dynamic modeling and simulation of an offshore combined ... · dynamic modeling and simulation of...

Dynamic Modeling and Simulation of an Offshore Combined Heatand Power (CHP) Plant

Jairo Rúa Rubén M. Montañés Luca Riboldi Lars O. Nord

Department of Energy and Process Engineering, NTNU - Norwegian University of Science and Technology,Trondheim - Norway, [email protected]

AbstractThe design and analyis of a flexible combined heat andpower (CHP) system where the exhaust of two gas tur-bines is utilized as the heat source for a steam Rankinecycle is proposed in this paper. The case of study is theJohan Castberg off-shore facility, located in the BarentsSea, Norway. The steady-state design of the CHP sys-tem is developed with a specialized software based on thepeak demand conditions of the platform, which accountfor 58 MW of electric and shaft power, and 52 MW ofheat. A multi-objective optimization approach is followedin order to attain optimal designs where high efficiencyis achieved while keeping reasonable weight to power ra-tios. Once the power cycle design is selected, the detaileddynamic modeling of the different components integrat-ing the cycle is presented and implemented in Modelicalanguage. Steady-state design and off-design validationof the thermal power plant model is carried out, and pre-liminary results are presented to show the ability of thedynamic model to provide reasonable information of thesteam bottoming cycle transient operation.Keywords: dynamic process simulation, steam Rankinecycle, waste heat recovery, multi-objective optimization,offshore flexible operation, Modelica, genetic algorithm.

1 IntroductionThe implementation of mitigation policies, like CO2 emis-sion taxation (Ministry of Environment, 2012) and theparticipation of Norway in the European Union emissiontrading system (ETS), has motivated the improvement ofheat and power generation systems employed in offshoreoil and gas facilities. The petroleum sector is responsibleof 30% of the total CO2 emissions of Norway, with thesimple gas turbine cycles currently employed in the Nor-wegian continental shelf being the source of more than80% of the CO2 emissions generated by this sector (Nor-wegian Ministry of Petroleum and Energy, 2017).

New power generation systems with better performanceand lower emissions are needed in order to mitigate the ef-fects of the oil and gas facilities on the environment, andmake this industry more competitive from an economicpoint of view. Combined cycles are regarded as a promis-ing and feasible alternative to the traditional gas turbinesdue to their higher efficiency and to their technology matu-

rity (Kloster, 1999). Low weight and operation flexibilityare also fundamental criteria in the design of combined cy-cles. The cost of offshore facilities increases rapidly withthe weight while the operation as a stand-alone systemsrequires that the fluctuations in power and heat demandmust be entirely matched by the power system. A trade-off among compactness, flexibility and high efficiencymay be achieved, even during off-design conditions, ifthe traditional heat recovery steam generator with severalpressures levels and steam drums is replaced by a once-through steam generator (OTSG) for offshore applications(Nord and Bolland, 2012, 2013). The low weight and flex-ibility of this basic configuration allows the installation ofdifferent tailor-made alternatives, which enhances the uti-lization of combined cycles for waste heat recovery appli-cations as different objectives may be achieved with dif-ferent bottoming cycles (Pierobon et al., 2014a).

In addition to the design and off-design performance,the analysis of unsteady operation is specially useful foroffshore combined cycles since they work in transientmode due to the variations in heat and power demandand fuel composition. Dynamic modeling and simula-tion of these systems may predict possible imbalances be-tween power generation and consumption, and may iden-tify unstable scenarios where a reliable and optimum per-formance cannot be guaranteed. Moreover, critical sce-narios as the trip of a gas turbine may be analyzed, ensur-ing the operation robustness and safety of the power plant(Benato et al., 2014).

