cogeneration salt recrystallization

Computers and Chemical Engineering 29 (2005) 14911505

Dynamic modelling and simulation oftallitos a,e Miis, 1045 Estar

2005

Abstract

The aim o rocessatmospheric conditions on the system. For this main goal it was built a dynamic model, which includes the cogeneration system, the plateheat exchangers and the salt production unit.

The cogeneration system was modelled and analysed in GateCycle 5.34.0.r. and the interface variables were used as input of the dynamicmodel of the remaining integrated process. This model was developed and exploited through gPROMS 2.3.

Some parsystem.

The best seach situatioto optimisehaving a tu

The efficiHowever, thof 7080%, 2005 Else

Keywords: D

1. Introdu

Processies as a newthe efficienprocess anoptimal strplex plantsmaterials asystematic

Up to 1were consi

CorresponE-mail ad

0098-1354/$doi:10.1016/jticular issues (start-up, scheduling and atmospheric conditions) were investigated to forecast the performance of the integrated

tart-up conditions were established. Several atmospheric conditions were studied and the minimum number of ponds required forn was calculated. The scheduling of the evaporation ponds in operation was also investigated to enhance the salt production and

the salt harvesting. The process simulation indicated that it is better to work with the corresponding minimum number of ponds,rbo pond that receives a larger quantity of heated brine.ency of the cogeneration system (thermal plus electric power divided by natural gas consumption) was approximately 92%.e global process efficiency (accounting for energy losses in the evaporation step of the salt production process) was in the rangedepending on the atmospheric and operational conditions considered.vier Ltd. All rights reserved.

ynamic modelling; Optimisation; Process integration; Industrial case study; Cogeneration; gPROMS; Crystallization process

ction

integration (PI) emerged in the decade of eight-area in Chemical Engineering with emphasis on

t use of primary energy by analysing the wholed not the stand alone units to find the best andeams heat exchanger network. Currently the com-are characterized by the existence of recycles of

nd energy making necessary their integration in aand rational way (Linnhoff et al., 1982).990, Process Synthesis and Process Integrationdered separately although complementary activi-

ding author.dress: [email protected] (H.A. Matos).

ties. The original definition in 1995 from International En-ergy Agency (IEA) states Process Integration as: System-atic and General Methods for Designing Integrated Pro-duction Systems, ranging from Individual Processes to To-tal Sites, with special emphasis on theEfficient Use ofEnergy and reducing Environmental Effects (Gundersen,2002).

However, in recent years the borderline between these twoactivities has practically disappeared (Smith, 1995). There-fore, Process Integration appears now as an optimal integra-tion of different units in process system and this goal is effi-ciently achieved using process simulation that was a formermain tool for analysis and synthesis. The power of modernsimulation techniques enables the study of complex processesclose to the real situation.

see front matter 2005 Elsevier Ltd. All rights reserved..compchemeng.2005.02.015integrated with a salt recrysRaquel Durana Moita a, Henrique A. Ma

Clemente Pedro Nunes a, Jorga Instituto Superior TecnicoDEQ, Av. Rovisco Pa

b Quimigal, Quinta da Industria, 3864-75Available online 9 March

f this study is to optimise a Portuguese industrial three integrated pa cogeneration systemzation process, Cristina Fernandes a,

guel Prior b

9-001 Lisboa, Portugalreja, Portugal

system, by studying the effect of some operational and

1492 R.D. Moita et al. / Computers and Chemical Engineering 29 (2005) 14911505

Nomenclature

A area (m2)Cp heat capacity (MJ/(kg C))Cp,air air heat capacity (J/(kg K))Econv energy loss by convection (MJ/(m2 h))Eevap enthalpy of the vapor water stream (MJ/(m2 h))ENaClpp enthalpy of the salt precipitated stream

(MJ/(m2 h))Erad energy loss by radiation (MJ/(m2 h))Esolar net solar energy that is effectively absorbed

through the brine (MJ/(m2 h))Ethermal effective thermal power (MJ/h)fEntP,i fraction of the brine flow rate QHE that is sent

to each pond ifExitP,i fraction of the brine flow rate (Qchannel) that

leaves each pond iFM salt mass fraction (%)hwater 1 enthalpy of the inlet water stream of the

economizer at temperature T1 (kJ/kg)hwater 2 enthalpy of the outlet water stream of the

economizer at temperature T2 (kJ/kg)H enthalpy of the liquid brine stream (MJ/h)HL,Tap,Ei enthalpy of the liquid brine stream entering

in Ei through the tap, per unit length of theelement (MJ/(h m))

HT total enthalpy of the accumulated brine(MJ/m2)

Kair air conductivity (W/(m K))Lc characteristic length (m)Mevap water evaporation rate (kg/(m2 h))MNaclpp salt precipitation rate (kg/(m2 h))MNaclpp,total total mass of salt precipitated (kg)Mwater mass flow rate of the water circulating in the

economizer (kg/h)n number of moles (moles)P water vapour partial pressure at temperature T

(Pa)Patm atmospheric pressure (Pa)PGateCycle thermal power determined through

GateCycle (MJ/h)Q brine volumetric flow rate (m3/h)QL,Tap,Ei brine volumetric flow rate entering in Ei

through the pond tap, per unit length of theelement (m3/(h m))

S salinity (%)Sol NaCl salt solubility in the water

(g NaCl/100g H2O)T brine temperature (C)T1 temperature of the cold water entering in the

economizer (C)T2 temperature of the heated water leaving from

the economizer (C)

