There is a growing interest in the deployment of off-grid renewable energy, especially for remote oil and gas facilities. This work is a novel attempt to optimally size a renewable energy system to power artificial lift for an oil well. It proposes a low-cost alternative to abandonment and decommissioning of old wells. Sucker-rod pump artificial lift simulators (QRodTM and PROSPERTM) are deployed to estimate the energy requirement of a well, with both intermittent and continuous pumping considerations. Simulation and optimization are performed using HOMER optimizerTM, which produces different system configurations and presents the possible configurations in order of increasing system costs. Based on economic and technical merits, continuous pumping using a hybrid renewable energy system consisting of a solar, wind and battery storage is chosen as the most feasible solution with 0 kWh/yr of unmet load, a capacity storage of 0.56 kWh/yr, net present cost of 145,150.50,levelizedcostofenergyof 0.51/kWh and an operating cost of $3,056.04/yr. The optimal configuration is finally examined to determine its sensitivity to variation in daily solar radiation and average wind speed. It is demonstrated to be the most preferred system design, even at the least daily average solar radiation.
Citation: Charles Aimiuwu Osaretin, Tariq Iqbal, Stephen Butt. Optimal sizing and techno-economic analysis of a renewable power system for a remote oil well[J]. AIMS Electronics and Electrical Engineering, 2020, 4(2): 132-153. doi: 10.3934/ElectrEng.2020.2.132
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Abstract
There is a growing interest in the deployment of off-grid renewable energy, especially for remote oil and gas facilities. This work is a novel attempt to optimally size a renewable energy system to power artificial lift for an oil well. It proposes a low-cost alternative to abandonment and decommissioning of old wells. Sucker-rod pump artificial lift simulators (QRodTM and PROSPERTM) are deployed to estimate the energy requirement of a well, with both intermittent and continuous pumping considerations. Simulation and optimization are performed using HOMER optimizerTM, which produces different system configurations and presents the possible configurations in order of increasing system costs. Based on economic and technical merits, continuous pumping using a hybrid renewable energy system consisting of a solar, wind and battery storage is chosen as the most feasible solution with 0 kWh/yr of unmet load, a capacity storage of 0.56 kWh/yr, net present cost of 145,150.50,levelizedcostofenergyof 0.51/kWh and an operating cost of $3,056.04/yr. The optimal configuration is finally examined to determine its sensitivity to variation in daily solar radiation and average wind speed. It is demonstrated to be the most preferred system design, even at the least daily average solar radiation.
1.
Introduction
During the vehicle movement, the performance of the vehicle is affected by various vehicle structures and functions, such as power steering system, suspension system, braking system, etc. Moreover, in complex and high-speed environment, the vehicle's vertical, roll and pitch displacements contain a strong coupling relationship. Therefore, considering the motion and coupling characteristics of vehicle structures is meaningful to investigate vehicle dynamics. On the basis of geometric structure parameters of vehicle system and the nonlinear characteristics of shock absorber and leaf spring, the authors in [1] establish a nonlinear dynamic model for heavy vehicle. The correctness of the dynamic model is verified by testing the vertical acceleration data of the driver's seat, front wheel, middle wheel and rear wheel. To investigate the longitudinal driving behaviors of vehicle dynamics in the platoons, by taking the acceleration capability of heavy-duty vehicle into account, numerous heavy-duty vehicle platoon models are proposed [2,3,4,5,6,7,8,9,10]. Furthermore, by considering the lateral and longitudinal displacement characteristics of the vehicle, [11] represents a 2 DOF model of the vehicle and two diver cab models with time delays. In order to further describe the vehicle dynamics characteristics, in accordance with the two driver cab models in [11]. [15] and [16] further investigate the nonlinear lateral dynamics of a 2 DOF vehicle model. Based on longitudinal vehicle dynamics and by analyzing the dynamic of engine, torque converter, tire and capacitor pack, the authors of [17] present a dynamic model for a heavy-duty vehicle.