The utilization of dynamic models can also improvethe design of control systems and strategies (Montañéset al., 2017). Traditional steady design procedures aim toachieve the highest possible efficiency or the correct bal-ance between efficiency and weight to power ratio. Un-steady performance is not considered at this stage but it isstudied when the control strategy is being designed, lead-ing to excessively aggressive control configurations wherethe off-design operation is worsen as a result of the limi-tations established by the dynamic operation. Evaluatingthe unsteady performance of a certain power plant designby means of a dynamic model may discard its implemen-tation due to the violation of specific performance con-straints, albeit its possible high efficiency or low weightduring nominal operation (Pierobon et al., 2014b). There-fore, the integration of dynamic models in the selection

DOI: 10.3384/ecp17138241 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

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criteria of a power cycle design can improve the overallperformance of the system. Dynamic response and effec-tiveness of the control strategy of a thermodynamic cyclefor waste heat recovery applications may be tested undercertain off-design conditions if a dynamic model is devel-oped for such purpose (Mazzi et al., 2015). A dynamicmodel of a small-scale ORC was also employed to pro-pose and compare three different control strategies, show-ing that with the correct control strategy the efficiency re-mains in reasonable levels even if the heat source condi-tions are modified (Quoilin et al., 2011).

Dynamic models can also be utilized to analyze criti-cal scenarios where extreme conditions for the equipmentmay be expected and steady-state models do not provideenough information. As a result, new start-up conditionswith higher thermal gradients but similar maximum tem-peratures that allow to halve the time required to gener-ate the maximum power may be achieved (Alobaid et al.,2008). A reduction in the start-up time without increasingthe stress limits was also found by (Casella and Pretolani,2006), who also proposed another strategy that reducesthe stress peak extending the lifetime without increasingthe start-up time.

This paper aims at developing dynamic models forpower plant components and testing their performanceduring transient operation of a combined heat and powerplant. In addition, preliminary results of the operationflexibility of the selected CHP design, i.e. the adaptabil-ity to fast operation changes, are shown. The descriptionof the case study and the methodology followed to assessthe dynamic performance of the CHP plant are presentedin Section 2. The modeling approach utilized for the de-velopment of the steady and dynamic model is covered inSection 3. Results of the dynamic simulations are reportedand discussed in Section 4. Concluding remarks are givenin Section 5.

2 Case study and methodologyThe case study is the power system needed in the JohanCastberg field, located in the Barents sea. The heat andpower requirements have been assessed for its lifetime,expecting heat demands between 32 MW and 52 MW, andpower demands ranging from 42 MW to 58 MW (StatoilASA, 2016).

A combined heat and power plant is proposed as an al-ternative power generation system where heat from the ex-haust gases of two gas turbines is utilized as a heat sourcefor a steam bottoming cycle. Figure 1 shows a simplifiedlayout of the CHP plant. Two GE LM2500+G4 gas tur-bines produce the majority of the required power whilethe energy contained in their exhaust gases is recoveredin a OTSG to produce the steam utilized in the bottomingcycle. The design point specifications of this gas turbinemodel are specified in Table 1. The high ratios betweenthe heat and power demand entail a challenge for the steamRankine cycle and a back-pressure steam turbine has to

Table 1. Design point specifications of the GE LM2500+G4 gasturbine.

Variable Design point value

Net power output [MW] 32.50Net efficiency [%] 36.50Exhaust gas flow rate [kg/s] 89.90Exhaust temperature [◦C] 552Net heat rate [kJ/kWh] 9867Gas turbine inlet ∆p [mbar] 10Gas turbine exhaust ∆p [mbar] 10Ambient temperature [◦C] 10Ambient pressure [bar] 1.0 13Air humidity [%] 60.00Gas turbine fuel Production gas

be utilized. Thus, the superheated steam produced in theOTSG is not totally expanded in order to have enough en-ergy to produce the required process heat. A fraction ofthis steam is sent to one of the condensers of the selectedparallel configuration where pressurized water at 150◦C isproduced to meet the heat demand. The remaining super-heated steam is condensed in the second branch condenserusing sea water as cooling fluid.