Tair Tdew-poinTskyUHE

VwindWXXmZ

Greek syHdiss

Tlm

evapair

0

air

Subscripconv

EiEntP,ievapExitP,iFHEradsatSolarTap

DomainsLt

AbbreviaCSEGPEPHE

Severalused in theactivities toof the indu2002).air temperature ( C)t dew-point temperature (C)sky temperature (C)service overall heat transfer coefficient of theplate heat exchanger (MJ/(m2 C h))wind velocity (m/s)

pond width (m)salt concentration in the brine solution (kg/m3)mole fraction of the waterbrine level (m)

mbolsheat of dissolution of the salt in the water(MJ/kg NaCl)logarithmic mean temperature difference (C)surface emissivityair relative humiditywater latent heat of vaporization (MJ/kg)air viscosity (N/(s m2))brine density (kg/m3)auxiliary variable used in brine densitycalculations (kg/m3)air density (kg/m3)StefanBoltzmann constant (W/(m2 K4))

ts and superscriptsconvectioninfinitesimal element i in each pondbrine stream entering in each pond ievaporationbrine stream exiting from each pond ifresh treated brineplate heat exchangerradiationsaturationsolar energypond tap for the heated brine entrance

axial (m)time (h)

tionscogeneration system efficiencyglobal process efficiencyplate heat exchanger

powerful systematic methodologies have beenlast two decades to support Process Integrationachieve a parametric and structural optimisation

strial sites (Relvas, Fernandes, Matos, & Nunes,

R.D. Moita et al. / Computers and Chemical Engineering 29 (2005) 14911505 1493

The main goal of this study is to build a model of anindustrial integrated system including three processes, andthrough simulation identify the best operational conditionsto maximize its global energy efficiency and to minimize theenvironmental impact, reducing the primary energy supplyand the raw materials usage. This industrial site is located atCarrico, Pombal (Portugal) and includes: a salt cavern construction process to build a natural gas

reservoir (owned by Transgas); a gas turbine cogeneration system (owned by Galp Power); a salt recrystallization process (owned by Renoeste).

The three processes considered as separated units are nei-ther efficient nor feasible. The integration of these three inde-pendent units, as shown in Fig. 1, improves the global systemefficiency. The leaching programme to construct the cavernsfor a future natural gas storage generates the brine needed tofeed the salt recrystallization ponds, minimizing the environ-mental damage. Those caverns will allow a strategic storagefor the Portuguese Natural Gas supply system, providing abuffer for eventual future supply fluctuations on the nationalsupply and consumption. The cogeneration system providesthe electricport towardassociatedprocess thrface betweeefficiency.Renoeste iindustrial smitted for p

2. Framew

A dynamthe cogene

rated sy

developed to determine the best conditions to maximize theglobal energy efficiency. This framework allows a very widerange of studies such as:

Analyse the behaviour and feasibility of the integrated pro-cesses, by verifying if crucial variables values (such asstream temperatures) are within the advisable operationalintervals, and determine the global energy efficiency.

Study by simulation several scenarios of operating condi-tions such as start up or ponds working scheduling.

Study the effect of different atmospheric cases on the per-formance of the integrated process.

To obtain a global description of this integrated system, itwas considered mainly the following procedure and tools:

1. modelling and simulation of the cogeneration systemthrough GateCycle 5.34.0.r of the GE Enter Software;

2. determination of a thermal power correlation, throughTableCurve 3D from SPSS Inc., using data from cogen-eration system;

3. design of a dynamic distributed model of the whole in-tegrated system (cogeneration, plate heat exchangers and

lt prod

sing dvariabg otheoncen

al effi

nalysi

e cogsts ofts assour se.5 m2,al power to satisfy the processes needs and to ex-s the regional net the remaining production. Its

thermal energy is used in the salt recrystallizationough a set of plate heat exchangers as an inter-n the two processes, improving the global energyThe pure salt (NaCl) produced in the ponds bys the main raw material to Quimigals chemicalite at Estarreja (Aveiro) (Moita et al., 2004, sub-ublication).

ork developed

ic model of the whole process, which includesration system and the salt production unit, was

Fig. 1. The three processes integ

sa

Ustateamon

and ctherm

3. A

Thconsiand iinto f2302stem.

uction process) via gPROMS 2.3 of the PSE Ltd.ifferent atmospheric and operational conditions asles it is possible to obtain as output of the model,r variables, the pond level, the brine temperature

tration profiles, the salt production and the processciency.

s of the cogeneration system

eneration system installed at the industrial sitea RollsRoyce natural gas turbine (RB211T DLE)ociated economizer. The economizer is dividedrial set of tubes, each having a superficial area ofin which circulates the water that will be heated


eCycle

with the eximately 50

The cogGateCycleallows to meral energyeration sysgas turbine

Fig. 2 shtem in this svalues for t

This moables, such

rculatrmancg. 3 illrmanc

umptiog. 4 hir enteable aom thhe air

FFig. 2. Model structure of the cogeneration system in Gat

haust turbine gases (leaving the turbine at approx-0 C).eneration system is modelled in the simulator5.34.0.r of the GE Enter Software. This softwareodel, simulate and predict the performance of sev-systems, such as combined cycle plants, cogen-

tems, combined heat-and-power plants, advanceds cycles, etc. (GateCycle Software Website, 2004).ows the model structure of the cogeneration sys-imulator, the general required input and the output

ter ciperfo

Fiperfocons

Fiwateavail

Frthat the nominal operating conditions.del allows the study of the influence of some vari-as the air and natural gas temperatures or the wa-

system respcauses a re

around 3%

ig. 3. Variation of net electric power, natural gas consumption, exhaust gases temp5.34.0.r (nominal conditions).

ion conditions, on the gas turbine and economizere.ustrates the effect of air temperature on gas turbinee, namely the net electric power, natural gas heatn, exhaust gases temperature and mass flow rate.ghlights the influence of air temperature and coldring into the economizer on the thermal powernd on the exit gases temperature.e analysis of these figures it is possible to concludetemperature strongly influences the cogeneration

onse: an increase of 10 C in Tair (above 15 C)

duction of almost 10% in the electric power andin the thermal power. The thermal power avail-

erature and mass flow rate with air temperature.


