- Email: [email protected]
Simulation of single acting natural gas Reciprocating Expansion Engine based on ideal gas model
Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Simulation of single acting natural gas Reciprocating Expansion Engine based on ideal gas model Mahmood Farzaneh Gord, Mohsen Jannatabadi* The Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 April 2014 Received in revised form 20 September 2014 Accepted 22 September 2014 Available online
The potential energy of high pressure gas destroyed in natural gas pressure reduction stations during pressure reduction when it passes through throttling valves. One way to recover this energy is to use a Reciprocating Expansion Engine coupled with a generator. The expansion engine is able to produce electricity as pressure decreases by recovering the potential energy. Although the expansion engine has been utilized in pressure reduction points for some time but it has not been analyzed for performance enhancement yet. In this work an advanced numerical simulation has been presented for the thermodynamic modeling of Natural Gas Single Acting Reciprocating Expansion Engine under various working conditions for high pressure ranges. The simulation has been carried out to understand the effects of various parameters and to improve performance of the engine. A range of geometric parameters such as suction diameter, piston diameter, crank radius, connecting rod length, speed were covered in this research. Because of the physical and numerical difficulties of the problem, the natural gas is assumed as an ideal gas. © 2014 Elsevier B.V. All rights reserved.
Keywords: Electricity Natural gas expansion engine Thermodynamic Numerical simulation
1. Introduction Natural gas is produced at high pressure about 50e70 bar and transported through pipelines from refinery to natural gas pressure drop stations usually called City Gate Stations (CGS). For consuming this gas, it is evident that the pressure of the gas must be reduced. In CGSs the pressure of the gas must be reduced to 15e20 bars (Po zivil). Reduction of high pressured gas can be achieved by gas expansion. For this purpose, usually the throttle valves are used which lost the potential energy of high pressure gas, while this potential energy could be used to produce electrical energy. If a Turbo-Expanders or an Expansion Engine coupled with a generator is used instead of throttle valves, the wasted potential energy of the gas could be recovered, (Rahman, 2010) and (Dehli, 1997). Reciprocating Expansion Engine is used to convert pressure into a rotating motion via a connecting rod and a crankshaft. In these engines unlike the usual engines there is no combustion and spark; the pressurized gases expand and pushes the piston to the bottom of the cylinder (BDC) and is returned to the cylinder top (TDC) with a flywheel. A gas with a high pressure enters the cylinder and exits without any consumption at lower pressure. Reciprocating * Corresponding author. E-mail addresses: [email protected] (M. Farzaneh Gord), m.jannatabadi@ minoodashtau.ac.ir, [email protected] (M. Jannatabadi). http://dx.doi.org/10.1016/j.jngse.2014.09.031 1875-5100/© 2014 Elsevier B.V. All rights reserved.
Expansion Engines can convert the pressure energy of a gas into mechanical work as the gas expands through it. They used for two purposes: cooling or producing power. If cooling a gas is the main goal, then the mechanical work is assumed as a byproduct; however, if producing power in pressure reduction process is the main objective, the cooling capacity will be a beneficial byproduct (Bloch and Soares, 2001). Fig. 1 shows the schematic of installing the expansion engine in city gate stations parallel to throttling valve. Unfortunately there is no report or paper about these systems and it can be said that this paper is the first manuscript that simulates the natural gas expansion engines. But since that physically it acts exactly reverse to reciprocating compressors and turbo expander from a thermodynamic point of view, combination of researches of these systems can be used for modeling the natural gas expansion engine. According to JouleeThompson effect (Rheuban, 2009), most gases will be cooled during the expansion process, therefore preheating the gas before entering the Expansion Engine is very important. Expansion Engines are relatively small and compact. It can be said that this is an Isentropic Process. Expansion Engine doesn't have any pollution since it produces the electricity without consumption any fuel; it can produce considerable chilling which can be used for air conditioning systems (Watson and Sorge, 2007). The produced electricity can be used for preheating the gas before
670
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Nomenclature A Cp D De d E f h K L Lr m P Q R Rj T u U V W Gr Nu
Area (m2) Specific heat at constant pressure (j/kg K) Diameter (m) Effective diameter (m) Port diameter (m) Energy of system (j) Friction factor Enthalpy (j/kg) Conduction heat transfer coefficient Connecting rod length (m) Ring width (m) Mass of gas (kg) Pressure (Pa) Heat transfer (kw) Crank radius (m) Thermal resistance Temperature (K) Internal energy (j/kg) Overall heat capacity (j/m2K) Volume (m3) Power (kw) Grashof number Nusselt number
entering the Expansion Engine and also for lightening environments of the gas stations. These engines are usually coupled with a generator in one power pack. Control slide valve is used to control the flow-rate of the gas. The power output from the Expansion Engine mainly depends on the pressure ratio, inlet temperature, and the flow rate (Rahman, 2010). Po zivil (Po zivil) showed that temperature drop in the throttle valve system can be about 0.45e0.6 C per bar of pressure drop, whereas in turbo-expanders it can be much higher, around 1.5e2 C per bar, depending on the gas composition. Mohammed (Rahman, 2010) with analyzing a number of producing wells and pressure reduction stations found that preheating the pressured gas before entering the turbo expander and before expansion is almost always necessary to avoid hydrate formation. Dehli (Dehli, 1997), (Dehli, 1994) and (Dehli, 1996) showed that if the temperature of the gas increases at the engine inlet, then a higher electrical energy will be produced. He proved that in a two
Fig. 1. Schematic of city gas station.
Pr Re x
q q0 qi qe hmech
Prandtl number Reynolds number Piston displacement (m) Circular velocity (rad/s) Angular velocity (rad/s) Kinematic viscosity (m2/s) Instant angle of connecting rod Initial guess for inlet port Time of opening of exit port Time of closing of exit port Mechanical efficiency
Subscript a b c cl d s o i ind f w fr
ambient brake cylinder Clearance volume discharge suction outer inner indicator Film wall friction
u ug w
or more gas expansion system with additional counter flow heat exchanger after engine, the efficiency of system will be improve too. Mirandola and Minca (Mirandola et al., 1986) analyzed the power generation from high pressure natural gas with several expansion stages, gas flow rates and pre-heating. In another paper, Mirandola and Macor (Mirandola et al., 1988) have presented experimental results with the effect of heat input for pre-heating the gas. They showed that the most of the pre-heating is recovered as electricity. Ardali and Heybatian (Ardali and Heybatian, 2009) compared using of throttle valve and Turbo expanders in CGS and showed that using Turbo expanders is more beneficiary than the throttle valve. They simulated their project with several gas flow rates and inlet pressures. They also showed that application of turbo expander in conjunction with the thermal power plants would be more beneficiary because the exhaust gas has very high temperature which can be used for pre-heating the gas. Farzaneh (Farzaneh Gord et al., 2007a) showed that pre-heating the inlet gas and increasing the inlet pressure in turbo expander will increase the exergy of system and the power output as well. Farzaneh-Gord and Magrebi (Farzaneh-Gord and Magrebi, 2009) studied exergy destruction due to reducing pressure of natural gas and showed that a pattern of natural gas field could produce 4200 MW of electricity using this pressure exergy. He (Farzaneh-Gord et al., 2007b) studied the effect of gas pre-heating and using the pressure exergy of natural gas in pressure reduction station on the amount of electricity generation. With measuring the amount of energy lost in natural gas pipeline distribution Farzaneh (Farzaneh-Gord et al., 2007c) showed that the huge amount of electricity will be generated from reduction of natural gas. He (Farzaneh-Gord and Deymi Dashtbayaz, 2008) has suggested preheat and using a turbo expander to catch this energy. Because of simple to operation, high availability and highly efficient electricity generation ([Online]), using of natural gas expansion engine is more preferable to reduce the high pressure
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
671
gas. It can be used as double acting, single or more stages, one to six cylinders in CGS. Because it acts reverse to compressor, for simulating and modeling this system, assumptions and equations of reciprocating compressors can be used. In this study, a comprehensive numerical program is used for simulate the single acting, one-stages, one cylinder natural gas expansion engine to measure the output power, heat transfer, minimum temperature drop and predict the gas temperature and pressure. The significant parameters of the expansion engine such as ports and piston diameter, engine speed, crank radius and connecting rod length are then identified. Thereafter, the effects of these parameters on mechanical efficiency are investigated too. 2. The thermodynamic modeling For modeling the operation of one cylinder single-stage singleacting Reciprocating Expansion Engine with a slider crank mechanism, Fig. 2, the computer programming with MATLAB code is used for control volume which is shown in Fig. 3. The model is based on the integration of the transient fluid conservation equations (continuity and energy) inside the expansion engine domain. In thermodynamic assumptions the behavior of the gas assumed as an Ideal gas, the process in inlet and outlet ports is an isentropic, no leakage through the piston rings is assumed and changes in kinetic and potential energy is ignored and circular velocity is assumed constant. The high pressure gas acts upon the piston and makes it to move along the cylinder axis and the potential energy which is stored in flywheel pull the piston to move back to top dead center. To convert the linear movement of the piston into the rotational movement, a crankshaft mechanism is used and with connecting this crankshaft to generator, electricity will be produced. To control the inlet and outlet mass, a sample slide valve is used. This valve opens and closes automatically, due to the pressure difference between the suction/discharge chamber and the cylinder. Pressure, temperature and density of fluid flow were calculated from continuity equation, energy equation and ideal gas equation of state respectively (Fig. 4).