The large variations in heat and power demand that maybe experienced in the offshore facility and the fact that thepower generation system operates as a stand-alone systemrequire that the CHP plant operates in a flexible manner.Therefore, the dynamic operation of the proposed designmust be assessed in order to ensure the correct functioningof the power plant under varying conditions. In addition,as previously mentioned, low weight and compactness arefundamental conditions in this kind of thermal power sys-tems. Thus, a dynamic analysis of a preliminary design ofthe CHP plant obtained from a multi-objective optimiza-tion was carried out in order to verify that the combinedcycle performs correctly during unsteady operation.

2.1 Steady state design and multi-objectiveoptimization

The life-time assessment of the energy requirements ex-pected for the offshore oil field shows that maximum de-mands of heat and power may occur simultaneously (Sta-toil ASA, 2016). Hence, the nominal operation point wasselected to correspond to peak demands of heat and power,52 MW and 58 MW respectively, in order to ensure thatthese conditions are met by the power generation system.

Once the design conditions of the CHP plant were de-fined, the steady state modeling and design was carriedout utilizing the specialized software Thermoflex (Ther-moflow Inc, 2016). The selection of this tool was basedon its reliability, as it has been extensively tested and val-idated with industrial data. The thermodynamic stateswere determined by means of mass and energy conser-vation laws, and the boundary conditions imposed to the

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P-2

P-3

P-4

P-5 P-6

P-10 P-9

P-11

P-1

P-15P-15

E-1

E-2

P-16

P-4

P-21

P-22

P-23

P-2

Air inlet

Air inlet

Fuel inlet

Steam turbine

Condenser

Once-

through

steam

generator

(OTSG)

Pump

Gas turbine

Gas turbine

Heat

removal

process

Fuel inlet

Generator

Generator

Generator

Figure 1. Simplified layout of the proposed power generation system for the offshore facility in Johan Castberg field.

model. From this data, the sizing of the components ofthe steam Rankine cycle was carried out. Subsequently,a constrained multi-objective optimization based on a ge-netic algorithm included in the global optimization MAT-LAB toolbox (MathWorks, 2017) was performed, wherethe heat rate and the weight to power ratio were the objec-tive functions to be minimized (Riboldi and Nord, 2017).The selected decision variables during the optimizationprocedure were the steam turbine inlet pressure, psteam,and temperature, Tsteam, the pinch point difference in theevaporating section of the OTSG, ∆Tpinch, and the gas tur-bine load of one turbine, GT2,load , utilizing the other unitto match the power demand. The bounds of the decisionvariables are reported in Table 2. A population size of 150was selected while a maximum of 15 generations wereallowed. Crossover and tolerance were set equal to 0,8and 10−3 respectively. The stopping criterion utilized inthis optimization procedure was either the exceedance inthe maximum number of generations or having an aver-age change in the spread of the Pareto front lower than thetolerance selected. A two-dimensional Pareto front wasobtained as a result of this procedure. The solution thatprovides the best balance for the requirements of the off-shore facility was selected.

2.2 Dynamic model development and un-steady performance assessment

A dynamic model of the preliminary CHP plant designmust be built in order to evaluate its operation under vary-ing scenarios, e.g. load changes or unit trips. The dynamicmodeling language Modelica was utilized for the develop-ment of such model, as its object-oriented nature and theexistence of specialized libraries ease the implementation

Table 2. Lower and upper bounds of the selected decision vari-ables.

Decision variables Lower bound Upper bound

psteam [bar] 10 40Tsteam [◦C] 400 515∆Tpinch [◦C] 10 30GT2,load [%] 75 94

of transient conservation laws, correlations and the com-ponent dimensions calculated in the previous step. In thiswork, the open-source library specialized in power plantsThermoPower (Casella and Leva, 2003) was employed.

