Simple ORC Model SQ110918

File:Z:\labo\these\final\modeles\simple_ORC_model.EES 24/02/2012 14:45:05 Page 1EES Ver. 8.940: #1206: Jean Lebrun, Laboratoire de Thermodynamique, Univ. Liege

This simple model of an Organic Rankine Cycle is designed for a quick evaluation of the cycle performance with imposedheat source and heat sink conditions and different working fluids. It is suitable for the 'screening method' describe in Chapter5.3. For realistic performance prediction of an ORC, more advanced models must be used (such a the one proposed in Chapter4).

Some inputs are commented. These inputs can be used provided some other inputs are removed (eg. the heat temperature canbe imposed if the equation imposing its flow rate of the working fluid rate is removed).This model is designed for subcritical operating conditions and azeotropic working fluids only.The model includes a recuperator, that can be removed by setting its effectiveness to zero.Thermodynamic digrams can be built by plotting the thermodynamic states recorded in the array table.

This code is provided for educational purpose. It can be freely used and reproduced as long as full credit to the original sourceis provided:Quoilin, S. (2011). Sustainable energy conversion through the use of Organic Rankine Cycles for waste heat recovery and solarapplications. Unpublished doctoral thesis, University of Lige, Lige, Belgium.

Sylvain Quoilin, 18 September 2011

Nomenclature:cp heat capacity (j/kgK)E exergy flow rate (W)h specific enthalpy, J/(kg K)M mass flow rate, kg/sp pressure, Papinch pinch point value, KQ Heat power, Wq specific heat flux, W/kgr ratio, -s specific entropy, J/(kg K)T temperature, Cw specific work, J/kgW mechanical or electrical power, Wx vapor quality, -

Greek symbols effectiveness differential efficiency density, kg/m3

Subscripts and superscripts0 Reference conditionscd Condensercf Cold fluidev Evaporatorex Exhaustexp Expanderl Liquidpp Pumprec Recuperators Isentropicsf Secondary fluidsu Supplytp Two-phasev Vapor


Inputs and parameters :

fluid$ = 'r245fa'

M = 1

T0 = 20

pressures :

Tev = 130

Tcd = 30

pinchev = 10

pinchcd = 10

heat source :

hf$ = 'airha'

phf;ev = 100000

Mhf = 5

heat sink :

cf$ = 'airha'

pcf;cd = 100000

Mcf = 10

Pressure drops in the heat exchangers :

pev = 0

pcd = 0

Overheating and subcooling :

Tex;ev = 5

Tex;cd = 5

Effectivenesses :

exp = 0,8

pp = 0,8

rec = 0


rp = psu;exppex;exp

rv = su;expex;exp

First processing :

Saturation pressures :

Tev = Tsat fluid$ ; P =psu;ev

Tcd = Tsat fluid$ ; P =pex;cd

pev = psu;ev psu;exp

pcd = pex;exp pex;cd

pev = psu;ev + psu;exp

2

pcd = pex;exp + pex;cd

2

Tex;ev = Tsu;exp Tsat fluid$ ; P =psu;exp

Tex;cd = Tsat fluid$ ; P =pex;cd Tex;cd

Expansion :

hsu;exp = h fluid$ ; T =Tsu;exp ; P =psu;exp

ssu;exp = s fluid$ ; T =Tsu;exp ; P =psu;exp

exp = hsu;exp hex;exphsu;exp hex;exp;s

hex;exp;s = h fluid$ ; P =pex;exp ; s =ssu;exp

tex;exp = T fluid$ ; P =pex;exp ; h =hex;exp

ex;exp = fluid$ ; P =pex;exp ; T =tex;exp

su;exp = fluid$ ; P =psu;exp ; T =Tsu;exp

Condenser :

hypothesis : the pressure drop is distributed in the heat exchanger proportionaly to the enthalpy change :