Fig. 3. Schematic of control volume (Lee, 1983).
clearance volume of 10%, expansion engine has the best performance. The volume of gas inside the cylinder will compute as:
VðqÞ ¼ xðqÞp
D2i 4
(2)
2.1. Geometrical modeling The instantaneous position of the piston displacement according to Top Dead Center is given by (Mabie and Reinholtz, 1987):
8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 2 < = R xðqÞ ¼ x0 þ Rð1 cos qÞ þ L 1 1 sin2 q : ; L
(1)
Where q ¼ ut and u is the angular velocity of crank and x0 is the length of the clearance volume. Results which achieved with selected geometrical parameters such as port and piston diameter, connecting rod, crank radius and so on showed that with a
Fig. 2. Slider crank mechanism.
Fig. 4. Single acting expansion engine.
672
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
dTc 1 dQ dVc dms dmd Pc ¼ þ CPs Ts CPd Td mc ðCP RÞ dq dq dq dq dq dms dmd ðCP RÞTc dq dq
2.2. First law of thermodynamic The first law of thermodynamic for the inside gas of the cylinder as a control volume on a time rate is (Moran et al., 2007):
X X dECV _ þ _ in _ out ¼ Q_ W ðmhÞ ðmhÞ dt
To calculate instantaneous value of temperature in next step based on the value of temperature and changes of it in previous step, the following equation can derived and from an ideal gas equation of state the pressure of each step can be achieved (Farzaneh-Gord and Deymi Dasht-bayaz, 2008):
(3)
In this equation the work term can be written as Pc(dVc/dq) (Moran et al., 2007). For simplicity it was assumed that the changes of internal energy of the control volume considered as a change of energy (Lee, 1983), it means dEcv/dt ¼ d(mcuc)/dt. The mass conservation law is:
Tc
dmc dms dmd ¼ dq dq dq
Pcjþ1 ¼
jþ1
(4)
j
j
¼ Tc þ dTc jþ1
Instantaneous inlet and outlet mass flow rates through suction and discharge ports which are assumed as an orifice are as follows (Oosthuizen and Carscallen, 1997):
if
if
g g1 Pc 2 > gþ1 Ps Pc Ps
(6)
With substituting these equations in Equation (5), following formula can be achieved (Lee, 1983):
duc 1 ¼ mc dq
dQ dVc dms dmd dms dmd Pc þ hs hd uc dq dq dq dq dq dq (7)
This equation can be used for both ideal and perfect gas. For ideal gas we have (Moran et al., 2007):
u ¼ CV T; h ¼ CP T; R ¼ CP CV ; PV ¼ mRT
(11)
2.3. Calculating mass flow rate
8 > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 gþ1 > > 1 q q 2g Pd g Pd g > i > > Ad Pc sin p > < u ðg 1ÞRT q q P Pc e c c i dmd ¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > dq gþ1 > > g1 > 1 q qi g 2 > > A P sin p > c d > > u RT g þ 1 q q e c i :
dðmc uc Þ duc dmc ¼ mc þ uc dq dq dq
jþ1
Vcjþ1
(5)
In this equation (Lee, 1983):
8 > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 gþ1 > > 1 q 2g Pc g Pc g > > > As Ps sin p > < u q ðg 1ÞRT P Ps s s 0 dms ¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > dq gþ1 > > g1 > 1 q g 2 > > A P sin p > s s > > u q0 RTs g þ 1 :
(10)
mc RTc
The simplified form of Equation (3) based on variation of crank angle is as follow (Lee, 1983):
dðmc uc Þ dQ dW dms dmd ¼ þ hs h dq dq dq dq dq d
(9)
(8)
Then for an Ideal gas, based on the energy conservation we have (Lee, 1983):
if
if
2 gþ1
g g1
9 > > > > > > > > > =
Pd 2 > gþ1 Pc Pd Pc
(12)
> > > > > > > > > ;
g g1
2 gþ1
g g1
9 > > > > > > > > > = > > > > > > > > > ;
(13)
Where g is the specific heat ratio which calculated as a function of temperature, R is the gas constant of methane, q0 is a closure angle of inlet port, qi is the opening time of output port and qe is the closing time of output port. These formulas are written based on the flow which passes through orifices (Oosthuizen and Carscallen, 1997). In these equations the chock condition is considered (Lee, 1983). In state of chocked flow, mass flow rate is constant, and then second equation in these formulas determines the constant flow rate based on chocked flow. It was assumed that there isn't happened any backward flow through ports. From Equations (12) and (13) it can be said that opening and closing time of ports are controlled mechanically. Inlet port is opened exactly at top dead center (TDC) and closed at a defined crank angle. In this process high pressure gas enters the cylinder and pushes the piston to move to bottom. From defined crank angle to bottom dead center (BDC) expansion process takes place. Before BDC outlet port is opened and closed at a defined angle.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
study the only useful correlation for reciprocating cylinder piston, it means Adair' equations are used (Adair et al., 1972).
2.4. Calculating heat capacity of methane In this study specific heat capacity of methane is considered as a function of the gas temperature via the equation (DIPPR@ 801, 2004):
h
A1 þ B1
CPi ðqÞ ¼
C1 =Tc sinhðC1 =Tc Þ
2
þ D1
E1 =TC coshðE1 =TC Þ
2
A1 ¼ 3:3298 104 ; B1 ¼ 7:9933 104 ; C1 ¼ 2:0869 103 ; D1 ¼ 4:1602 10 ; E1 ¼ 9:9196 10
Nui ðqÞ ¼
hi ðqÞDe ðqÞ ¼ 0:053½ReðqÞ0:8 ½PrðqÞ0:6 Ki ðqÞ
2
(14)
ReðqÞ ¼
rc ðqÞD2e ðqÞug ðqÞ 2mðqÞ
Overall correlation for modeling heat transfer is assumed as follows (Ardali and Heybatian, 2009):
AðqÞ ¼
UðqÞ ¼
4
Aw
þ
1 P
4Vcl þ pDxðqÞ D
1 pDi xðqÞhi ðqÞ
(18)
Ro ðqÞ ¼
1 pDo xðqÞho ðqÞ
(19)
Rw ðqÞ ¼
ln ðDo =Di Þ 2pKw xðqÞ
(20)
Natural convection is occurred if the Expansion Engine is considered as a horizontal cylinder. In this case the air heat transfer coefficient outside the cylinder is as follow (Annand, 1963):
" #0:25 Grair Pr2air ho Do pffiffiffiffiffiffiffiffiffiffi ¼ Kair 2:435 þ 4:884 Prair þ 4:953Prair
The heat transfer coefficients in the expansion engine surfaces has been considered constant but heat transfer coefficients of the gas has been considered variant. In this equation Grashof Number is (Lee, 1983):
Grair ¼
(25)
ug is annular velocity and De is effective diameter (Lee, 1983): ug ðqÞ ¼
pDo 2
g Tf
m2air
8 < 2uð1:04 þ cos cosð2qÞÞ :
uð1:04 þ cos cosð2qÞÞ
9 3p p
6 pD 6VðqÞ 4 xðqÞ ¼ 2 AðqÞ pDxðqÞ þ 2p D
(26)
(27)
4
u is the circular velocity. Inside thermal conductivity of methane assumed as (DIPPR@ 801, 2004):
ki ðqÞ ¼
A3 TcB3 1 þ CT3c þ DT 23
; A3 ¼ 8:3983 106 ; B3 ¼ 1:4268;
c
(28)
C3 ¼ 4:9654 10; D3 ¼ 1:9
2.6. Calculating indicated, friction and brake power To calculate the indicated work which means the work done on the gas by the piston in one cycle we have (Moran et al., 2007): q¼360 Z
Wind ¼
P dV
(29)
q¼0
And the brake or output work can be calculated from (Ueno et al., 2003):
(21)
r2air
c
(17)
3
; A2 ¼ 5:2546 107 ; B2 ¼ 5:9 101 ;
2
Ri ðqÞ ¼
2 1 þ CT2c þ D T2
C2 ¼ 1:056 102 ; D2 ¼ 0:18
De ðqÞ ¼ Rj
A2 TcB2
(16)
VCL is the clearence volume, D is the piston diameter and Rj is the summation of inside convection resistance, wall conduction resistance and outside convection resistance as follow (Lee, 1983):
Nuo ðqÞ ¼
mi ðqÞ ¼
(15)
In modeling heat transfer the piston-ring leakage was illuminated. In this relationship A(q) is the total heat transfer area of piston, dead volume and cylinder wall which exposed to heat transfer and U(q) is the overall heat transfer coefficient (Lee, 1983):
pD2
(24)
Cinematic viscosity of methane as an ideal gas is (DIPPR@ 801, 2004):
2.5. Calculating heat transfer
Q_ ¼ UðqÞAðqÞ½Ta Tc ðqÞ
(23)
Where in this formula definition of Reynolds Number is as follow (Lee, 1983):
M 4
673
ðTa Tw Þ (22)
Where properties of air are calculated based on Tf, film temperature, Tf ¼ TwþTa/2. There are a few research about the inside heat transfer coefficient (Annand, 1963), (Eichelberg, 1939), (Hassan, 1971), (Hohenberg, 1979) and (Woschni, 1967), but in present
Wb ¼ Wind Wfr
(30)
Oil free friction work of piston ring can be calculated as follows (Hanlon):
Wf ¼ pf Pav Lr ð1:24Di þ 1Þ
(31)
Where Lr is the ring width, f is the friction coefficient of PTFE, and Pav is the average pressure which can be calculated as follow (Hanlon):
1=g Pav ¼
Pd g
Ps Pd
Ps ð2 gÞ 2ðg 1Þ
(32)
674
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Then we can calculate the mechanical efficiency of engine with (Ueno et al., 2003):