Open-loop simulations, i.e. without control, may becarried out from this model in order to achieve a deeperunderstanding of the intrinsic unsteady behavior of thecycle. However, a suitable control strategy with appro-priate tuning parameters was implemented in the dynamicmodel in order to simulate real plant operation. The steamturbine was operated in sliding pressure mode, while themass flow rate of steam through the primary condenserwas utilized to regulate the temperature of the pressurizedwater employed as a process heat means. The water levelof this condenser was controlled in order to ensure a sta-ble operation of the system, whereas the water level ofthe secondary condenser was allowed to vary, absorbingthe fluctuations of the process heat section and acting as awater buffer under off-design loads. In addition, the livesteam temperature was controlled by means of the massflow rate circulating in the Rankine cycle. PI controllerswere utilized in order to ensure a stable operation.

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3 Modeling Approach3.1 Gas turbine modelGas turbines’ dynamics were not considered as their tran-sient operation is much faster than that of the steam Rank-ine cycle. Instead, the gas turbines were modeled withvalidated quasi-static models, and the exhaust gas streamwas utilized as boundary conditions to the dynamic pro-cess model (Montañés et al., 2017). Off-design conditionswere obtained from the compressor and turbine maps ofthe gas turbine validated by Thermoflex, and a variablecharacteristic that simulates the fluctuating exhaust gasconditions was implemented in the dynamic model.

3.2 OTSG modelThe different sections of the OTSG were modeled asthree individual heat exchangers: an economizer, a once-through boiler (OTB), and a superheater. The preheatingof the liquid fluid takes place in the economizer, wheresufficient difference between the boiling point and the out-let temperature, i.e. an approach point, was left in orderto ensure that no evaporation occurred in this componentduring off-design operation. The OTB mainly modeledthe vaporization of the working fluid, but it also includedthe preheating of the water leaving the economizer untilsaturation conditions and some superheating of the steamduring design operation. The final degree of superheat-ing of the steam produced in the OTB is achieved in thesuperheater.

Each of the heat exchangers was spatially discretizedin (N-1) cells, where mass and energy conservation laws,and heat transfer correlations were applied (see Figure 2).Momentum conservation law was not included as the iner-tia of the fluid was neglected and the pressure drops weremodeled as lumped parameters at the outlet of each com-ponent.

The mass and energy conservation laws were equallymodeled in the three heat exchangers and for both gas andwater/steam sides. The discretized mass conservation ex-pression for a one-dimensional flow is:

N−1

∑j=1

dM j

dt= min− mout (1)

where min and mout are, respectively, the mass flow ratesat the inlet and outlet of each heat exchanger; and M j isthe mass of fluid in each cell, given by:

dM j

dt=Vj ·

(∂ρ

∂h

∣∣∣j·

dh′jdt

+∂ρ

∂ p

∣∣∣j· d p

dt

)(2)

being Vj the volume of each cell, and with the averagepartial derivatives of density respect to enthalpy and pres-

sure, ∂ρ

∂h

∣∣∣j

and ∂ρ

∂ p

∣∣∣j, in the center of the cell calculated

from their nodes values.

∂ρ

∂h

∣∣∣j=

12

(∂ρ

∂h

∣∣∣j+1

+∂ρ

∂h

∣∣∣j

)(3)

∂ρ

∂ p

∣∣∣j=

12

(∂ρ

∂ p

∣∣∣j+1

+∂ρ

∂ p

∣∣∣j

)(4)

The one-dimensional spatially discretized energy conser-vation law is:

Vj · ρ j ·dh′jdt− ¯m j · (h j+1−h j) = Q j +Vj ·

d pdt

(5)

where ρ j is the average density of each discretization, h′jis the enthalpy state variable at the center of the cell, h jthe fluid specific enthalpy evaluated at the nodes, Q j theheat flow from or to the wall, p is the pressure, and ¯m j themass flow rate in each cell, defined as:

¯m j = min−j−1

∑j=1

dM j

dt− 1

2dM j

dt(6)

