drilling rig is
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also verified by the field tests. The mathematical model of the new rig lowering the drill stem was derived and simulation analysis was conducted. Through simulation the laws of the drill stem weight and displacement of the variable pump-motor affecting the lowering velocity and lowering time of the drill stem were obtained. References [1] Cohen JH, Maurer WC, Westcott PA. High-power TSP bits. J Energy Res Technol 1994;116(3):33–7. [2] Zhou S, Hua J. Introduction to petroleum machinery. Beijing, China: Petroleum Industry Press; 2002. [3] Moak R. New hydraulic lift rig for drilling and workover. World Oil 1996;217(7):41–2. [4] Yang H, Sun W, Xu B. New investigation in energy regeneration of hydraulic elevators. IEEE/ASME Trans Mechatron 2007;12(5):519–26. [5] Lin X, Guan C, Pei L, Pan S. Research on the system of arm potential energy recovery in hybrid hydraulic excavators. Trans Chin Soc Agric Mach 2009;40(4):96–101. [6] Jefferson CM, Ackerman M. A flywheel variator energy storage system. Energy Convers Manage 1996;37(10):1481–91. [7] Uzunoglu M. Alam MS.Dynamic modeling, design and simulation of a PEM fuel cell/ultra-capacitor hybrid system for vehicular applications. Energy Convers Manage 2007;48(5):1544–53. [8] Suda Y, Shiiba T. New hybrid suspension system with active control and energy regeneration. Veh Syst Dynam 1996;25(Suppl.):641–54. [9] Beers D, Biswas WK. A regional synergy approach to energy recovery: The case of the Kwinana industrial area, Western Australia. Energy Convers Manage 2008;49(11):3051–62. [10] Mordas JB. Accumulators-The neglected components. Hydraul Pneumat 1994;47(7):41–3. [11] Boresi AP, Schmidt RJ. Engineering mechanics. Chongqing, China: Chongqing University Press; 2005. [12] Deng X. Mechanical and electrical transmission control. Wuhan, China: Huazhong University of Science and Technology Press; 2002. [13] Norton RL. Design of machinery: an introduction to the synthesis and analysis of mechanisms and machines. New York (US): McGraw-Hill; 2001. [14] Jin Z. Hydraulic hydromechanics. Beijing, China: National Defence Industry Press; 1994. [15] Jiang J, Song J, Gao C. Hydraulic and pneumatic transmission. Beijing, China: Higher Education Press; 2002. [16] Xu D, Chen Y. Simulating technology based on Matalab/Simulink. Beijing, China: Tsinghua University Press; 2002.