hmech ¼
Wb Wind
(33)
3. Results and discussion Initial conditions of this study are given in Table 1. Suction pressure and temperature is considered as uniform pressure and temperature in the suction line; similarly discharge pressure considered as discharge line. Along the flow direction for the inlet and outlet velocity and outlet temperature the gradient is assumed as zero. Also there isn't any heat transfer during the injection and exhaust phases of the cycle. The whole derived equations describe in the previous section by means of an algorithm is iteratively solved, at each time-step. On each iterate temperature and pressure was calculated from energy equation and equation of state respectively, Equations 9e11. As mentioned before, there are several parameters which affect on reciprocating engines, such as inlet port diameter, crank radius, connecting rod length, circular velocity, suction and discharge pressure and so on. In present study the effects of the ratio of inlet port to piston diameter(ds/Di), the variation of crank radius to connecting rod length (R/L) and the effect of changes of engine speed on performance of expansion engine has been studied. By using this method proposed for expansion engine design, not only the design time will be lessened, but also the performance of expansion engine can be predicted and then the need for experimental research will be reduced. 3.1. Effect of motor speed In this section the effect of variation of motor speed on expansion engine performance is analyzed. Fig. 5, Fig. 6 and Fig. 7 show the engine indicator diagram based on selected port and cylinder geometries, Table 1. It is found that for operation at 2000 rpm the outlet port would close 10 later than operation at 1000 rpm, 335 for the first case and 345 for second. Inlet port is closed at 75 and outlet port is opened at 160 of crank revolution. Fig. 5 shows the indicator diagram for operation at 1000 rpm and Fig. 6 shows this diagram for operation at 2000 rpm with the same inlet conditions of Fig. 5. Fig. 7 shows the effect of expansion engine speed on the indicator work. The closing time of inlet port, opening and closing of outlet port does not change in this graph. It can be found that indicator work of engine is decreased as speed is increased. But indicated power is increased with arising speed because of reduction of the time of cycle. The main cause of this phenomenon is that the inlet and outlet gas flow and therefore the mass of gas inside the cylinder are decreased at higher speed, Fig. 8 and Fig. 9. This occurs from the fact that the total time period of the gas flowing
Fig. 5. Indicator diagram, 1000 rpm.
through the inlet orifice decreases with increase of speed. All indicated power, friction power and brake power are increased with speed increments, but mechanical efficiency of engine reduced with it. As speed is increased, the cylinder pressure drop occurring during the suction process becomes more and then the gas flow per cycle reduces. Fig. 10 shows the effect of pressure drop against crank angle in various speed. Another effect of speed variations on gas pressure is that on higher speeds, in the movement from bottom dead center to top dead center the gas pressure is increased more than lower engine speed. Table 2 compares the power calculations of engine between 1000 and 2000 rpm. Results show that the amounts of heat transfer is very low which the assumption of isentropic process for expansion engine is correct. In Fig. 11 it has been shown that in high motor speed the temperature loss of gas is more than in low speed. Table 1 shows the indicated power, friction power and brake or output power in 1000 and 2000 rpm. It can be seen that although the brake power
Table 1 Initial guess and physical parameters of Expansion Engine. Operating condition
Data
Operating condition
Data
Ps Pd Ts ds dd Vcl f
60 bar 15 bar 285 K 5 cm 5 cm 10% Vd 0.3
Di Do Ta Kw R L Lr
13.7 cm 15 cm 298 K 50 W/m.K 7 cm 20 cm 1.5 mm
Fig. 6. Indicator diagram, 2000 rpm.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
675
Fig. 9. Mass of gas for several speeds.
Fig. 7. Indicator diagram for several speeds.
increased with motor speed, but the mechanical efficiency of expansion engine reduced with it. Since the friction power depends on speed of motor directly, the ratio of increase of indicated power is more than the ratio of increase of brake power. It can be seen that generally the gas temperature and pressure variations are not significantly affected by a variation of engine speed, although the average gas velocity would be higher at raised engine speed. 3.2. Effect of inlet port diameter over constant piston diameter In this section the piston diameter was considered constant provided that the inlet port diameter varies from 3 cm to 5 cm. In Fig. 12 and Fig. 13 it has been given the instantaneous variation of gas temperature and pressure against crank angle, respectively. In this analysis the closing and opening time of inlet and outlet ports are 75 and 160 of crank revolution. It was found that for plotting the rational PeV diagram the outlet port should be closed at least at 338 of crank revolution, because before that time the difference pressure between inside gas in dead volume and suction manifold
Fig. 8. Suction and discharge mass flow rate for several speeds.
did not adequate to flowing the gas into cylinder. In this section the closing time of outlet port was considered 340 , motor speed was 1000 rpm and clearance volume was 5% of swept volume. From these figures it was found that increasing the ratio of inlet port diameter to piston diameter doesn't affect variation of pressure and temperature of gas significantly. From Fig. 12 it was found that in higher inlet diameter to piston diameter ratio, the temperature loss of gas is more than lower value of this ratio and from Fig. 13 it can be seen that the variation of inlet port doesn't affect the gas pressure. There is another point here with increasing the ratio, the value of exit temperature will decrease. In Fig. 14 instantaneous alternation of inside mass has been shown. Evidently at the charging and discharge process the mass flow rate with raising the diameter ratio will be increased. Between 75 to 160 and 340e360 of crank angle it is assumed that both inlet and outlet ports are closed. It means that after 340 the residual mass reaches at its first value and will be constant until the beginning stage of the charging process. This is the mass of clearance volume. Fig. 15 shows that with increasing the diameter ratio it is evident that the amount of mass which enters the cylinder will
Fig. 10. Pressure variations for several speeds.
676
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Table 2 Calculation of power and efficiency. Results
N ¼ 1000 rpm
N ¼ 2000 rpm
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
86.3 4.089 82.21 0.0286 2.51 MPa 84%
141.3 4.088 137.23 0.0245 2.05 MPa 61%
imep hmech
Fig. 13. Pressure variations for several inlet port/piston diameter.
Fig. 11. Temperature variations for several speeds.
be increased too and subsequently the amount of discharge flow rate will raised too. From the indicated diagram of expansion engine based on variation of inlet port to piston diameter ratio as shown in Fig. 16, it can be seen that by increasing this ratio the indicator work will be increased too, and from Table 3 it was concluded that there is a small increase in the mechanical efficiency of expansion engine. This phenomenon can be described in another way. Since that the gas temperature is less than the ambient temperature the Expansion Engine can be used to cooling its surrounding space. Then the total heat transfer in each cycle can be evaluated too. With
Fig. 14. Suction and discharge mass flow rate for several inlet port/piston diameter.