The heat flows between the hot and cold fluids, sub-index h and c respectively, and the metal tube were calcu-lated in the center of each cell as:

Q j,h = γh ·A j,h ·(

Tj+1,h +Tj,h

2−Twall, j,h

)(7)

Q j,c = γc ·A j,c ·(

Tj+1,c +Tj,c

2−Twall, j,c

)(8)

being Tj+1 and Tj the temperatures at the nodes, Twall, jthe temperature of the wall in the outer or inner tube sur-faces evaluated at the center of the cell, A j the heat transfersurface for each fluid, and γ the convection heat transfercoefficient. In the gas side this coefficient can be calcu-lated with the relation (Incropera et al., 2007):

γ = γnom

(m

mnom

)0.6

(9)

where γnom is the convection heat transfer coefficient dur-ing steady-state nominal operation utilized in Thermoflex.

In the water side of the economizer and superheaterconstant heat transfer coefficients were employed sincethey were calculated in the design stage and the main ther-mal resistance was the heat transfer in the gas side. How-ever, the value of this coefficient in the water side of theOTB varies substantially due to the phase changes that oc-cur, and an overall coefficient could not be utilized. Thus,the Dittus-Boelter correlation with constant heat transfervalue consisting on the saturated boiling region heat trans-fer coefficient was employed:

γ = 0.023k

DhydRe0.8Pr0.4 (10)

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244

ṁc,1

Mc,1

h c,1

hc,1

Qc,1

Tc,1

Twall,c,1 Twall,c,2 Twall,c,j Twall,c,N-2 Twall,c,N-1

Twall,h,j Twall,h,2 Twall,h,N-2 Twall,h,1 Twall,h,N-1

Tm,1 Tm,2 Tm,j Tm,N-2 Tm,N-1

Cold Fluid

Hot Fluid

Mc,2

h c,2

Qc,2

Mc,j

h c,j

Qc,j

Mc,N-2

h c,N-2

Qc,N-2

Mc,N-1

h c,N-1

Qc,N-1 ṁc,2

hc,2

Tc,2

ṁc,3

hc,3

Tc,3

ṁc,j

hc,j

Tc,j

ṁc,j+1

hc,j+1

Tc,j+1

ṁc,N-2

hc,N-2

Tc,N-2

ṁc,N-1

hc,N-1

Tc,N-1

ṁc,N

hc,N

Tc,N

Mh,N-1

h h,N-1

Qh,N-1

Mh,N-2

h h,N-2

Qh,N-2

Mh,j

h h,j

Qh,j

Mh,2

h h,2

Qh,2

Mh,1

h h,1

Qh,1

ṁh,N

hh,N

Th,N

ṁh,N-1

hh,N-1

Th,N-1

ṁh,N-2

hh,N-2

Th,N-2

ṁh,j+1

hh,j+1

Th,j+1

ṁh,j

hh,j

Th,j

ṁh,3

hh,3

Th,3

ṁh,2

hh,2

Th,2

ṁh,1

hh,1

Th,1

Figure 2. Modeling paradigm of the once-through steam generator.

where k is the thermal conductivity of the fluid, Dhyd isthe hydraulic diameter, Re is the Reynolds number, and Pris the Prandtl number.

The heat capacity of the metal tubes that accounts forthe thermal inertia of the heat exchangers during dynamicoperation is included in the model as:

Vm ·ρm ·Cpm ·dTm

dt= Qh + Qc (11)

Here, Vm is the volume of metal, ρm is the metal density,and Cpm is the metal heat capacity. Tm is the temperaturein between both sides of the metal tube, and Qh and Qcare the heat flows coming from the hot and cold sides,respectively.

The heat conduction through the metal tubes is definedas:

Qh = Nt ·λ

2πLN−1 · (Twall,h−Tm)

log(

2·rextrext+rint

) (12)

Qc = Nt ·λ

2πLN−1 · (Twall,c−Tm)

log(

rext+rint2·rint

) (13)

where Nt is the number of tubes, L is the length of thetubes, rext and rint are the external and internal radius, andλ is the conduction coefficient of the tubes.