Fig. 4. Variation of thermal power and exit gases temperature with air temperature and with cold water temperature.

able is also very dependent on the temperature of the coldwater entering in the economizer (T1): an increase of 10 Cin T1 leadsFurthermoraround 15

Fig. 5 shthe economwater tempadvisable owater in th

Throughthat air husystem andincreases that the site (

It was apower as atemperaturwhich wasin the next

4. Dynamic model of the integrated system

e integrated system includes the cogeneration system,our plunit ins, a fe. This

tions ue glos all th

icalcn of mhermofer, etal mod

Cogen

e cogr corrto a reduction of around 2% in the thermal power.e, the maximum thermal power is reached at TairC, with the smallest working T1 value.ows the temperature of the heated water leavingizer (T2) as a function of Tair and of the cold

erature T1. In this figure it is also represented theperational temperature interval for the circulatione economizer: T2 = 90 5 C and T1 = 65 5 C.

simulation in GateCycle it was also concludedmidity does not have a significant effect on the

that the pre-heating of the natural gas slightlye turbine efficiency in the temperature range used35 C).lso possible to obtain a correlation of thermalfunction of cold water temperature (T1) and air

e (Tair), using TableCurve 3D from SPSS Inc.,included in the integrated process model discussedsection.

Ththe fThispondFig. 6equa

Thcludephysvatioand ttransment

4.1.

ThpoweFig. 5. Variation of heated water temperature with air temperature aate heat exchangers and the salt production unit.volves, mainly, a maximum of six recrystallizationed tank and a collecting channel, as illustrated insection presents all the algebraic and differentialsed to model each one of these physical units.bal dynamic model of the integrated process in-ese mathematical equations. It is based on known

hemical relationships, which includes the conser-ass and energy, as well as transport phenomenadynamics relationships (phase equilibrium, heat

c.), and therefore it can be classified as a funda-el (Bequette, 1998).

eration system

eneration system is modelled via the thermalelation obtained through the simulated values ofnd with cold water temperature.


xchang

the cogenedue to genepends on thentering inther heat na pseudo-sentering wa

PGateCycle =

EThermal =The con

Table 1.

4.2. Plate

The planecting settallization pequation, hterial balanaccumulati

The PHin a countechanger sin

qual:

rmal =

e the souling(AHE)rence

= (T

Table 1Constants a, b

a

45 078Fig. 6. Integrated process: cogeneration system, plate e

ration systemEq. (1), which was reduced in 3%ral energy losses in the pathwayEq. (2). It de-e temperature of the air (Tair) and of the cold waterthe economizer (T1). In this system there is nei-

or mass accumulation, that is, it is treated as if inteady-state since there is a time variation on theter stream and atmospheric conditions:[a+ bT1 +

8i=1

ciTiair

]3.6 (1)

0.97P (2)

are e

EThe4

wherder farea

diffe

TlmGateCycle

stant values for a, b and c1 to c8, are given in

heat exchangers set

te heat exchangers (PHE) are the physical con-between the cogeneration system and the recrys-rocess. The PHE set was included using its design

eat balances at both water and brine sides and ma-ces, assuming there is neither mass nor energyon inside the exchangers.E design equation Eq. (3) (Kakac & Liu, 2002),r-current flow arrangement, is applied to each ex-ce it is considered that all four heat exchangers

T1, T2, Ttaheated wattank and th

The PHbased on thues in Gatand hwater 2the triple-pfor the diff500 kPa; ou

EThermal =hwater1 = 4hwater 2 = 4

and c1 to c8, for the thermal power correlation (Eq. (1))b c1 c2 c3 c4 c588.73 910.5 244.6 40.49 3.56 0.17ers and salt production unit.

UHEAHE Tlm (3)

ervice overall heat transfer coefficient (UHE), un-conditions, is 24.69 MJ/(m2 C h), the exchangeris 78.2 m2 and the logarithmic mean temperatureTlm is a function given by:

2 THE) (T1 Ttank)ln[T2THET1Ttank

] (4)

nk and THE are the temperatures of the cold ander in the economizer and of the exit streams of thee PHE, respectively.E heat balance on the water side (Eq. (5)) ise linear correlations obtained via simulated val-eCycle for the water stream enthalpies (hwater 1). The zero-point of enthalpy is liquid water atoint: 0 C (GateCycle, 2001). It is also accountederent pressures values in the water streams (inlet:tlet: 490 kPa):Mwater[hwater2 hwater1]103 (5).1835T1 + 0.02714 (6).2040T2 1.5812 (7)

c6 c7 c8

0.00457 6.356 105 3.577 107


: solid

Mwater is ththe econom

Eq. (8) rin which Hinlet stream

EThermal =

The enthresponds to25 C (thatthalpy of acentrationdeterminedHoughen, W

H = Q[(+X

where Cwpues calculand Green0.8712 1lution Hdrelation basWagman et

Hdiss =[

where n recomponent

Thus, ththrough eqquate value

The brintemperaturtion was obdifferent tein Perry anMathemati

FM(F

0.5

1001

e Qalculalt (E

pitati

tank

Xtank

Splitt

fter lis di. Thi

red topond

P,i =

PondFig. 7. Phase thermodynamics equilibrium

e mass flow rate of the water stream circulating inizer and is equal to 1.47 106 kg/h.epresents the PHE heat balance on the brine side,HE and Htank are the enthalpies of the outlet ands in the exchangers set, respectively:

HHE Htank (8)

alpy reference state considered in all streams cor-the components in their state of aggregation atis, liquid water and solid NaCl). Thus, the en-

liquid brine stream with a flow rate (Q), salt con-(X), temperature (T) and brine density () will be

through Eq. (9) (Coulson & Richardson, 1989;atson, & Ragatz, 1972):

X)Cwaterp (T 25)+XCNaClp (T 25)Hdiss] (9)

ater and CNaClp are mean heat capacity val-ated using the expressions given by Perry

(1997), and are equal to 4.189 103 and03 MJ/(kg C), respectively. The heat of disso-iss (Eq. (10)) is determined through a linear cor-ed on the enthalpies of formation values given byal. (1982), for X> 150 kg/m3:(

nwater) ]

3

nate

=

0 =

Thare c

the sapreci

Qtank

Qtank

4.3.

AbrineFig. 6requieach

QEnt

4.4.

1.3712

nNaCl+ 19.4063 10 (10)

presents the number of moles of the respective.e enthalpies values HHE and Htank are determineduations Eqs. (9) and (10), by considering the ade-s for Q, X, T and .e density is related with brine concentration and

e values through Eqs. (11) and (12). This correla-tained using the tabulated values of the density atmperatures and salt mass fractions (FM) presentedd Green (1997). The expression was modified inca 4.1.0.9 of the Wolfram Research Inc. to elimi-

As it isinvolves afor modell

The dyand differelibrium th(see Fig. 7in the variathe expectthe heatedtaps in eacwell as co, liquid and gas.

M = 100X/):

0 +20 + 400X(7.7780 0.0063176T )

(11)

.23 0.22715T 0.0020480T 2 (12)

and X values of the brine stream leaving the PHEted via the material balances for the brine and for

qs. (13) and (14)). It is assumed that there is no salton within the exchangers:

= QHEHE (13)

= QHEXHE (14)

er unit

eaving the plate heat exchangers set, the heatedvided into the working ponds, as it can be seen ins is an isothermal process, and therefore it is onlydetermine the brine flow rate fraction entering in

:

fEntP,iQHE, i = 1, . . . , 6 (15)

unitillustrated in Fig. 6, the salt production processmaximum of six recrystallization ponds, which

ing purposes are considered to be equal.namic model proposed is built through algebraicntial equations taking into account the phase equi-ermodynamics: solid, liquid and gas equilibrium). It is a distributed model, since there is a changebles within both time and axial domain, providing

ed profile inside the ponds and allowing modellingbrine entrance through one or both the two existingh pond. It involves material and heat balances, as

nstitutive relationships (Bequette, 1998).


4.4.1. Material balancesConsider a parallelepiped volume element V (in the ax-

ial domain L) and a time element t, in which there is acontinuouselement, wthe law of min the elemtion, result(Bequette,

EiW(Z)t

where W,infinitesim

QL,Tap,Etap, per unipond, locatis either equtotal flow eflow fractioelement lenof element

The watconcentrati(T) and ofhumidity mixed lami

Mevap =

[

Lc is the cdirection isgiven by:

Xm = 1+

and the salinity S:

S = 100 X

(19)

rine anir temtion Eand a

exp[

+ 4.1

e saltinfini

alt preumedn of tvaluelpp,Ei

(Eq. (2. If thee balauatio

.05

(XEL

uatio

lpp,Ei

XEiZ

t

e brigh eq

=Sol

e the s26) (L

ity sa:

35.51

e toClpp,to

NaClpp,tbrine flow, a brine entrance through the tap in theater evaporation and salt precipitation. Applyingass conservation for the brine solution contained

ent considered, and after mathematical manipula-s into the brine material balance equation Eq. (16)1998):

= (EiQEi)L

Mevap,EiW MNaClpp,EiW+QL,Tap,EiTap,Ei (16)

the pond width, is 54.8 m and Ei represents theal element i.i is the brine flow rate entering in Ei through thet length of the element. There are two taps in eached in specific axial positions. Therefore, QL,Tap,Eial to 0 (no tap exists in the element) or equal to the

ntering the pond multiplied by the brine entrancen in the tap (between 0 and 1) and divided by thegth (pond length182.5 m divided by the number

s considered).

er evaporation rate (Mevap) is a function of the salton (X), of the temperature of the brine solutionthe atmospheric conditions (air temperature Tair,and wind velocity Vwind), and corresponds to thenar-turbulent flow regime (Sartori, 1991, 2000):

0.00407V 0.8windL0.2c 0.01107L1c ] [XmPbrine Pair]3600

Patm(17)

haracteristic length (equal to 54.8 m when windnorth), and the mole fraction of the water Xm is

10.621 S100S

(18)

Pband aequabrine

P =

Thsame

the sis asstratiotionMNaCtion(21))by th

EqXEi = Xsat,Ei + 0

XEiW (Z)t

=

EqMNaC

W (

Ththrou

Xsat

wherEq. (densvalue

Sol =

Th(MNa(MXdPair are the water vapour partial pressure at brineperature, respectively, and are determined throughq. (20) (Perry & Green, 1997) by considering their temperatures:

73.649 7258.2T + 273.15 7.3037 ln[T + 273.15]