On the other side of research, the above mentioned vehicle models are mostly used to evaluate vehicle lateral and longitudinal dynamics characteristics, the influence of vehicle lateral and yaw dynamics characteristics are not considered enough. In practice, the tires not only provide horizontal and vertical forces to the vehicle, but also give vertical forces to the suspension system, especially in complex driving situations such as lane changes, cornering, or obstacle avoidance. In these cases, the vehicle's vertical, roll, and pitch dynamics are clearly coupled with lateral and yaw motion. Due to large inertia, high center of gravity and high roll center, heavy vehicles have poor stability when entering a turn or lane change, and the three-way coupling effect is large. Therefore, it is necessary to establish a three dimensional coupled vehicle model and study the influence of steering process on vehicle dynamics. More recently, more and more works focus on the coupling property of the vehicle. To reflect the steering influence on the overall response of the vehicle, [18] designs a novel 4 DOF hydraulic power steering (HPS) system. Simultaneously, [18] develops a 24 DOF model by taking the HPS system, the steering hand wheel angle, rack displacement, and hand wheel angles into account. According to the nonlinear characteristics of suspension damping and tire stiffness, [19] establishes a nonlinear three-way coupled lumped parameter model, and an improved nonlinear delay preview driver model was proposed based on [11], which was connected with the TCLP model to form a driver-vehicle closed-loop system. [20] establishes a complete vehicle model of a heavy truck, which not only investigates the nonlinear characteristics of suspension damping and tire stiffness, but also contains a modified preview driver model with nonlinear time delays to calculate the right front wheel steering angle for driving the vehicle along the desired route. In this paper, the kinematics and dynamics equations of cab and body are established by analyzing the three-way coupling effect of cab and body, as well as the dynamic characteristics of tire and suspension. Firstly, the dynamic relation of the tyre with deflection angle is introduced. Secondly, the coupling dynamics equation of cab was established by analyzing the three-way coupling effect of cab. Then, considering the dynamic characteristics of the vehicle suspension, the three-way coupling dynamic equation of the vehicle body is established. Finally, the kinematic and dynamic equations of cab and body are established based on the dynamic characteristics of tire and suspension and the Euler rotation theorem.
2.
Nomenclature
Table 1.
The symbols of the heavy-duty vehicle.
Definition
Symbol
forward traction (lateral traction) of the i−th tire
Fxi(i=1,⋯,6)(Fyi)
steering angle of the i−th wheel
δi
steering angular speed of the front axle tires
ωt
transverse (longitudinal) component of i−th tire along the coordinate system {B}
FXi(FYi)
suspension force, damping coefficient and spring constant of the j−th spring between cab and body
Fcj,Hcj and Kcj(j=1,2,3,4)
vertical displacement of the cab (body)
zc(zb)
pitching angle of the cab (body)
φc(φb)
roll displacements of the cab (body)
ϕc(ϕb)
longitudinal distance between origin of coordinates {C} and cab rear (front) spring
l5(l6)
the distance between the origin of coordinates {C} and {B}
l4
the angle between the origin of coordinate {B} and the sprung mass bar center of suspension
φ0
transverse distance betweencab front spring and rear spring
bc
resultant force of the cab inthe direction of axes XC, YC and ZC
Fxc,Fyc and Fzc
resultant moment of the cab in the direction of axes XC, YC and ZC
Nxc,Nyc and Nzc
total mass of the vehicle, cab and body
ms,mt and mb
velocity vectors of the cab in the coordinate system {C} and {B}
uc,vc and wc, ub,vb and wb
roll angle rate, pitch angle rate and yaw angle rate of the coordinate system {C} and {B}
pc,qc and rc, pb,qb and rb
vertical and transverse distance from the origin of {C} and {B} to the center of gravity of cab
hos and eos, hob and eob
moment of inertia of a vehicle about axle XC,YC,ZC,XB,YB and ZB
Ixxc,Iyyc and Izzc,Ixxb,Iyyb and Izzb
moment of inertia of the cab about the axis XC and YC (XB and YB)
Ixxsc and Iyysc(Ixxsb and Iyysb)
integral of the product of the XC and YC(XB and YB) deviation of an area element in a vehicle
Ixzc(Ixzb)
compression displacement of the j−th spring between cab and body
xcj
cab center of gravity (body center of gravity) to cab front and rear spring transverse distance
l7 and l8(l15 and l16)
transverse (longitudinal) distance of cab center of gravity to set 1, set 2 and set 3 tires
l9,l10 and l11(l12,l13 and l14)
distance between the front axle and the rear axle in a suspension system
l3
resultant force of the cab in the direction of axes XB,YB and ZB
Fxb,Fyb and Fzb
suspension force, damping coefficient and springconstant of the j−th spring between the front axle or rear axle and the body of the suspension system
Fsj,Hsj and Ksj
longitudinal transverse distance from the center of gravity of suspension system to the front axis of the suspension system
l1
pitching angle of the left and right balance bars of the suspension system
φp1 and φp2
vertical displacement of the j−th axle
zuj
angle of inclination of the j−th wheel shaft
ϕuj
lateral distance between the left and right springs of the suspension system
bs1,bs2 and bs3
damping forces of front suspension left and right springs
Fd1 and Fd2
resultant moment of the cab in the direction of axes XB,YB and ZB
Nxb,Nyb and Nzb
transverse (longitudinal) distance of cab center of gravity to set 1, set 2 and set 3 bearing spring
l17,l18 and l19(l22,l23 and l24)
transverse (longitudinal) distance of body center of gravity to set 1, set 2 and set 3 tires
l25,l26 and l27(l28,l29 and l30)
transverse distance (longitudinal distance) between the body center of gravity and the cab front (rear) spring
l20(l21)
longitudinal distance from the center of gravity of the suspension system to the center of gravity of the rear axle of the suspension
In this paper, the kinematic characteristics of a heavy-duty vehicle are considered to construct a 26 DOF vehicle body and a cab model. As shown in Figs. 1-4, the considered heavy vehicle has one front axle and two rear axles, which is called a three-axial vehicle. The degrees of freedom are vertical, roll and pitch displacements of the diver cab, vehicle body, the vertical and roll motion of three wheel axles, the pitch angles of the left and right balancing pole on rear suspension, and roll angle the of each tire. To further study the coupling property with each part, the vertical, roll and pitch motion of cab and body is modeled independently. Before introducing the related coordinate systems, the Euler's laws of motion is firstly given.