hsu;cd = hex;vap;rec

Tsu;cd = Tex;vap;rec

hex;cd = h fluid$ ; P =pex;cd ; T =Tex;cd

hcd;v = h fluid$ ; P =pcd;v ; x =1


hcd;l = h fluid$ ; P =pcd;l ; x =0

pcd;v = pex;exp pcd hex;exp hcd;vhex;exp hex;cd

pcd;l = pex;exp pcd hex;exp hcd;l

hex;exp hex;cd

Tcd;v = T fluid$ ; P =pcd;v ; x =1

Tcd;l = T fluid$ ; P =pcd;l ; x =0

hcf;su;cd = h cf$ ; T =tcf;su;cd ; P =pcf;cd

Mcf hcf;ex;cd hcf;su;cd = M hsu;cd hex;cd

Mcf hcf;su;tp hcf;su;cd = M hcd;l hex;cd

Mcf hcf;ex;tp hcf;su;cd = M Min hcd;v ; hsu;cd hex;cd

Tcf;ex;cd = T cf$ ; h =hcf;ex;cd ; P =pcf;cd

Tcf;su;tp = T cf$ ; h =hcf;su;tp ; P =pcf;cd

Tcf;ex;tp = T cf$ ; h =hcf;ex;tp ; P =pcf;cd

Tcf;cd = Tcf;ex;cd tcf;su;cd

pinchcd = Min Tex;cd tcf;su;cd ; Tcd;v Tcf;ex;tp ; Tsu;cd Tcf;ex;cd

Pump :

hsu;pp = hex;cd

vsu;pp = v fluid$ ; P =pex;cd ; h =hex;cd

ssu;pp = s fluid$ ; P =pex;cd ; h =hex;cd

hex;pp = hsu;pp + vsu;pp psu;ev pex;cd

pp

Second method:

hex;pp;s = h fluid$ ; s =ssu;pp ; P =psu;ev

pp = hex;pp;s hsu;pp

hex;pp;bis hsu;pp

tex;pp = T fluid$ ; h =hex;pp ; P =psu;ev

Recuperator :

Pressure drop :


pvap;rec = pcd hex;exp hex;vap;rec

hex;exp hex;cd

pex;vap;rec = psu;vap;rec pvap;rec

psu;vap;rec = pex;exp

hsu;liq;rec = hex;pp

Tsu;liq;rec = tex;pp

p liq;rec = psu;ev

Hsu;vap;rec = hex;exp

Tsu;vap;rec = tex;exp

pvap;rec = psu;vap;rec + pex;vap;rec

2

cp liq;rec = Cp fluid$ ; T =Tsu;liq;rec ; P =p liq;rec

cpvap;rec = Cp fluid$ ; T =Tsu;vap;rec ; P =pvap;rec

C liq;rec = M cp liq;rec

Cvap;rec = M cpvap;rec

Cmin;rec = Min C liq;rec ; Cvap;rec

Cmax;rec = Max C liq;rec ; Cvap;rec

Q rec = rec Cmin;rec Tsu;vap;rec Tsu;liq;rec

Q rec = M Hsu;vap;rec hex;vap;rec

Q rec = M hex;liq;rec hsu;liq;rec

Tex;vap;rec = T fluid$ ; h =hex;vap;rec ; P =pvap;rec

Tex;liq;rec = T fluid$ ; h =hex;liq;rec ; P =p liq;rec

Evaporator :

hsu;ev = hex;liq;rec

Tsu;ev = Tex;liq;rec

hex;ev = hsu;exp

hev;l = h fluid$ ; P =pev;l ; x =0

hev;v = h fluid$ ; P =pev;v ; x =1

pev;l = psu;exp + pev hex;ev hev;l

hex;ev hsu;ev


pev;v = psu;exp + pev hex;ev hev;vhex;ev hsu;ev

Tev;l = T fluid$ ; x =0 ; P =pev;l

Tev;v = T fluid$ ; x =1 ; P =pev;v

secondary fluid :

