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Multi-objective approach for a combined heat and power geothermal plant optimization

Fabien Marty ORCID logo, Sabine Sochard, Sylvain Serra ORCID logo and Jean-Michel Reneaume

Abstract

This paper presents the simultaneous optimization of the design and operation in nominal conditions of a geothermal plant where the geothermal fluid is split into two streams to feed an Organic Rankine Cycle (ORC) and a District Heating Network (DHN). The topology of the DHN is also investigated. A Mixed Integer Non-Linear Programming (MINLP) optimization problem is formulated and solved using the GAMS software in order to determine the ORC sizing and the DHN topology. In this study, only R-245fa is used as ORC working fluid, an optional Internal Heat Exchanger (IHE) is considered in the ORC and consumers in DHN can be definite or optional. A multi-objective optimization is performed by maximizing the annual net profit and minimizing the total exergy losses in the plant. The weighted sum of objective functions is used to solve the problem. By varying the weight factor, a Pareto front is obtained and the distance to the ideal, but infeasible, solution enabled to choose the best compromise. Four different DHN topologies are observed depending on the weight factor. Using a suitable criterion to make a decision, the selected configuration corresponds to the most expanded DHN with the smallest value of profit. A sensitive analysis shows that, in case of lower geothermal temperature, it is possible to obtain a unique DHN topology whatever the weight factor.


Corresponding author: Sylvain Serra, Université de Pau et des Pays de l’Adour, E2S UPPA, LaTEP, Pau, France, E-mail:

Funding source: ADEME : Agence de la transition écologique

Nomenclature
A

heat transfer area, m2

BigM

high value coefficient

Constraints

refer to all constraints.

C p

specific heat capacity, J/kg/K

C TCI

investment cost, €

C TPC

annual working cost, € by year

d o

outside tube diameter, m

D direct

direct distance to the ideal solution

D normalized

normalized distance to the ideal solution

dist

distance, m

ex

specific mass exergy, J/kg

E ˙ x

exergy flow rate, W

Exist

existence (binary variable)

h

enthalpy, J/kg

L

tube length, m

m ˙

mass flow rate, kg/s

N t

number of tubes per pass

Obj

multi-objective function

P

pressure, Pa

Pinch

difference temperature at pinch the point in heat exchanger, K

Profit

annual profit, € by year

Q ˙

heat transfer rate, W

s

entropy, J/kg/K

S

sale, € by year

T

temperature, K

tx imp

corporate tax rate

Tx div

division rate

V ˙

volumetric flow rate, m3/h

Var

refer to all continuous variables

W ˙

mechanical work, W

Greek symbols
α

coefficient of decrease of temperature, K/km

ΔP

pressure drop, Pa

pressure drop (in pipe)

ΔT

temperature decrease in pipe, K

ρ

density, kg/m3

η

efficiency, %

ω

weight factor between the two objective functions

Subscripts and superscripts
0

reference

c/h

cold/hot fluid

cons

consumer

condensation

condensation

component

plant components

cw

cooling water

d

destruction (refer to exergy)

DHN

District Heating Network

District Heating Network

elec

electricity

evaporation

evaporation

exch

exchanger

gen

electrical generator

gw

geothermal water

heat

heat

i/j

refer to DHN nodes (producer and consumers)

IHE

Internal Heat Exchanger

Internal Heat Exchanger

in/out

inlet/outlet

is

isentropic

l

liquid

loss

losses (refer to exergy)

max

maximal

min

minimal

net

net electricity produced

outward/return

outward path/return path

ORC

Organic Rankine Cycle

Organic Rankine Cycle

path, ij

path between i and j

pipe

pipe

prod

producer

pump

pump

Q

heat losses (in pipe)

reinjection

geothermal water reinjection

return, i

outlet of consumer iafter mixing in return path

tot

total

turbine

turbine

user

DHN user

water

water

wf

working fluid

ΔP

pressure drop, Pa

pressure drop (in pipe)

Acronyms
CHP

Combined Heat and Power

DHN

District Heating Network

IHE

Internal Heat Exchanger

MINLP

Mixed Integer Non-Linear Programming

NLP

Non-Linear Programming

OF

Objective Function

ORC

Organic Rankine Cycle

SIC

Specific Investment Cost

Acknowledgment

The authors thank the ADEME through the “Appel à Manifestation d’Intérêts (AMI)”. They also thank the Enertime society, for its expertise about the ORC systems, and the “FONROCHE Géothermie” society, which is the coordinator of the FONGEOSEC project.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: The study was funded by ADEME : Agence de la transition écologique.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A: Development of equations presented in Table 5

Equations (6) and (7) are used to determine exergy flow destruction for each component of the plant.