3.3 Steam turbine modelA quasy-static model of the steam turbine was utilized inthis work. The dynamics of this unit are faster than thoseof the OTSG, and since frequency fluctuations were notanalyzed, the dynamic behavior of the steam turbine was

neglected. Therefore, the differential conservation equa-tions are reduced to algebraic equations.

The steam turbine performance during off-design op-eration was predicted by means of Stodola’s cone law(Stodola, 1927):

min = Kt

√√√√ρin pin

√1−(

1PR

)2

(14)

with Kt being the Stodola’s coefficient, ρin and pin thedensity and pressure at the inlet of the steam turbine, andPR the pressure ratio, defined as:

PR =pin

pout(15)

where pout is the pressure after the expansion.The mechanical power, Pm, extracted by the steam tur-

bine from the steam is obtained by:

Pm = ηmech · w · (hin−hout) (16)

where ηmech is the mechanical efficiency, w is the massflow rate along the turbine, and hout is obtained, assumingconstant isentropic efficiency ηiso, from:

ηiso =hin−hout

hin−hiso(17)

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3.4 Condenser modelThe modeled condenser is a shell and tube heat exchangerwhere the cooling fluid circulates within the tubes whilethe condensing fluid flows through the tube bundle on theshell side. The utilization of a back-pressure steam tur-bine implies that the steam entering the condensers is su-perheated. Thus, this feature must be taken into accountin the model of the component.

The modeling of the cooling flow on the tube side isdone similarly as in Section 3.2. Mass conservation isgiven by Eq. (1), whereas Eq. (5) is utilized to describethe energy balance. Heat transfer to the cooling fluid ismodeled by Eq. (8) where the heat transfer coefficient iscalculated by means of the Dittus-Boelter correlation (seeEq. (10)). The thermal dynamics of the metal tubes of thecondenser are accounted by the utilization of Eqs. (11) and(13).

Since the working fluid enters the condenser as super-heated steam, the shell side is discretized in order to ac-count for the change in temperature and fluid properties.Saturated conditions at the outlet of the shell side and con-stant volume of the shell, Vshell , are set as constraints of themodel. The division of this volume into sub-units, Vshell, j,is done gradually in order to obtain more accuracy at theoutlet of the shell, where the density changes of the two-phase mixture are abrupt and a lot of detail is required.Hence, the volume of each discretization is defined as:

Vshell, j =Vshell

2 j (18)

The mass of working fluid in each volume, Mshell, j, andthe energy it contains, Eshell, j, are calculated using the av-erage of the density, ρ j, and the specific enthalpy, h j, atboth nodes of the cell:

Mshell, j =Vshell, j ·ρ j+1 +ρ j

2(19)

Eshell, j = Mshell, j ·h j+1 +h j

2− p ·Vshell, j (20)

Dynamic mass and energy conservation are employedto model the flow in the shell side:

dMshell, j

dt= m j− m j+1 (21)

dEshell, j

dt= m j ·h j− m j+1 ·h j+1− Q j (22)

where dMshell, j/dt and dEshell, j/dt are the time rate ofmass and energy change in the center of the cell, m j andm j+1 the mass flow rates evaluated at the nodes of the cell,and Q j is the heat flow from the discretized volume, whichis calculated from Eq. (7).

The modeling of the hotwell was done in order to ac-count for the increase in the outlet pressure, pout , due to

the static pressure of the water column and the time rateof mass change, dMhotwell

dt . Hence:

pout = pin−hhotwell ·g · ρhotwell (23)

dMhotwell

dt= min− mout (24)

being hhotwell the level of water, pin the inlet pressure,and ρhotwell the average density of the water contained inthe hotwell.