Fig. 12. Suction and discharge mass flow rate for several inlet port/piston diameter.
Fig. 15. Mass of gas for several inlet port/piston diameter.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Fig. 16. Indicator diagram for several inlet port/piston diameter.
Fig. 18. Pressure variations for several crank radius.
Table 3 Work and efficiency results in 1000 rpm. Results
ds/Di ¼ 0.2190
ds/Di ¼ 0.3650
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
68.94 4.09 64.85 0.026 2 MPa 80%
83.79 4.09 79.7 0.026 2.4 MPa 84%
imep hmech
increasing the ratio the heat transfer rate increased very little. It means that irreversibility will decreased and then the power must be increased.
3.3. Effect of crank radius to connecting rod length ratio The variation of crank radius to connecting rod length ratio has been analyzed too, Fig. 17e20. For this main crank radius and connecting rod length were considered 4e7 and 20e24 cm
Fig. 19. Mass of gas for several R/L ratio.
Fig. 17. Temperature variations for several crank radius.
Fig. 20. Suction & discharge mass of gas for several R/L ratio.
677
678
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Fig. 24. Pressure variations for L ¼ 24 cm.
Fig. 21. Indicator diagram for several R/L ratio.
Fig. 22. Indicator diagram for L ¼ 24 cm.
respectively. Results have shown that the variation of connecting rod length doesn't affect the gas properties and in cylinder mass of gas, but the change of crank radius has a direct effect on the properties of the gas inside the cylinder. From Fig. 21 it can be seen that in a sample crank radius, increasing connecting rod length doesn't affect on indicated and subsequently on friction and brake powers, but Fig. 22 shows that if crank radius increased in constant connecting rod length, indicated power will increase sharply. Since the friction power increased significantly, the brake power of expansion engine doesn't rise considerably, and then variation of crank radius in constant connecting rod length can't improve the generation of electricity from using expansion engine in CGS. Fig. 23 and Fig. 24 show that the outlet temperature and pressure in high crank radius is more than in low amount of it and from Figs. 17 and 18 it can be seen that variation of the ratio of these parameters doesn't affect the minimum value of gas pressure and temperature. Results showed that if crank radius is considered constant, with increasing the connecting rod length the amount of indicated, friction and brake powers will decrease inconsiderably. Table 4 Shows values of these power and amount of heat transfer and mechanical efficiency of expansion engine for four cases. It can be seen that mechanical efficiency will decreased significantly if connecting rod length considered constant whereas crank radius increased too. But there is a little variation of heat transfer and mechanical efficiency in this case. 4. Conclusion Directly measured data for the gas inside the expansion engine are not available at the moment. The mathematical model using the Table 4 Calculations for several ratios of R/L.
Fig. 23. Temperature variations for L ¼ 24 cm.
Results
R ¼ 4 cm L ¼ 20 cm
R ¼ 7 cm L ¼ 20 cm
R ¼ 5 cm L ¼ 20 cm
R ¼ 5 cm L ¼ 24 cm
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
48.8 4.09 44.7 0.019 91%
83.8 4.09 79.7 0.026 84%
60.8 4.09 56.7 0.022 88.7%
59.7 4.09 55.6 0.022 88.6%
hmech
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Ideal gas equation provided the simulation of a single-acting reciprocating Gas Expansion Engine system with modeling the heat transfer. This model can be used for the optimum design and predicting of the performance of expansion engine. Over a wide range of parameters which affected this system, the inlet port diameter, connecting rod length, crank radius and engine speed has been studied in present research. Results showed that variation of connecting rod length doesn't affect on the power which be achieved from pressure reduction of gas in Expansion Engine and also doesn't change other parameters of gas such as temperature and pressure. Instead, increasing the crank radius and inlet port diameter bring that system produced more power and increasing the motor speed causes to have higher output power too. References Adair, R.P., Qvale, E.B., Pearson, J.T., 1972. Instantaneous heat transfer to the cylinder wall in reciprocating compressors. In: International Compressor Engineering Conference. Paper 86. Annand, W.J.D., 1963. Heat transfer in the cylinder of reciprocating internal combustion engine. Proc. Instn. Mech. Eng. 177 (36), 973e990. Ardali, E.K., Heybatian, E., 5e9 October 2009. Energy regeneration in natural Gas pressure reduction stations by use of Gas turbo-expander; evaluation of available potential in Iran. In: 24th World Gas Conference, Buenos Aires, Argentina. Bloch, H., Soares, C., 2001. Turbo Expanders & Process Applications. Gulf Professional Publishing. Dehli, M., 1994. Prozesse zur verbesserung der wirksamkeit von Gas-Expansion sanlagen unter thermodynamischen gesichtspunkten. Dehli, M., 1996. energier uckgewinnung mit Gas Expansion sanlagen, pp. 196e206. Dehli, M., 28e30 January 1997. Concepts of Gas Expansion at High Temperature. Netherland. DIPPR@ 801, 2004. Evaluated Standard Thermophysical Property Values. Design Institute for Physical Properties, Sponsored by AIChE. Eichelberg, G., 1939. Some new investigation on old combustion engine problems. Engineering 148, 463e466. Farzaneh-Gord, M., Deymi Dasht-bayaz, M., 2008. Recoverable energy in natural gas pressure drop stations: a case study of the Khangiran gas refinery. Energy Explor. Exploit. 26, 71e82.
679
Farzaneh Gord, M., Eftekhari, H., Tvakkoli, M.M., 12e13 June 2007a. Using of natural Gas pressure reducing station to produce power and Refrigeneration. In: Sixth National Energy. Farzaneh-Gord, M., Magrebi, J., 2009. Exergy of natural gas flow in Iran's natural gas fields. Int. J. Exergy 6, 131e142. Farzaneh-Gord, M., et al., March 24-27, 2007b. Using pressure exergy of natural gas in Bandar-Abbas refinery gas pressure drop station. In: The Second International Conference on Modelling, Simulation, and Applied Optimization, Abu Dhabi. UAE. Farzaneh-Gord, M., Hashemi, S., Sadi, M., 2007c. Energy destruction in Iran's natural gas pipe line network. Energy Explor. Exploit. 25, 1e10. Hanlon, Paul C. Compressor Handbook. McGraw-Hill. Hassan, H., 1971. Unsteady heat transfer in a motored I.C. engine cylinder. Proc. Instn. Mech. Eng. 185, 1139e1147. Hohenberg, G.F., 1979. Advanced Approaches for Heat Transfer Calculations. SAE Pap. No.79825. Lee, S., 1983. First Law Analysis of Unsteady Processes with Application to Charging Process and a Reciprocating Compressor. The Ohio State University. Mabie, H.H., Reinholtz, C.F., 1987. Mechanics and Dynamics of Machinery, fourth ed. John Wiley and Sons, Inc. Mirandola, A., Minca, L., Aug. 25-29, 1986. Energy recovery by expansion of high pressure natural gas. In: Proc. of the 21st Intersociety Energy Conversion Engineering Conference, pp. 16e21. Mirandola, A., Macor, A., July 31-Aug. 5, 1988. Experimental analysis of an energy recovery plant by expansion of natural gas. In: Proc. of the 23rd Intersociety Energy Conversion Engineering Conference, pp. 33e38. Moran, Michael J., Shapiro, Howard N., Boettner, Daisie D., Bailey, Margaret B., 2007. Fundamentals of Engineering Thermodynamics. John Wiley & Sons, Inc. [Online]. http://www.spilling.info/products/gas-expansion-engines.html. Oosthuizen, P.H., Carscallen, W.E., 1997. Compressible Fluid Flow. McGraw-Hill. Po zivil, J. Use of expansion turbines in natural Gas pressure reduction stations. In Acta Montanistica Slovaca, pp. 258e260. Rahman, M.M., December 2010. Power generation from pressure reduction in the natural gas supply chain in Bangladesh, ME 41 (2). Rheuban, Jacob, March 9th 2009. Turboexpanders: Harnessing the Hidden Potential of Our Natural Gas Distribution System. www.jacobrheyban.com. Ueno, K., Bye, R.E., Hunter, K.S., May 12th, 2003. Compressor Efficiency Definitions. University of Colorado, PhD. Watson, D.B., Sorge, G.W., 2007. System and method of use of expansion engine to increase overall fuel efficiency. 272e932 B2. Woschni, G., 1967. A Universally Applicable Equation for Instantaneous Heat Transfer in the Internal Combustion Engine. SAE Pap. No.670931, 76.