653 106(T + 273.15)2]

(20)

material balance is determined by applying to thetesimal element the law of mass conservation forsented in the brine solution (Eqs. (21)(24)). Itthat precipitation only occurs when the concen-

he brine solution is 0.05 kg/m3 above its satura-(XEi Xsat,Ei 0.05). The salt precipitation rateis determined through the material balance equa-2)) and the salt concentration value is fixed (Eq.solution is not supersaturated,Xwill be computednce equation (Eq. (24)), with MNaClpp,Ei = 0:ns used if XEi Xsat,Ei 0.05:

(21)

iQEi) MNaClpp,EiW +QL,Tap,EiXTap,Ei (22)

ns used if XEi Xsat,Ei < 0.05= 0 (23)) = (XEiQEi)

L+QL,Tap,EiXTap,Ei (24)

ne saturation concentration Xsat is calculateduation Eq. (25):Sol+ 100sat (25)

alt solubility in the water Sol is given by equationanger & Offermann, 1982), and the saturation

t by equations Eqs. (11) and (12), using the Xsat

49 0.23125T0.0069163T

(26)

tal salt mass obtained in the whole pondtal) is determined by:

total) = L=182.5L=0

MNaClpp,EiW dL (27)


4.4.2. Energy balancesThe same parallelepiped volume element V and time

element t were considered. In this case, it will also be ac-counted fotion, as wethe brine sosulting ene

W(HT,Ei)

t

The enthalare comput)Ei and (Q

The totthrough eqstate as be(Hdiss,Ei)and X value

HT = Z[(+X

The ententhalpy re

Eevap = Mwith the waand the latebased on th

evap = [25Thus, th

through Eqelement Ei

The radsurface (Er(IncroperaErad = [

where isStefanBolTsky is the1996):

Tsky = [Tai

The dewperature an

sented by Perry and Green (1997), and is computed by:Pdew-point = Pair (34)

ew-poipointned thecauseare e

ndent(air teminede (Inc= [d

constarties:

0.037

871K

e they (airs, ass giveair te0.30.e enthelem

lpp,Ei

e exthere,e time(10 y), at

tion thion anum o

eWitt,o-Diesuns

A valuis refleasses

nergybed ben (19depth

. Bous the min thefor th

entratir the energy losses due to radiation and convec-ll as the solar energy, which is absorbed throughlution contained in the defined element. The re-

rgy balance is given by:

= (HEi)L

Eevap,EiW Erad,EiWEconv,EiW + ENaclpp,EiW + Esolar,EiW+HL,Tap,Ei (28)

py of the liquid brine streams HEi and HL,Tap,Eied via equations Eqs. (9) and (10), using (Q, X, T,L, X, T, )Tap,Ei values, respectively.

al enthalpy in the element HT,Ei is calculateduation Eq. (29), for the same enthalpy referencefore, and the heat of dissolution in the elementdetermined by Eq. (10), with the corresponding Ts of Ei:

X)Cwaterp (T 25)+XCNaClp (T 25)Hdiss] (29)

halpy of a vapor water stream, according to theference state defined, is determined by:

evap[evap + Cwaterp (T 25)] (30)ter evaporation rate Mevap determined by Eq. (17)nt heat of vaporizationevap by a linear correlatione values given by Daubert (1985):03.0 2.432T ]103 (31)e enthalpy stream value Eevap,Ei is computeds. (30) and (31) at the brine temperature in the

.iation energy losses through the horizontal brinead) depends on the sky and brine temperatures& DeWitt, 2001):(T + 273.15)4 (Tsky + 273.15)4]3.6 103

(32)the surface emissivity (equal to 0.95), is thetzmann constant (5.67 108 W/(m2 K4)) andsky temperature calculated by Eq. (33) (Sartori,

r + 273.15][

0.8+ Tdew-point250

]1/4 273.15 (33)

-point temperature is correlated with the air tem-d humidity through the psychometric charts pre-

Pddew-termi

Btheredepetionsdeterregim

Econv

Theprope

d1 =

d2 =whercositlationvaluemean

d2 = 2Th

in the

ENaC

Thmospon thvalue(2004radiasorptis a s& DCastrusingNASfacerest pthe eabsorNielsbrine

4.4.3A

tionsfinedconcnt and Pair are the water vapour partial pressure atand dry air temperature, respectively, and are de-ough equation Eq. (20), by replacing those values.of the air movement above the liquid brine surface

nergy losses due to forced convection. These areon both brine temperature and atmospheric condi-mperature Tair and wind velocity Vwind), and areby considering the mixed laminar-turbulent flowropera & DeWitt, 2001):

1V0.8windL

0.2c d2L1c ][T Tair]3.6 103 (35)

nts values d1 and d2 depend on the air physical

K2/3air C

1/3p,air

7/15air

0.8air (36)

2/3air C

1/3p,air

1/3air (37)

air conductivity (Kair), heat capacity (Cp,air), vis-) and density (air) are calculated through corre-a function of temperature, based on the tabulatedn by Perry and Green (1997). Thus, using themperature value of 25 C gives: d1 = 6.006 and

alpy of the salt (NaCl solid) precipitated stream,ent Ei, is computed by:

= CNaClp (TEi 25)MNaClpp,Ei (38)raterrestrial solar radiation, at the top of the at-depends on the geographic coordinates as well asof the day, month and year. Its monthly averageears data) can be retrieved from NASA Websitelatitude: 39.983 and longitude: 8.8. The solarat reaches the earths surface is lower due to ab-d scattering by the atmospheric constituents, andf the direct and diffuse contributions (Incropera2001). These values are estimated through the

z, Aladaos-Arboledas, and Jimenez (1989) work,hine data collected at the site and the retrievedes. Part of the radiation that reaches the brine sur-cted (Weinberger, 1964), part is absorbed and thethrough. The net solar energy value considered inbalance equation Eq. (28),Esolar,Ei, is the radiationy the brine, which is calculated using the Rabl and75) work, assuming a light path of two times the.

ndary and initial conditionsodel includes first order partial differential equa-spatial domain boundary conditions must be de-

e distributed state variables, namely, for the brineon (Eq. (39)), temperature (Eq. (40)), flow rate


(Eq. (41)) and salt precipitation rate (Eq. (42)):X

L

L=0

= 0 (39)

T

L

L=0

=

Q|L=0 = 0MNaClpp

L

It is alsovariables, tlevel (Z), beach eleme(MNaCl,total

4.5. Chann

The brintank througnel will bestate condievaporationand therefoered to be athe tank (EQExitP,i =

The temthe channein the exit s

Xchannel =

Tchannel =

4.6. Tank u

The tanproductionbe seen in Flected in ththen sent topurge. It isequations,ances and istate variab

Equatiorial balanceinto accouning the smastirring due

there is no salt precipitation:

tankAtank(Ztank) = QFF +Qchannelchannel

rine dEqs. (ms. Thtank, repute

tank vf 4 m

ual toe brin

minedequatydroded tos. This brineeen th

=

e brinassoci

k =

n a stamputetion anlem, dtion Ederiva48): Ve corq. (4(Xta

e tanto then and

idered

(HT0 (40)

(41)

=0 = 0 (42)necessary to define the initial values of the state

hat is, at time zero. Initial values for the brinerine concentration (XEi) and temperature (TEi) innt Ei, as well as for the total salt mass precipitated), are given.

el unit

e leaving from each working pond flows to theh the channel. For modelling purposes, the chan-

considered as a collecting unit only. It is in steady-tions, without neither salt precipitation nor water. All hydrodynamics phenomenon are ignored,re the brine flow rate leaving each pond is consid-fraction of the total brine flow rate that goes into

q. (43)):fExitP,iQchannel, i = 1, . . . , 6 (43)perature and salt concentration of the brine leavingl is the weighted mean of its corresponding valuestreams from the ponds (Eqs. (44) and (45)):6

i=1XExitP,iQExitP,i6i=1QExitP,i

(44)

6i=1TExitP,iQExitP,i6

i=1QExitP,i(45)

nit

k is the physical connecting unit between the saltprocess and the plate heat exchangers set, as it canig. 6. Through this unit it is received the brine col-e channel, mixed with the fresh treated brine, and

the heat exchangers set, discounting the systemmodeled using algebraic and ordinary differentialwhich consist in the brine and salt material bal-ts energy balance. It is a lumped model, since theles change only with time (Bequette, 1998).n Eq. (46) represents the macroscopic brine mate-, assuming a perfectly mixed system, and takingt for all entering and exiting streams. Consider-ll dimensions of the tank and its permanent fluidto the strong pumps suction, it is assumed that

The btionsstreaandTis comand X(Lc) ois eq

ThdeterextraAll hsiderpondpondbetw

Ztank

Thalso

Ztan

t

Wheto coequaprobequatimeand (

Thtion E

Atank

ThDuediatiocons

Atankt

Qpurgetank QtanktankMevap,tankAtank (46)

ensity value of each stream is determined by equa-11) and (12), usingX and T values on its respectivee purge stream X and T values are equal to Xtankspectively. The water evaporation rate (Mevap,tank)

d by equation Eq. (17) replacing T andXwith Ttankalues, and by considering a characteristic length, if wind direction is north. Tank area value (Atank)40 m2.e flow rate collected by the channel (Qchannel) isthrough Eq. (46), and therefore it is necessary an

ion to calculate the brine level in the tankZtank.ynamics phenomenon are ignored, so Ztank is con-be associated with the brine level inside all thes value is obtained by the weighted mean of the

levels (Zi, i= 1, . . ., 6) plus the 50 cm differencee tank and ponds floor (Eq. (47)):6i=1ZiQExitP,i

6i=1QExitP,i

+ 0.5 (47)

e level time variation inside the tank (Ztank/t) isated with its variation inside the ponds:

6i=1

[Zit

]QExitP,i6

i=1QExitP,i(48)

te variable is specified in a DAE system in ordera term on the right hand side of a differentialindex problem could arise. To avoid this index

ue to the calculation of the state variable Ztank byq. (47), it was used an auxiliary variable for thetive of the tank brine level in equations Eqs. (46)AR = (Ztank)/t.responding salt material balance is given by equa-9):nkZtank)t

= QFXF +QchannelXchannelQpurgeXtank QtankXtank (49)

k energy balance equation is given by Eq. (50).tank small surface area the energy losses by ra-convection, as well as the solar energy, were not

:

,tank)t

= HF +Hchannel Hpurge HtankEevap,tankAtank (50)


The total enthalpy inside the tankHT,tank is calculated throughequation Eq. (29), withHdiss,tank value obtained by Eq. (10),using Ttank and Xtank values.

The enthalpy of the liquid brine streams HF, Hchannel,Hpurge and Htank are computed via equations Eqs. (9) and(10), using its (Q, X, T, ) respective values.

The enthalpy value Eevap,tank is determined by Eqs. (30)and (31), using Ttank.

The brine concentration and temperature initial values, attime zero, are given.