In addition, the change in the outlet mass flow rate dueto the accumulation of water and the increase in staticpressure was modeled based on:

mout =√

2ghhotwell ·Aduct · ρhotwell (25)

with Aduct being the area of the duct leaving the hotwell.

3.5 Pump modelA variable speed pump model was employed in this work,i.e. the mass flow rate is adapted by modifying the rotationspeed. A third-order polynomial equation was utilized todescribe the curves relating the mass flow to the head sincethe map of performance of the pump was not available.This equation was generated as a regression curve fromthe set of data generated by Thermofex in order to smooththe transient behavior of the pump model. The enthalpyincrease through the unit was given by an energy balance.Constant efficiency during off-design conditions was as-sumed.

4 Results and discussion4.1 CHP plant static designThe Pareto front of solutions of the preliminary design ofthe CHP plant obtained from the multi-objective optimiza-tion are shown in Figure 3. From this set of results, themost suitable alternative for the off-shore facility was cho-sen. Table 3 displays the main design characteristics of theselected solution.

Table 3. Nominal characteristics of the preliminary plant design.

Variable Nominal value

Gas turbine 1 load [%] 72.38Gas turbine 2 load [%] 85.19Steam turbine inlet pressure [bar] 33.79Steam turbine inlet temperature [◦C] 444.20Steam turbine outlet pressure [bar] 4.76OTB temperature difference [◦C] 20.30Efficiency [%] 40.81Weight [kg] 207068

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0.394 0.396 0.398 0.4 0.402 0.404 0.406 0.408 0.41 0.412 0.414

Efficiency [%]

1.6

1.8

2

2.2

2.4

2.6

2.8

Weight[kg]

×105 Pareto front

Figure 3. Pareto front of optimum solutions for the preliminarydesign of the CHP plant. The selected design configuration ismarked in red.

4.2 Dynamic model validationA thorough validation of the dynamic model was per-formed in order to ensure that results generated by thedynamic simulations are reliable. Dynamic data was notavailable, neither experimental nor generated by Ther-moflex, and hence only a validation of the dynamic pro-cess model under steady-state operating conditions wascarried out.

Several operation points including both design and off-design gas turbine loads were simulated, being the resultsproduced by the dynamic model in satisfactory agreementwith the validation data. For brevity, only design valida-tion results for the heat transferred in the OTSG sectionsand the primary condenser, the shaft power produced inthe steam turbine, and the steam live pressure and temper-ature are shown (see Table 4). Extensive validation dataduring both design and off-design steady-state operationmay be found in the literature (Rúa, 2017). Absolute er-rors between results generated by Dymola and Thermoflexwere calculated as:

Error∣∣∣u=|uDymola−uT hermo f lex|

uT hermo f lex(26)

where u may be any variable included in Table 4.

4.3 Dynamic simulationThe ability of the developed combined heat and powerplant model to simulate operation under transient condi-tions was assessed by a dynamic simulation where the loadof both gas turbines was decreased from nominal opera-tion point, i.e. 72.38% and 85.19%, to 60%. This wasequivalent to a reduction of 20% in the power demand ofthe entire thermal power plant. In addition, the modifi-cation of the gas turbines load means an increase of the

Table 4. Validation results during nominal operation.

Dymola Thermoflex Error

Qeconomizer [MW] 10.403 10.343 0.580%Qevaporator [MW] 40.497 40.582 0.209%Qsuperheater [MW] 9.729 9.652 0.798%Pm [MW] 8.348 8.601 2.942%Qcondenser,1 [MW] 52.015 52.050 0.067%Tsteam [◦C] 442.220 442.600 0.086%psteam [bar] 33.809 33.730 0.234%

exhaust gas temperature of more than 20 ◦C. Therefore,two step changes, one decreasing the exhaust gas massflow rate and the other increasing its temperature (see Fig-ure 4), were implemented simultaneously in order to testability of the steam cycle to handle a disturbance in thegas turbine load.