Contents lists available at ScienceDirect
Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Simulation of single acting natural gas Reciprocating Expansion Engine based on ideal gas model Mahmood Farzaneh Gord, Mohsen Jannatabadi* The Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 April 2014 Received in revised form 20 September 2014 Accepted 22 September 2014 Available online
The potential energy of high pressure gas destroyed in natural gas pressure reduction stations during pressure reduction when it passes through throttling valves. One way to recover this energy is to use a Reciprocating Expansion Engine coupled with a generator. The expansion engine is able to produce electricity as pressure decreases by recovering the potential energy. Although the expansion engine has been utilized in pressure reduction points for some time but it has not been analyzed for performance enhancement yet. In this work an advanced numerical simulation has been presented for the thermodynamic modeling of Natural Gas Single Acting Reciprocating Expansion Engine under various working conditions for high pressure ranges. The simulation has been carried out to understand the effects of various parameters and to improve performance of the engine. A range of geometric parameters such as suction diameter, piston diameter, crank radius, connecting rod length, speed were covered in this research. Because of the physical and numerical difficulties of the problem, the natural gas is assumed as an ideal gas. © 2014 Elsevier B.V. All rights reserved.
Keywords: Electricity Natural gas expansion engine Thermodynamic Numerical simulation
1. Introduction Natural gas is produced at high pressure about 50e70 bar and transported through pipelines from refinery to natural gas pressure drop stations usually called City Gate Stations (CGS). For consuming this gas, it is evident that the pressure of the gas must be reduced. In CGSs the pressure of the gas must be reduced to 15e20 bars (Po zivil). Reduction of high pressured gas can be achieved by gas expansion. For this purpose, usually the throttle valves are used which lost the potential energy of high pressure gas, while this potential energy could be used to produce electrical energy. If a Turbo-Expanders or an Expansion Engine coupled with a generator is used instead of throttle valves, the wasted potential energy of the gas could be recovered, (Rahman, 2010) and (Dehli, 1997). Reciprocating Expansion Engine is used to convert pressure into a rotating motion via a connecting rod and a crankshaft. In these engines unlike the usual engines there is no combustion and spark; the pressurized gases expand and pushes the piston to the bottom of the cylinder (BDC) and is returned to the cylinder top (TDC) with a flywheel. A gas with a high pressure enters the cylinder and exits without any consumption at lower pressure. Reciprocating * Corresponding author. E-mail addresses: [email protected] (M. Farzaneh Gord), m.jannatabadi@ minoodashtau.ac.ir, [email protected] (M. Jannatabadi). http://dx.doi.org/10.1016/j.jngse.2014.09.031 1875-5100/© 2014 Elsevier B.V. All rights reserved.
Expansion Engines can convert the pressure energy of a gas into mechanical work as the gas expands through it. They used for two purposes: cooling or producing power. If cooling a gas is the main goal, then the mechanical work is assumed as a byproduct; however, if producing power in pressure reduction process is the main objective, the cooling capacity will be a beneficial byproduct (Bloch and Soares, 2001). Fig. 1 shows the schematic of installing the expansion engine in city gate stations parallel to throttling valve. Unfortunately there is no report or paper about these systems and it can be said that this paper is the first manuscript that simulates the natural gas expansion engines. But since that physically it acts exactly reverse to reciprocating compressors and turbo expander from a thermodynamic point of view, combination of researches of these systems can be used for modeling the natural gas expansion engine. According to JouleeThompson effect (Rheuban, 2009), most gases will be cooled during the expansion process, therefore preheating the gas before entering the Expansion Engine is very important. Expansion Engines are relatively small and compact. It can be said that this is an Isentropic Process. Expansion Engine doesn't have any pollution since it produces the electricity without consumption any fuel; it can produce considerable chilling which can be used for air conditioning systems (Watson and Sorge, 2007). The produced electricity can be used for preheating the gas before
670
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Nomenclature A Cp D De d E f h K L Lr m P Q R Rj T u U V W Gr Nu
Area (m2) Specific heat at constant pressure (j/kg K) Diameter (m) Effective diameter (m) Port diameter (m) Energy of system (j) Friction factor Enthalpy (j/kg) Conduction heat transfer coefficient Connecting rod length (m) Ring width (m) Mass of gas (kg) Pressure (Pa) Heat transfer (kw) Crank radius (m) Thermal resistance Temperature (K) Internal energy (j/kg) Overall heat capacity (j/m2K) Volume (m3) Power (kw) Grashof number Nusselt number
entering the Expansion Engine and also for lightening environments of the gas stations. These engines are usually coupled with a generator in one power pack. Control slide valve is used to control the flow-rate of the gas. The power output from the Expansion Engine mainly depends on the pressure ratio, inlet temperature, and the flow rate (Rahman, 2010). Po zivil (Po zivil) showed that temperature drop in the throttle valve system can be about 0.45e0.6 C per bar of pressure drop, whereas in turbo-expanders it can be much higher, around 1.5e2 C per bar, depending on the gas composition. Mohammed (Rahman, 2010) with analyzing a number of producing wells and pressure reduction stations found that preheating the pressured gas before entering the turbo expander and before expansion is almost always necessary to avoid hydrate formation. Dehli (Dehli, 1997), (Dehli, 1994) and (Dehli, 1996) showed that if the temperature of the gas increases at the engine inlet, then a higher electrical energy will be produced. He proved that in a two
Fig. 1. Schematic of city gas station.
Pr Re x
q q0 qi qe hmech
Prandtl number Reynolds number Piston displacement (m) Circular velocity (rad/s) Angular velocity (rad/s) Kinematic viscosity (m2/s) Instant angle of connecting rod Initial guess for inlet port Time of opening of exit port Time of closing of exit port Mechanical efficiency
Subscript a b c cl d s o i ind f w fr
ambient brake cylinder Clearance volume discharge suction outer inner indicator Film wall friction
u ug w
or more gas expansion system with additional counter flow heat exchanger after engine, the efficiency of system will be improve too. Mirandola and Minca (Mirandola et al., 1986) analyzed the power generation from high pressure natural gas with several expansion stages, gas flow rates and pre-heating. In another paper, Mirandola and Macor (Mirandola et al., 1988) have presented experimental results with the effect of heat input for pre-heating the gas. They showed that the most of the pre-heating is recovered as electricity. Ardali and Heybatian (Ardali and Heybatian, 2009) compared using of throttle valve and Turbo expanders in CGS and showed that using Turbo expanders is more beneficiary than the throttle valve. They simulated their project with several gas flow rates and inlet pressures. They also showed that application of turbo expander in conjunction with the thermal power plants would be more beneficiary because the exhaust gas has very high temperature which can be used for pre-heating the gas. Farzaneh (Farzaneh Gord et al., 2007a) showed that pre-heating the inlet gas and increasing the inlet pressure in turbo expander will increase the exergy of system and the power output as well. Farzaneh-Gord and Magrebi (Farzaneh-Gord and Magrebi, 2009) studied exergy destruction due to reducing pressure of natural gas and showed that a pattern of natural gas field could produce 4200 MW of electricity using this pressure exergy. He (Farzaneh-Gord et al., 2007b) studied the effect of gas pre-heating and using the pressure exergy of natural gas in pressure reduction station on the amount of electricity generation. With measuring the amount of energy lost in natural gas pipeline distribution Farzaneh (Farzaneh-Gord et al., 2007c) showed that the huge amount of electricity will be generated from reduction of natural gas. He (Farzaneh-Gord and Deymi Dashtbayaz, 2008) has suggested preheat and using a turbo expander to catch this energy. Because of simple to operation, high availability and highly efficient electricity generation ([Online]), using of natural gas expansion engine is more preferable to reduce the high pressure
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
671
gas. It can be used as double acting, single or more stages, one to six cylinders in CGS. Because it acts reverse to compressor, for simulating and modeling this system, assumptions and equations of reciprocating compressors can be used. In this study, a comprehensive numerical program is used for simulate the single acting, one-stages, one cylinder natural gas expansion engine to measure the output power, heat transfer, minimum temperature drop and predict the gas temperature and pressure. The significant parameters of the expansion engine such as ports and piston diameter, engine speed, crank radius and connecting rod length are then identified. Thereafter, the effects of these parameters on mechanical efficiency are investigated too. 2. The thermodynamic modeling For modeling the operation of one cylinder single-stage singleacting Reciprocating Expansion Engine with a slider crank mechanism, Fig. 2, the computer programming with MATLAB code is used for control volume which is shown in Fig. 3. The model is based on the integration of the transient fluid conservation equations (continuity and energy) inside the expansion engine domain. In thermodynamic assumptions the behavior of the gas assumed as an Ideal gas, the process in inlet and outlet ports is an isentropic, no leakage through the piston rings is assumed and changes in kinetic and potential energy is ignored and circular velocity is assumed constant. The high pressure gas acts upon the piston and makes it to move along the cylinder axis and the potential energy which is stored in flywheel pull the piston to move back to top dead center. To convert the linear movement of the piston into the rotational movement, a crankshaft mechanism is used and with connecting this crankshaft to generator, electricity will be produced. To control the inlet and outlet mass, a sample slide valve is used. This valve opens and closes automatically, due to the pressure difference between the suction/discharge chamber and the cylinder. Pressure, temperature and density of fluid flow were calculated from continuity equation, energy equation and ideal gas equation of state respectively (Fig. 4).