Lemma 3.1.Observed from an inertial reference frame, the force applied to a rigid body is equal to the product of the mass of the rigid body and the acceleration of the center of mass, i.e.
Fe=mac
where Fe is the resultant external force of the rigid body, m is the rigid body mass, and ac is the acceleration of center of mass.
Lemma 3.2.. The fixed point O (for example, the origin) of an inertial reference frame is set as the reference point. The net external moment applied to the rigid body is equal to the time rate of change of the angular momentum, i.e.
MO=dLOdt
where MO is the is the external torque at point O, LOis the angular momentum at point O.
3.1. Establishing the related coordinate systems
To analyze the motion of heavy-duty vehicle, the corresponding coordinate frames are elaborated to describe the movement of the vehicle and indicated in Fig. 1. The moving coordinate frame {B} is fixed to the vehicle's body and is called the body-fixed reference frame. The second coordinate frame {C} is fixed to the cab and is called the cab-fixed reference frame. The third coordinate frame {E} is fixed to the earth and is called the earth-fixed reference frame. The last coordinate frame {Ti} is fixed to the i−th, (i=1,2,3,4,5,6) tire and is called the tire-fixed reference frame. In this paper, we assume that the body axes XB,YB,ZB, the tire axes XTi,YTi, and the cab axes XC,YC,ZC, of heavy vehicle coincide with the principal axes of inertia, which are usually defined as:
∙XB/XTi/XC -longitudinal axis (directed from aft of the body/tire/cab to front).
∙YB/YTi/YC -transverse axis (directed to right side of body/tire/cab).
∙ZB/ZC -normal axis (directed from top to bottom).
3.2. Analysis of tire motion characteristics
To extract the kinetic model for the considered three-axial heavy-duty vehicle, the coordinate frame Ti is designed for each tire, the corresponding schematic diagram is shown in Fig. 2. By taking the yaw angle into account, the forces produced by the engine are transformed into the forward traction and longitudinal traction on the suspension of heavy-duty vehicle. Based on the coordinate frame and Fig. 2, the forward and lateral traction of each tire can be expressed as
In this subsection, the vertical, roll and pitch motion of the cab are considered to further accurately reflect the performance of spring suspension force between the cab and the body in the actual scenario. In accordance with the coordinate frame {C} and Figs. 3-4, the spring force between the cab and body can be given as
When the vehicle is moving, the spring will produce spring force whether it is in a state of compression or tension. However, the direction of the force is opposite, so this paper considers the sign function and the direction of the spring displacement to determine the direction of the spring force. In order to obtain the dynamic force equation of the vehicle cab and body, we assume that the cab and body mass are evenly distributed, that is, the transverse distance between the cab and body center of gravity from the left and right tires is the same. By considering the definition of resultant force and resultant moment, the kinetic formula of longitudinal, transverse and vertical forces acting on the cab, as well as the yaw, pitch and roll moments is described as
where sign(⋅) denotes the symbolic function, c(⋅)=cos(⋅) and s(⋅)=sin(⋅).