hhf;su;ev = h hf$ ; T =thf;su;ev ; P =phf;ev

Mhf hhf;su;ev hhf;ex;ev = M hex;ev hsu;ev

Mhf hhf;su;ev hhf;ex;tp = M hex;ev hev;l

Mhf hhf;su;ev hhf;su;tp = M hex;ev hev;v

Thf;ex;ev = T hf$ ; h =hhf;ex;ev ; P =phf;ev

Thf;ex;tp = T hf$ ; h =hhf;ex;tp ; P =phf;ev

Thf;su;tp = T hf$ ; h =hhf;su;tp ; P =phf;ev

Thf;ev = thf;su;ev Thf;ex;ev

pinchev = Min Thf;ex;ev Tsu;ev ; Thf;ex;tp Tev;l ; Thf;su;tp Tsu;exp

T-s diagram :

s1 = s fluid$ ; T =tex;pp ; P =psu;ev

t1 = tex;pp

p1 = psu;ev

h1 = hex;pp

s2 = s fluid$ ; T =Tex;liq;rec ; P =psu;ev

t2 = Tex;liq;rec

p2 = psu;ev

h2 = hex;liq;rec

s3 = s fluid$ ; P =pev;l ; x =0

t3 = Tev;l

p3 = pev;l

h3 = hev;l

s4 = s fluid$ ; P =pev;v ; x =1


t4 = Tev;v

h4 = hev;v

p4 = pev;v

s5 = ssu;exp

t5 = Tsu;exp

h5 = hsu;exp

p5 = psu;exp

5 = Visc fluid$ ; T =Tsu;exp ; P =psu;exp

k5 = k fluid$ ; T =Tsu;exp ; P =psu;exp

s6 = s fluid$ ; h =hex;exp ; P =pex;exp

t6 = tex;exp

h6 = hex;exp

p6 = pex;exp

6 = Visc fluid$ ; T =tex;exp ; P =pex;exp

k6 = k fluid$ ; T =tex;exp ; P =pex;exp

6 = fluid$ ; T =tex;exp ; P =pex;exp

s7 = s fluid$ ; h =hex;vap;rec ; P =pex;vap;rec

t7 = Tex;vap;rec

h7 = hex;vap;rec

p7 = pex;vap;rec

s8 = Min s5 ; s fluid$ ; P =pcd;v ; x =1

t8 = Tcd;v

h8 = Min hex;exp ; hcd;v

p8 = Min pex;exp ; pcd;v

s9 = s fluid$ ; P =pcd;l ; x =0

t9 = Tcd;l

h9 = hcd;l

p9 = pcd;l


MM = MolarMass 'Toluene'

s10 = s fluid$ ; h =hex;cd ; P =pex;cd

t10 = Tex;cd

h10 = hex;cd

p10 = pex;cd

s11 = s1

t11 = t1

h11 = h1

p11 = p1

T profile in heat exhangers :

Thf;2 = Thf;ex;ev

Thf;3 = Thf;ex;tp

Thf;4 = Thf;su;tp

Thf;5 = thf;su;ev

Tcf;7 = Tcf;ex;cd

Tcf;8 = Tcf;ex;tp

Tcf;9 = Tcf;su;tp

Tcf;10 = tcf;su;cd

Efficiency :

wexp = hsu;exp hex;exp

wpp = hex;pp hsu;pp

wnet = wexp wpp

qev = hex;ev hsu;ev

cycle = wexp wpp

qev

W net = wnet M

W exp = wexp M

W pp = wpp M

Second law efficiency:


Ehf = Mhf hhf;su;ev hhf;0 T0 shf;su;ev shf;0

shf;su;ev = s hf$ ; h =hhf;su;ev ; P =phf;ev

hhf;0 = h hf$ ; T =T0 ; P =phf;ev

shf;0 = s hf$ ; T =T0 ; P =phf;ev

II = W netEhf

Fluid quality at the end of the expansion :

x = x fluid$ ; h =hex;exp ; P =pex;exp

1000 1250 1500 1750 2000

-50

0

50

100

150

s [J/kg-K]

T [C

]

0,2 0,4 0,6 0,8

R245fa

Simple ORC Model SQ110918

Documents

Transcript of Simple ORC Model SQ110918