Fig. 3. Schematic of control volume (Lee, 1983).
clearance volume of 10%, expansion engine has the best performance. The volume of gas inside the cylinder will compute as:
VðqÞ ¼ xðqÞp
D2i 4
(2)
2.1. Geometrical modeling The instantaneous position of the piston displacement according to Top Dead Center is given by (Mabie and Reinholtz, 1987):
8 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi9 2 < = R xðqÞ ¼ x0 þ Rð1 cos qÞ þ L 1 1 sin2 q : ; L
(1)
Where q ¼ ut and u is the angular velocity of crank and x0 is the length of the clearance volume. Results which achieved with selected geometrical parameters such as port and piston diameter, connecting rod, crank radius and so on showed that with a
Fig. 2. Slider crank mechanism.
Fig. 4. Single acting expansion engine.
672
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
dTc 1 dQ dVc dms dmd Pc ¼ þ CPs Ts CPd Td mc ðCP RÞ dq dq dq dq dq dms dmd ðCP RÞTc dq dq
2.2. First law of thermodynamic The first law of thermodynamic for the inside gas of the cylinder as a control volume on a time rate is (Moran et al., 2007):
X X dECV _ þ _ in _ out ¼ Q_ W ðmhÞ ðmhÞ dt
To calculate instantaneous value of temperature in next step based on the value of temperature and changes of it in previous step, the following equation can derived and from an ideal gas equation of state the pressure of each step can be achieved (Farzaneh-Gord and Deymi Dasht-bayaz, 2008):
(3)
In this equation the work term can be written as Pc(dVc/dq) (Moran et al., 2007). For simplicity it was assumed that the changes of internal energy of the control volume considered as a change of energy (Lee, 1983), it means dEcv/dt ¼ d(mcuc)/dt. The mass conservation law is:
Tc
dmc dms dmd ¼ dq dq dq
Pcjþ1 ¼
jþ1
(4)
j
j
¼ Tc þ dTc jþ1
Instantaneous inlet and outlet mass flow rates through suction and discharge ports which are assumed as an orifice are as follows (Oosthuizen and Carscallen, 1997):
if
if
g g1 Pc 2 > gþ1 Ps Pc Ps
(6)
With substituting these equations in Equation (5), following formula can be achieved (Lee, 1983):
duc 1 ¼ mc dq
dQ dVc dms dmd dms dmd Pc þ hs hd uc dq dq dq dq dq dq (7)
This equation can be used for both ideal and perfect gas. For ideal gas we have (Moran et al., 2007):
u ¼ CV T; h ¼ CP T; R ¼ CP CV ; PV ¼ mRT
(11)
2.3. Calculating mass flow rate
8 > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 gþ1 > > 1 q q 2g Pd g Pd g > i > > Ad Pc sin p > < u ðg 1ÞRT q q P Pc e c c i dmd ¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > dq gþ1 > > g1 > 1 q qi g 2 > > A P sin p > c d > > u RT g þ 1 q q e c i :
dðmc uc Þ duc dmc ¼ mc þ uc dq dq dq
jþ1
Vcjþ1
(5)
In this equation (Lee, 1983):
8 > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 gþ1 > > 1 q 2g Pc g Pc g > > > As Ps sin p > < u q ðg 1ÞRT P Ps s s 0 dms ¼ s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi > dq gþ1 > > g1 > 1 q g 2 > > A P sin p > s s > > u q0 RTs g þ 1 :
(10)
mc RTc
The simplified form of Equation (3) based on variation of crank angle is as follow (Lee, 1983):
dðmc uc Þ dQ dW dms dmd ¼ þ hs h dq dq dq dq dq d
(9)
(8)
Then for an Ideal gas, based on the energy conservation we have (Lee, 1983):
if
if
2 gþ1
g g1
9 > > > > > > > > > =
Pd 2 > gþ1 Pc Pd Pc
(12)
> > > > > > > > > ;
g g1
2 gþ1
g g1
9 > > > > > > > > > = > > > > > > > > > ;
(13)
Where g is the specific heat ratio which calculated as a function of temperature, R is the gas constant of methane, q0 is a closure angle of inlet port, qi is the opening time of output port and qe is the closing time of output port. These formulas are written based on the flow which passes through orifices (Oosthuizen and Carscallen, 1997). In these equations the chock condition is considered (Lee, 1983). In state of chocked flow, mass flow rate is constant, and then second equation in these formulas determines the constant flow rate based on chocked flow. It was assumed that there isn't happened any backward flow through ports. From Equations (12) and (13) it can be said that opening and closing time of ports are controlled mechanically. Inlet port is opened exactly at top dead center (TDC) and closed at a defined crank angle. In this process high pressure gas enters the cylinder and pushes the piston to move to bottom. From defined crank angle to bottom dead center (BDC) expansion process takes place. Before BDC outlet port is opened and closed at a defined angle.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
study the only useful correlation for reciprocating cylinder piston, it means Adair' equations are used (Adair et al., 1972).
2.4. Calculating heat capacity of methane In this study specific heat capacity of methane is considered as a function of the gas temperature via the equation (DIPPR@ 801, 2004):
h
A1 þ B1
CPi ðqÞ ¼
C1 =Tc sinhðC1 =Tc Þ
2
þ D1
E1 =TC coshðE1 =TC Þ
2
A1 ¼ 3:3298 104 ; B1 ¼ 7:9933 104 ; C1 ¼ 2:0869 103 ; D1 ¼ 4:1602 10 ; E1 ¼ 9:9196 10
Nui ðqÞ ¼
hi ðqÞDe ðqÞ ¼ 0:053½ReðqÞ0:8 ½PrðqÞ0:6 Ki ðqÞ
2
(14)
ReðqÞ ¼
rc ðqÞD2e ðqÞug ðqÞ 2mðqÞ
Overall correlation for modeling heat transfer is assumed as follows (Ardali and Heybatian, 2009):
AðqÞ ¼
UðqÞ ¼
4
Aw
þ
1 P
4Vcl þ pDxðqÞ D
1 pDi xðqÞhi ðqÞ
(18)
Ro ðqÞ ¼
1 pDo xðqÞho ðqÞ
(19)
Rw ðqÞ ¼
ln ðDo =Di Þ 2pKw xðqÞ
(20)
Natural convection is occurred if the Expansion Engine is considered as a horizontal cylinder. In this case the air heat transfer coefficient outside the cylinder is as follow (Annand, 1963):
" #0:25 Grair Pr2air ho Do pffiffiffiffiffiffiffiffiffiffi ¼ Kair 2:435 þ 4:884 Prair þ 4:953Prair
The heat transfer coefficients in the expansion engine surfaces has been considered constant but heat transfer coefficients of the gas has been considered variant. In this equation Grashof Number is (Lee, 1983):
Grair ¼
(25)
ug is annular velocity and De is effective diameter (Lee, 1983): ug ðqÞ ¼
pDo 2
g Tf
m2air
8 < 2uð1:04 þ cos cosð2qÞÞ :
uð1:04 þ cos cosð2qÞÞ
9 3p p
6 pD 6VðqÞ 4 xðqÞ ¼ 2 AðqÞ pDxðqÞ þ 2p D
(26)
(27)
4
u is the circular velocity. Inside thermal conductivity of methane assumed as (DIPPR@ 801, 2004):
ki ðqÞ ¼
A3 TcB3 1 þ CT3c þ DT 23
; A3 ¼ 8:3983 106 ; B3 ¼ 1:4268;
c
(28)
C3 ¼ 4:9654 10; D3 ¼ 1:9
2.6. Calculating indicated, friction and brake power To calculate the indicated work which means the work done on the gas by the piston in one cycle we have (Moran et al., 2007): q¼360 Z
Wind ¼
P dV
(29)
q¼0
And the brake or output work can be calculated from (Ueno et al., 2003):
(21)
r2air
c
(17)
3
; A2 ¼ 5:2546 107 ; B2 ¼ 5:9 101 ;
2
Ri ðqÞ ¼
2 1 þ CT2c þ D T2
C2 ¼ 1:056 102 ; D2 ¼ 0:18
De ðqÞ ¼ Rj
A2 TcB2
(16)
VCL is the clearence volume, D is the piston diameter and Rj is the summation of inside convection resistance, wall conduction resistance and outside convection resistance as follow (Lee, 1983):
Nuo ðqÞ ¼
mi ðqÞ ¼
(15)
In modeling heat transfer the piston-ring leakage was illuminated. In this relationship A(q) is the total heat transfer area of piston, dead volume and cylinder wall which exposed to heat transfer and U(q) is the overall heat transfer coefficient (Lee, 1983):
pD2
(24)
Cinematic viscosity of methane as an ideal gas is (DIPPR@ 801, 2004):
2.5. Calculating heat transfer
Q_ ¼ UðqÞAðqÞ½Ta Tc ðqÞ
(23)
Where in this formula definition of Reynolds Number is as follow (Lee, 1983):
M 4
673
ðTa Tw Þ (22)
Where properties of air are calculated based on Tf, film temperature, Tf ¼ TwþTa/2. There are a few research about the inside heat transfer coefficient (Annand, 1963), (Eichelberg, 1939), (Hassan, 1971), (Hohenberg, 1979) and (Woschni, 1967), but in present
Wb ¼ Wind Wfr
(30)
Oil free friction work of piston ring can be calculated as follows (Hanlon):
Wf ¼ pf Pav Lr ð1:24Di þ 1Þ
(31)
Where Lr is the ring width, f is the friction coefficient of PTFE, and Pav is the average pressure which can be calculated as follow (Hanlon):
1=g Pav ¼
Pd g
Ps Pd
Ps ð2 gÞ 2ðg 1Þ
(32)
674
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Then we can calculate the mechanical efficiency of engine with (Ueno et al., 2003):