5. Dynamic simulations

The whole integrated system was modelled through thegeneral-purpose modelling, simulation and optimisation toolgPROMS2.3, of the Process System Enterprise Ltd. This soft-ware allows to adequately handling process discontinuities,lumped and distributed systems and many different types ofoperating procedures (gPROMS, 2004).

Fig. 8 is an information flow diagram illustrating the dy-namic model structure implemented in this software. Thereare five subical unit, inneeded to dthe brine flodensity ()

The gloas the Recrthe plate hepower (TP)FlowSeparindependen. . ., 6) all m(such as: eqcharacterizsalt concen

into account the brine received from each working pond al-lowing to characterize the brine entering in the feed tank(model Tank). Through this model Tank it is included the in-formation on the fresh treated brine fed to the recrystallizationunit and the purge of the system.

The external atmospheric conditions are included in themodels Heating and Pond i.

The model described in Section 4.4 is axially distributed.For this kind of systems the selection of an appropriate dis-cretisation method is crucial (gPROMS, 1998). For purelyconvective problems the finite method is suggested with ageneral rule: discretisation method opposite to the directionof the flow. As the axial domain goes from top to bottom itwas chosen the backward finite difference method.

The total number of model variables depends on the num-ber of discretisation intervals used in the axial distributed do-main. For 20 intervals its value is approximately 5800, whilefor 60 intervals is around 15,000. An increase of the numberof intervals requires a greater computational effort.

Among all the model variables, it is important to identifythe decision and the state variables. The decision variables arethe ones that allow verifying if the system response is within

gion onal inodel derature colle

2). Thderabrefullyvariabic conitions,rate of2 sum

sing ththroug

rated p-models, each corresponding to an industrial phys-cluding the algebraic and differential equationsescribe each system. Some variables referring tow rate (Q), concentration (X), temperature (T) andare used as connecting sub-models information.

bal model that includes all these units is labelledystallization Unit model. Model Heating refers toat exchangers equation set using also the thermalcorrelation determined previously. In the modelation the brine flow rate fraction that is sent to eacht pond is determined. In the model Pond i (i= 1,ass and heat balances equations and other relationsuilibrium, heat and mass transfer) are included toe the brine profiles (for instance: temperature andtration) inside the ponds. Model Channel takes

its reeratiothe mtempin thand Tconsibe castatesphercondflowTable

Ucess,

Fig. 8. Structure of the dynamic model of the integf working feasibility. In this case, to respect the op-tervals of the temperature of the circulation water,ecision variables would be either the heated watereT2 (withT2 = 90 5 C) or the brine temperaturecting channel (since it can be correlated with T1e state variables are independent variables with a

le influence in the system behaviour, and shouldanalysed. So, for the integrated process the main

les are: the number of ponds in service, the atmo-ditions, the fresh brine flow rate, the initial brinethe number of plate exchangers working and thethe brine pumped into the plate heat exchangers.marizes the model mathematical structure.

e developed dynamic model of the integrated pro-h simulation in gPROMS, it is possible to analyse

rocess in gPROMS 2.3.


Table 2Mathematical structure the dynamic model

Main input variables Main output variables Typical performance statistics for 60 elements

Atmospheric conditions (d(t)) Distributed Number of variablesTair, Vwind, , Esolar T Differential: 1114

X Algebraic: 14 538Operational conditions (u(t)) MNaClpp

Number of working ponds Mevap Number of equations: 15 652Taps used in each pondNumber of exchangers working Others Process time horizon: 1 monthBrine flow rate Qtank Z gPROMS execution time: 150 saFraction fEntP for each pond EthermalFresh treated brine: QF, XF, TF T1 and T2Initial conditions to the ponds and the tank: Z(0), T(0), X(0), MNaCl(0) Process efficiencies: CSE and GPE

u(t): input variables that can be manipulated to optimise the system performance.d(t): Input variables that correspond to external disturbances.

a Pentium 4, 2.0 GHz, 524 MB RAM.

the effect of some of these state variables on the system andto study so

5.1. Start-

Since itup the recrydeterminemum numbbrine flowatmospherisystem resrate. Amonconcludedthermal enthree pondstemperatursponse in tconditions.dependent

5.2. Scena

To addrescenarios oThus, four

nario there are four ponds in service receiving the thermalr throd scerst pof heating pocenariing siFig. 9): Tair =energr all secon

It wasworkirios 1f heatrio. T8 Culingarting2 C avaporonlys 3 athirdme scenarios in some special conditions.

up conditions

was necessary to have an operational plan to start-stallization process, several studies were made to

the best start-up conditions: function of the mini-er of ponds, the initial brine levels and the fresh

rate. The simulations allowed concluding that thec conditions have a very strong influence on theponse since they modify the water evaporationg several possible atmospheric conditions, it wasthat it is not possible to start the reception of theergy from the cogeneration system with less than

in service, to respect the operational intervals ofes. The brine level only influences the system re-he beginning, since it led to the same steady stateThe flow rate of fresh brine allowed is also very

on the evaporation rate.

rios of scheduling working ponds

ss one of the main objectives of this work severalf scheduling working ponds have been analysed.different scenarios were evaluated. In the first sce-

powesecon

the fitity oworklast swork(seewere

solarFo

in thevals.threescena

tity oscena

up tosched

StT= 2the esaltnarioTheFig. 9. Fraction of heated brine entering in each pond for sevugh an identical flow rate of heated brine. In thenario there are also four ponds working, howevernd is a turbo because it receives a larger quan-ed brine. The third scenario considers only threends, with one of them as a turbo pond. In theo there are four ponds involved but only three aremultaneously, and the first pond is also a turbo. The average atmospheric conditions considered12 C, Vwind = 4.5 m/s, humidity = 82% and net

y = 3.7 MW.cenarios, the temperatures of the water circulatingomizer are within their defined operational inter-observed that in the scenarios 3 and 4, with onlyng ponds, water evaporates up to 6% more than inand 2. Having a pond that receives a larger quan-

ed brine than the others is even a more favourablehe brine temperature in the turbo pond increases. Thus, amongst all scenarios the more efficientprocedure was the third one.from the initial status (no solid, level = 1.5 m,nd X= 215 kg/m3) the salt production follows

ation profile, therefore the precipitation of theoccurs when three ponds were utilized (sce-nd 4), for the period time interval assumed.scenario was also the more adequate, since iteral scheduling scenarios.