For heat exchangers:

E ˙ x d , e x c h = m ˙ h [ h h , i n h 0 T 0 ( s h , i n s 0 ) ] + m ˙ c [ h c , i n h 0 T 0 ( s c , i n s 0 ) ] m ˙ h [ h h , o u t h 0 T 0 ( s h , o u t s 0 ) ] m ˙ c [ h c , o u t h 0 T 0 ( s c , o u t s 0 ) ]

After simplification and considering m ˙ h ( h h , i n h h , o u t ) = m ˙ c ( h c , o u t h c , i n ) equation becomes

E ˙ x d , e x c h = T 0 [ m ˙ h ( s h , o u t s h , i n ) + m ˙ c ( s c , o u t s c , i n ) ]

For turbine:

E ˙ x d , t u r b i n e = m ˙ w f [ h t u r b i n e , i n h t u r b i n e , o u t T 0 ( s t u r b i n e , i n s t u r b i n e , o u t ) ] W ˙ e l e c

with W ˙ e l e c corresponds to the produced electricity equal to

W ˙ e l e c =   η g e n W ˙ t u r b i n e = η g e n m ˙ w f ( h t u r b i n e , i n h t u r b i n e , o u t )

then

E ˙ x d , t u r b i n e = m ˙ w f [ ( 1 η g e n ) ( h t u r b i n e , i n h t u r b i n e , o u t ) T 0 ( s t u r b i n e , i n s t u r b i n e , o u t ) ]

For ORC pump:

E ˙ x d , O R C p u m p = m ˙ w f [ h O R C p u m p , i n h O R C p u m p , o u t T 0 ( s O R C p u m p , i n s O R C p u m p , o u t ) ] + W ˙ O R C p u m p

With W ˙ O R C p u m p = m ˙ w f ( h O R C p u m p , o u t h O R C p u m p , i n ) then

E ˙ x d , O R C p u m p = m ˙ w f T 0 ( s O R C p u m p , o u t s O R C p u m p , i n )

For DHN pump:

In the same way than for ORC pump, the obtained expression is

E ˙ x d , D H N p u m p = m ˙ D H N T 0 ( s D H N p u m p , o u t s D H N p u m p , i n )

For water, entropy difference is obtained by Equation (8)

E ˙ x d , D H N p u m p = m ˙ D H N T 0 T D H N p u m p , i n T D H N p u m p , o u t C p l , w a t e r T d T

First, C p l , w a t e r is assumed constant between the inlet and the outlet of the pump, expression is then

E ˙ x d , D H N p u m p = m ˙ D H N T 0 C p l , w a t e r ln T D H N p u m p , o u t T D H N p u m p , i n

Next, the increase temperature in pump is low (0.05 K), logarithm can be approximated by a first-order limited development around 1.

E ˙ x d , D H N p u m p = m ˙ D H N T 0 C p l , w a t e r T D H N p u m p , o u t T D H N p u m p , i n T D H N p u m p , i n

Since C p l , w a t e r is assumed constant, this corresponds to

E ˙ x d , D H N p u m p = W ˙ D H N p u m p T 0 T D H N p u m p , i n

For pressure drop in pipes:

The destroyed exergy linked to pressure drops is due to the work dissipated by friction and is determined by:

E ˙ x d , Δ P = m ˙ D H N [ h D H N p u m p , o u t h D H N p u m p , i n T 0 ( s D H N p u m p , o u t s D H N p u m p , i n ) ]

Which corresponds to

E ˙ x d , Δ P =   W ˙ D H N p u m p E ˙ x d , D H N p u m p

By replacing with the previous expression

E ˙ x d , Δ P =   W ˙ D H N p u m p   ( 1 T 0 T D H N p u m p , i n )

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Received: 2020-02-07
Accepted: 2020-05-29
Published Online: 2020-08-06

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