hmech ¼
Wb Wind
(33)
3. Results and discussion Initial conditions of this study are given in Table 1. Suction pressure and temperature is considered as uniform pressure and temperature in the suction line; similarly discharge pressure considered as discharge line. Along the flow direction for the inlet and outlet velocity and outlet temperature the gradient is assumed as zero. Also there isn't any heat transfer during the injection and exhaust phases of the cycle. The whole derived equations describe in the previous section by means of an algorithm is iteratively solved, at each time-step. On each iterate temperature and pressure was calculated from energy equation and equation of state respectively, Equations 9e11. As mentioned before, there are several parameters which affect on reciprocating engines, such as inlet port diameter, crank radius, connecting rod length, circular velocity, suction and discharge pressure and so on. In present study the effects of the ratio of inlet port to piston diameter(ds/Di), the variation of crank radius to connecting rod length (R/L) and the effect of changes of engine speed on performance of expansion engine has been studied. By using this method proposed for expansion engine design, not only the design time will be lessened, but also the performance of expansion engine can be predicted and then the need for experimental research will be reduced. 3.1. Effect of motor speed In this section the effect of variation of motor speed on expansion engine performance is analyzed. Fig. 5, Fig. 6 and Fig. 7 show the engine indicator diagram based on selected port and cylinder geometries, Table 1. It is found that for operation at 2000 rpm the outlet port would close 10 later than operation at 1000 rpm, 335 for the first case and 345 for second. Inlet port is closed at 75 and outlet port is opened at 160 of crank revolution. Fig. 5 shows the indicator diagram for operation at 1000 rpm and Fig. 6 shows this diagram for operation at 2000 rpm with the same inlet conditions of Fig. 5. Fig. 7 shows the effect of expansion engine speed on the indicator work. The closing time of inlet port, opening and closing of outlet port does not change in this graph. It can be found that indicator work of engine is decreased as speed is increased. But indicated power is increased with arising speed because of reduction of the time of cycle. The main cause of this phenomenon is that the inlet and outlet gas flow and therefore the mass of gas inside the cylinder are decreased at higher speed, Fig. 8 and Fig. 9. This occurs from the fact that the total time period of the gas flowing
Fig. 5. Indicator diagram, 1000 rpm.
through the inlet orifice decreases with increase of speed. All indicated power, friction power and brake power are increased with speed increments, but mechanical efficiency of engine reduced with it. As speed is increased, the cylinder pressure drop occurring during the suction process becomes more and then the gas flow per cycle reduces. Fig. 10 shows the effect of pressure drop against crank angle in various speed. Another effect of speed variations on gas pressure is that on higher speeds, in the movement from bottom dead center to top dead center the gas pressure is increased more than lower engine speed. Table 2 compares the power calculations of engine between 1000 and 2000 rpm. Results show that the amounts of heat transfer is very low which the assumption of isentropic process for expansion engine is correct. In Fig. 11 it has been shown that in high motor speed the temperature loss of gas is more than in low speed. Table 1 shows the indicated power, friction power and brake or output power in 1000 and 2000 rpm. It can be seen that although the brake power
Table 1 Initial guess and physical parameters of Expansion Engine. Operating condition
Data
Operating condition
Data
Ps Pd Ts ds dd Vcl f
60 bar 15 bar 285 K 5 cm 5 cm 10% Vd 0.3
Di Do Ta Kw R L Lr
13.7 cm 15 cm 298 K 50 W/m.K 7 cm 20 cm 1.5 mm
Fig. 6. Indicator diagram, 2000 rpm.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
675
Fig. 9. Mass of gas for several speeds.
Fig. 7. Indicator diagram for several speeds.
increased with motor speed, but the mechanical efficiency of expansion engine reduced with it. Since the friction power depends on speed of motor directly, the ratio of increase of indicated power is more than the ratio of increase of brake power. It can be seen that generally the gas temperature and pressure variations are not significantly affected by a variation of engine speed, although the average gas velocity would be higher at raised engine speed. 3.2. Effect of inlet port diameter over constant piston diameter In this section the piston diameter was considered constant provided that the inlet port diameter varies from 3 cm to 5 cm. In Fig. 12 and Fig. 13 it has been given the instantaneous variation of gas temperature and pressure against crank angle, respectively. In this analysis the closing and opening time of inlet and outlet ports are 75 and 160 of crank revolution. It was found that for plotting the rational PeV diagram the outlet port should be closed at least at 338 of crank revolution, because before that time the difference pressure between inside gas in dead volume and suction manifold
Fig. 8. Suction and discharge mass flow rate for several speeds.
did not adequate to flowing the gas into cylinder. In this section the closing time of outlet port was considered 340 , motor speed was 1000 rpm and clearance volume was 5% of swept volume. From these figures it was found that increasing the ratio of inlet port diameter to piston diameter doesn't affect variation of pressure and temperature of gas significantly. From Fig. 12 it was found that in higher inlet diameter to piston diameter ratio, the temperature loss of gas is more than lower value of this ratio and from Fig. 13 it can be seen that the variation of inlet port doesn't affect the gas pressure. There is another point here with increasing the ratio, the value of exit temperature will decrease. In Fig. 14 instantaneous alternation of inside mass has been shown. Evidently at the charging and discharge process the mass flow rate with raising the diameter ratio will be increased. Between 75 to 160 and 340e360 of crank angle it is assumed that both inlet and outlet ports are closed. It means that after 340 the residual mass reaches at its first value and will be constant until the beginning stage of the charging process. This is the mass of clearance volume. Fig. 15 shows that with increasing the diameter ratio it is evident that the amount of mass which enters the cylinder will
Fig. 10. Pressure variations for several speeds.
676
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Table 2 Calculation of power and efficiency. Results
N ¼ 1000 rpm
N ¼ 2000 rpm
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
86.3 4.089 82.21 0.0286 2.51 MPa 84%
141.3 4.088 137.23 0.0245 2.05 MPa 61%
imep hmech
Fig. 13. Pressure variations for several inlet port/piston diameter.
Fig. 11. Temperature variations for several speeds.
be increased too and subsequently the amount of discharge flow rate will raised too. From the indicated diagram of expansion engine based on variation of inlet port to piston diameter ratio as shown in Fig. 16, it can be seen that by increasing this ratio the indicator work will be increased too, and from Table 3 it was concluded that there is a small increase in the mechanical efficiency of expansion engine. This phenomenon can be described in another way. Since that the gas temperature is less than the ambient temperature the Expansion Engine can be used to cooling its surrounding space. Then the total heat transfer in each cycle can be evaluated too. With
Fig. 14. Suction and discharge mass flow rate for several inlet port/piston diameter.
Fig. 12. Suction and discharge mass flow rate for several inlet port/piston diameter.