Fig. 10. Variation of the circulation water temperatures for two atmospheric cases, with the number of ponds indicated (( ) feasible working region).

enhances and accelerates the salt production (3.6 timesmore).

5.3. Effect

Fig. 10 scirculatingatmospherimidity = 41has the sama wind velservice (rethen five pofinally all thsible to anathe systemspheric con

four ponds. However, when the wind velocity is smaller, andtherefore the water evaporation rate is reduced, it becomesnecessary to use at least five ponds, to obey the operational

ed tem

Inueitions

nce thur it ipatterveloc

g profihich th

(dur) to 50ergy v

Fig.of atmospheric conditions

hows the variation of the temperature of the waterin the economizer (T1 and T2) for two differentc cases. In the first case study Tair = 20.7 C, hu-.7% and Vwind = 1.5 m/s. The second case studye values for the air temperature and humidity, but

ocity of 2.0 m/s. In both cases, four ponds are inceiving heated brine) while the fifth is filled up,nds are in service while the sixth is filled up, ande six ponds are working. From this figure it is pos-lyse the strong influence of the wind velocity onand to conclude that for the most favourable atmo-ditions (Vwind = 2 m/s) it is only required the use of

defin

5.4.cond

Sihavionightwindsprinin w20 Cnightlar en11. Effect of the day and night patterns on the water circulation temperatures withperature intervals.

nce of day and night patterns of atmospheric

e atmospheric conditions influence the system be-s essential to analyse how the different day andns of air temperature, humidity, solar energy andity values affect the system response. A typicalle for the atmospheric conditions was assumed,e air temperature varies from 5 C (at night) to

ing the day). Air humidity varies from 85% (at% (at daylight). The wind velocity and the net so-ary from 0.5 to 3.5 m/s and 0 to 3.5 kWh/(m2 day),3, 4 and 3 + 1 ponds (( ) feasible working region).


respectivelit would beto respect tas illustratehas confirmcirculation

6. Determ

The coggrated procover naturaon the atmimately 92energy lossfrom the oFig. 12. Energy distribution in the recrystallization ponds

y. From this study it was possible to conclude thatadvisable to use an extra pond during the night

he mentioned operational temperatures intervals,d in Fig. 11. The industrial experience at the siteed that the highest temperatures values for the

water were observed in the morning.

ination of the process energy efciencies

eneration system efficiency (CSE) of the inte-ess is the ratio of thermal and electrical powerl gas heat consumption. This value is dependentospheric conditions and in average it is approx-%. During the recrystallization process there arees due for instance to radiation and convectionpen-air ponds. So, the global process efficiency

(GPE) of thThe GPE eoration powconsumptiooperationalSimulationthe range o

7. Conclu

A dynaof an integtem and thsome variastudied usiof the whofor two example cases.

e integrated process is inferior to its CSE value.fficiency is calculated by the ratio between evap-er plus electrical power and the natural gas heatn. It is strongly dependent on the atmospheric andconditions considered, as illustrated in Fig. 12.

s showed that the global process efficiency is inf 7080%.

sions and future work

mic model was built to simulate the behaviourrated process that includes the cogeneration sys-e salt recrystalisation process. The influence ofbles on the cogeneration system performance wasng GateCycle 5.34.0.r. Then, a dynamic modelle integrated process was developed and simu-


lated in gPROMS 2.3. Different scenarios were explored withthe purpose of maximizing the global process efficiency, byanalysing the influence of several atmospheric and opera-tional conditions on the integrated system.

The advantage of a model that can simulate the main pro-cesses is to minimize the negative influence caused by someadverse atmospheric conditions to achieve the highest possi-ble global efficiencies. Furthermore, the better understandingof the integrated system acquired by simulating the processunder different possible scenarios, allows the definition of animproved set of operational conditions to obtain a long-termprofitable business.

Future work will include the study of the spray systemeffect on the salt production and long-term time simulations,accounting for day and night patterns of atmospheric condi-tions. Moreover this will allow to obtain in advance the saltharvesting

Acknowled

The autfrom the P(Grupo Nahas been oProcess In

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Coulson, J. MLisboa: F

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gPROMS. (2004). gPROMS introductory user guide. London: ProcessSystems Enterprise Ltd.

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Dynamic modelling and simulation of a cogeneration system integrated with a salt recrystallization processIntroductionFramework developedAnalysis of the cogeneration systemDynamic model of the integrated systemCogeneration systemPlate heat exchangers setSplitter unitPond unitMaterial balancesEnergy balancesBoundary and initial conditions

Channel unitTank unit

Dynamic simulationsStart-up conditionsScenarios of scheduling working pondsEffect of atmospheric conditionsInfluence of day and night patterns of atmospheric conditions

Determination of the process energy efficienciesConclusions and future workAcknowledgementsReferences

cogeneration salt recrystallization

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