3.4. Analysis of suspension
For the considered heavy duty vehicle, two hydraulic dampers are fixed to the left and right front suspensions, and the balanced suspension does not have any shock absorbers. Thus, to represent the force situation of leaf spring in suspension system, the damping force of the two hydraulic dampers is considered for the front axle. The kinetic equation is given by
This is analogous to the diver cab part, taking the body as a rigid body and according to the Lemmas 3.1 and 3.2, the force equation of body model can be expressed as
Recalling the problem of spring force direction and the assumption of uniform distribution of body mass, the longitudinal, transverse and vertical forces acting on the body are:
uc=[05×1((FX2−FX1)l9+(FX4−FX3)l10+(FX5−FX6)l11Izzc+(FY1+FY2)l12−(FY3+FY4)l13−(FY5+FY6)l14))],t(⋅) represents the tangent function. The expansion equation of the matrix Fc(υc) is
According to kinetic equations (18)-(42) and employing the Euler rotation theorem, the dynamic and kinetic equation of body are designed as
˙ηb=Jb(ηb)υb,˙υb=Gb(ηb,υb)[F∗Xi,F∗Yi]T+Fb(υ)+ub,
(3.43)
where ηb=[xb,yb,z,bϕb,φb,δ1]T,Jb(ηb)=[J1(ηb)03×303×3J2(ηb)],Gb(ηb,υb)=[J3(ηb)03×2],υb=[ub,vb,wb,pb,qb,rb]T, F∗Yi=∑6i=1FXi, Fb(υb)=[Fb1(υb),Fb2(υb),Fb3(υb),Fb4(υb),Fb5(υb),Fb6(υb)]T,J2(ηb)=[1s(ϕb)t(φb)c(ϕb)t(φb)0s(ϕb)−s(ϕb)0s(ϕb)/c(φb)c(ϕb)/c(φb)],F∗Xi=∑6i=1FXi, J3(ηb)=[c(δ1)c(φb)mt−s(δ1)c(ϕb)+s(ϕb)s(φb)c(δ1)mts(δ1)c(φb)mt+c(δ1)c(ϕb)+s(ϕb)s(φb)s(δ1)mt−s(φb)mbs(ϕb)c(φb)mb],ub=[05×1((FX2−FX1)l25+(FX4−FX3)l26+(FX5−FX6)l27Izzb+(FY1+FY2)l28−(FY3+FY4)l29−(FY5+FY6)l30)],J1(ηb)=[c(δ1)c(φb)−s(δ1)c(ϕcb)+s(ϕb)s(φb)c(δ1)s(δ1)c(φb)c(δ1)c(ϕb)+s(ϕb)s(φb)s(δ1)−s(φb)s(ϕb)c(φb)
In complex working conditions, there is a coupling relationship of the vertical, lateral and longitudinal dynamics of vehicles. By considering the kinetic character of the vertical, roll and pitch motion of the diver cab, vehicle body, the vertical and roll behavior of three wheel axles, the pitch angles of the left and right balancing pole on rear suspension, and roll angle the of each tire. In this paper, a common model of three-axles heavy-duty vehicle with 26 DOF have been proposed to extrude the kinetic characterization diver cab and vehicle body.
Acknowledgment
This work was supported by the National Natural Science Foundation of China under Grants U22A2043 and 62173172.
Conflict of interest
The author declares that there is no conflicts of interest in this paper.
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Charles Aimiuwu Osaretin, Tariq Iqbal, Stephen Butt. Optimal sizing and techno-economic analysis of a renewable power system for a remote oil well[J]. AIMS Electronics and Electrical Engineering, 2020, 4(2): 132-153. doi: 10.3934/ElectrEng.2020.2.132
Charles Aimiuwu Osaretin, Tariq Iqbal, Stephen Butt. Optimal sizing and techno-economic analysis of a renewable power system for a remote oil well[J]. AIMS Electronics and Electrical Engineering, 2020, 4(2): 132-153. doi: 10.3934/ElectrEng.2020.2.132
Figure 2. Hybrid renewable microgrid system with integrated components
Figure 3. Monthly average solar radiation (global horizontal Irradiance GHI) data in HOMER
Figure 4. Monthly average wind speed plot for Medicine Hat
Figure 5. Daily load profile for scenario A: Intermittent production (diurnal, during the day)
Figure 6. Monthly (seasonal) load profile for scenario A: (diurnal, during the day)
Figure 7. Daily load profile for scenario B: continuous pumping
Figure 8. Monthly load profile for scenario B: continuous pumping
Figure 9. (a) Design inputs for beam pumped well in Qrod, (b) Design inputs for beam pumped well in PROSPER, (c) Design results showing size and power rating of pump required
Figure 10. System structure optimized in HOMER with components integrated (for intermittent pumping)
Figure 11. Monthly electricity production for system type 1A
Figure 12. (a) Monthly electricity production for system type 2A, (b) Cost summary for system type 2A showing cost contribution of system components
Figure 13. Monthly electricity production for system type 3A
Figure 14. System structure showing integrated components in HOMER (for continuous pumping)
Figure 15. Monthly electricity production for system type 1B
Figure 16. Monthly electricity production for system type 2B
Figure 17. Monthly electricity production for system type 3B
Figure 18. (a) to (e) Compares key indices for continuous and intermittent pumping for the six (6) 100% renewable architectures
Figure 19. Optimization system type plot showing type 1 and type 2 architectures for respective average wind speed and daily solar radiation
Figure 20. Surface plot showing the sensitivity of total net present cost to variations in average wind speed and average daily solar radiation
Figure 21. Optimization surface plot showing least cost combinations of solar PV generators (kW) and battery storage (number of strings) for the cheapest/ least cost configuration (type 1A)