Fig. 15. Mass of gas for several inlet port/piston diameter.
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Fig. 16. Indicator diagram for several inlet port/piston diameter.
Fig. 18. Pressure variations for several crank radius.
Table 3 Work and efficiency results in 1000 rpm. Results
ds/Di ¼ 0.2190
ds/Di ¼ 0.3650
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
68.94 4.09 64.85 0.026 2 MPa 80%
83.79 4.09 79.7 0.026 2.4 MPa 84%
imep hmech
increasing the ratio the heat transfer rate increased very little. It means that irreversibility will decreased and then the power must be increased.
3.3. Effect of crank radius to connecting rod length ratio The variation of crank radius to connecting rod length ratio has been analyzed too, Fig. 17e20. For this main crank radius and connecting rod length were considered 4e7 and 20e24 cm
Fig. 19. Mass of gas for several R/L ratio.
Fig. 17. Temperature variations for several crank radius.
Fig. 20. Suction & discharge mass of gas for several R/L ratio.
677
678
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Fig. 24. Pressure variations for L ¼ 24 cm.
Fig. 21. Indicator diagram for several R/L ratio.
Fig. 22. Indicator diagram for L ¼ 24 cm.
respectively. Results have shown that the variation of connecting rod length doesn't affect the gas properties and in cylinder mass of gas, but the change of crank radius has a direct effect on the properties of the gas inside the cylinder. From Fig. 21 it can be seen that in a sample crank radius, increasing connecting rod length doesn't affect on indicated and subsequently on friction and brake powers, but Fig. 22 shows that if crank radius increased in constant connecting rod length, indicated power will increase sharply. Since the friction power increased significantly, the brake power of expansion engine doesn't rise considerably, and then variation of crank radius in constant connecting rod length can't improve the generation of electricity from using expansion engine in CGS. Fig. 23 and Fig. 24 show that the outlet temperature and pressure in high crank radius is more than in low amount of it and from Figs. 17 and 18 it can be seen that variation of the ratio of these parameters doesn't affect the minimum value of gas pressure and temperature. Results showed that if crank radius is considered constant, with increasing the connecting rod length the amount of indicated, friction and brake powers will decrease inconsiderably. Table 4 Shows values of these power and amount of heat transfer and mechanical efficiency of expansion engine for four cases. It can be seen that mechanical efficiency will decreased significantly if connecting rod length considered constant whereas crank radius increased too. But there is a little variation of heat transfer and mechanical efficiency in this case. 4. Conclusion Directly measured data for the gas inside the expansion engine are not available at the moment. The mathematical model using the Table 4 Calculations for several ratios of R/L.
Fig. 23. Temperature variations for L ¼ 24 cm.
Results
R ¼ 4 cm L ¼ 20 cm
R ¼ 7 cm L ¼ 20 cm
R ¼ 5 cm L ¼ 20 cm
R ¼ 5 cm L ¼ 24 cm
_ W ind ðk WattÞ _ ðk WattÞ W fr _ ðk WattÞ W b _ Q ðk WattÞ
48.8 4.09 44.7 0.019 91%
83.8 4.09 79.7 0.026 84%
60.8 4.09 56.7 0.022 88.7%
59.7 4.09 55.6 0.022 88.6%
hmech
M. Farzaneh Gord, M. Jannatabadi / Journal of Natural Gas Science and Engineering 21 (2014) 669e679
Ideal gas equation provided the simulation of a single-acting reciprocating Gas Expansion Engine system with modeling the heat transfer. This model can be used for the optimum design and predicting of the performance of expansion engine. Over a wide range of parameters which affected this system, the inlet port diameter, connecting rod length, crank radius and engine speed has been studied in present research. Results showed that variation of connecting rod length doesn't affect on the power which be achieved from pressure reduction of gas in Expansion Engine and also doesn't change other parameters of gas such as temperature and pressure. Instead, increasing the crank radius and inlet port diameter bring that system produced more power and increasing the motor speed causes to have higher output power too. References Adair, R.P., Qvale, E.B., Pearson, J.T., 1972. Instantaneous heat transfer to the cylinder wall in reciprocating compressors. In: International Compressor Engineering Conference. Paper 86. Annand, W.J.D., 1963. Heat transfer in the cylinder of reciprocating internal combustion engine. Proc. Instn. Mech. Eng. 177 (36), 973e990. Ardali, E.K., Heybatian, E., 5e9 October 2009. Energy regeneration in natural Gas pressure reduction stations by use of Gas turbo-expander; evaluation of available potential in Iran. In: 24th World Gas Conference, Buenos Aires, Argentina. Bloch, H., Soares, C., 2001. Turbo Expanders & Process Applications. Gulf Professional Publishing. Dehli, M., 1994. Prozesse zur verbesserung der wirksamkeit von Gas-Expansion sanlagen unter thermodynamischen gesichtspunkten. Dehli, M., 1996. energier uckgewinnung mit Gas Expansion sanlagen, pp. 196e206. Dehli, M., 28e30 January 1997. Concepts of Gas Expansion at High Temperature. Netherland. DIPPR@ 801, 2004. Evaluated Standard Thermophysical Property Values. Design Institute for Physical Properties, Sponsored by AIChE. Eichelberg, G., 1939. Some new investigation on old combustion engine problems. Engineering 148, 463e466. Farzaneh-Gord, M., Deymi Dasht-bayaz, M., 2008. Recoverable energy in natural gas pressure drop stations: a case study of the Khangiran gas refinery. Energy Explor. Exploit. 26, 71e82.
679
Farzaneh Gord, M., Eftekhari, H., Tvakkoli, M.M., 12e13 June 2007a. Using of natural Gas pressure reducing station to produce power and Refrigeneration. In: Sixth National Energy. Farzaneh-Gord, M., Magrebi, J., 2009. Exergy of natural gas flow in Iran's natural gas fields. Int. J. Exergy 6, 131e142. Farzaneh-Gord, M., et al., March 24-27, 2007b. Using pressure exergy of natural gas in Bandar-Abbas refinery gas pressure drop station. In: The Second International Conference on Modelling, Simulation, and Applied Optimization, Abu Dhabi. UAE. Farzaneh-Gord, M., Hashemi, S., Sadi, M., 2007c. Energy destruction in Iran's natural gas pipe line network. Energy Explor. Exploit. 25, 1e10. Hanlon, Paul C. Compressor Handbook. McGraw-Hill. Hassan, H., 1971. Unsteady heat transfer in a motored I.C. engine cylinder. Proc. Instn. Mech. Eng. 185, 1139e1147. Hohenberg, G.F., 1979. Advanced Approaches for Heat Transfer Calculations. SAE Pap. No.79825. Lee, S., 1983. First Law Analysis of Unsteady Processes with Application to Charging Process and a Reciprocating Compressor. The Ohio State University. Mabie, H.H., Reinholtz, C.F., 1987. Mechanics and Dynamics of Machinery, fourth ed. John Wiley and Sons, Inc. Mirandola, A., Minca, L., Aug. 25-29, 1986. Energy recovery by expansion of high pressure natural gas. In: Proc. of the 21st Intersociety Energy Conversion Engineering Conference, pp. 16e21. Mirandola, A., Macor, A., July 31-Aug. 5, 1988. Experimental analysis of an energy recovery plant by expansion of natural gas. In: Proc. of the 23rd Intersociety Energy Conversion Engineering Conference, pp. 33e38. Moran, Michael J., Shapiro, Howard N., Boettner, Daisie D., Bailey, Margaret B., 2007. Fundamentals of Engineering Thermodynamics. John Wiley & Sons, Inc. [Online]. http://www.spilling.info/products/gas-expansion-engines.html. Oosthuizen, P.H., Carscallen, W.E., 1997. Compressible Fluid Flow. McGraw-Hill. Po zivil, J. Use of expansion turbines in natural Gas pressure reduction stations. In Acta Montanistica Slovaca, pp. 258e260. Rahman, M.M., December 2010. Power generation from pressure reduction in the natural gas supply chain in Bangladesh, ME 41 (2). Rheuban, Jacob, March 9th 2009. Turboexpanders: Harnessing the Hidden Potential of Our Natural Gas Distribution System. www.jacobrheyban.com. Ueno, K., Bye, R.E., Hunter, K.S., May 12th, 2003. Compressor Efficiency Definitions. University of Colorado, PhD. Watson, D.B., Sorge, G.W., 2007. System and method of use of expansion engine to increase overall fuel efficiency. 272e932 B2. Woschni, G., 1967. A Universally Applicable Equation for Instantaneous Heat Transfer in the Internal Combustion Engine. SAE Pap. No.670931, 76.