The variation of the relevant temperature variables, i.e.the steam live temperature and the process heat streamtemperature, was analyzed under both open-loop condi-tions and with a control strategy implemented. The be-havior of these two variables is represented in Figure 5.The former covers the live steam temperature while thelatter shows the temperature of the process heat producedin the primary condenser. As it may be observed, bothvariables return to their set-point when the control strat-egy is applied, albeit the large change in operation con-ditions. However, the requirements of the offshore facil-ity are unfulfilled when the plant is operated in open-loopconditions. A more restrictive control, i.e. with a largercontroller gain, was designed for the process heat temper-ature in order to ensure that big fluctuations from the setpoint did not occur, as the pressurized high-temperaturewater stream is employed in the treatment of the productsproduced in the offshore facility and large deviations fromthe defined operating temperature may damage such prod-ucts.

The dynamics of the controlled temperatures are slowerthan their open-loop counterparts. This phenomena mayalso be observed in Figure 6a, where the live steam pres-sure reaches faster a new steady-state operation pointwhen no control is applied. This behavior is because ofvariation of the working fluid mass flow rate, which is thevariable manipulated to control the steam live tempera-ture, is also slow (see Figure 6b).

The water level fluctuation of both condensers is shownin Figure 7. The level of the primary condenser was con-trolled in order to ensure a stable operation. The con-trol strategy applied to the primary water level respondedproperly to the changes experienced in the mass flow. Thestep changes in both exhaust gas mass flow and temper-ature produced, after an initial increase, a deep decreasein the steam live temperature that originated a decreasein the mass flow circulating in the bottoming cycle (seeFigure 5a and Figure 6b). Thus, the water levels in the

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0 1000 2000 3000 4000 5000 6000 7000

Time [s]

146

148

150

152

154

156

158

160

162

164

GasMass

Flow

[kg s]

Exhaust Gas Mass Flow

(a) Exhaust gas mass flow rate.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

515

520

525

530

535

540

545

GasTem

perature

[◦C]

Exhaust Gas Temperature

(b) Exhaust gas temperature.

Figure 4. Dynamic model boundary conditions.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

410

420

430

440

450

460

470

Tem

perature

[◦C]

Steam Live Temperature

Open-LoopControl

(a) Steam live temperature variation.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

148

148.5

149

149.5

150

150.5

151

Tem

perature

[◦C]

Temperature Process Heat

Open-LoopControl

(b) Process heat temperature variation.

Figure 5. Variation of the controlled temperatures.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

33.2

33.3

33.4

33.5

33.6

33.7

33.8

33.9

34

34.1

Pressure

[bar]

Live Steam Pressure

Open-LoopControl

(a) Steam live pressure variation.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

19.6

19.8

20

20.2

20.4

20.6

20.8

21

21.2

Mass

Flow

[kg s]

Working Fluid Total Mass Flow Rate

Open-LoopControl

(b) Working fluid mass flow variation.

Figure 6. Variation of the working fluid mass flow and the steam live pressure.

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0 1000 2000 3000 4000 5000 6000 7000

Time [s]

2.44

2.46

2.48

2.5

2.52

2.54

2.56

2.58

2.6Level

[m]

Primary Condenser Level

(a) Water level in the primary condenser.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

0

0.005

0.01

0.015

Level

[m]

Secondary Condenser Level

(b) Water level in the secondary condenser.

Figure 7. Water level in both condenser hotwells.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

19.4

19.6

19.8

20

20.2

20.4

20.6

Mass

Flow

[kg s]

Primary Condenser Mass Flows

InletOutlet

(a) Working fluid mass flow in the primary condenser.

0 1000 2000 3000 4000 5000 6000 7000

Time [s]

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35Mass

Flow

[kg s]

Secondary Condenser Mass Flows

InletOutlet

(b) Working fluid mass flow in the secondary condenser.

Figure 8. Working fluid mass flow in both condensers.

hotwells were firstly reduced and then increased as a con-sequence of the variations in the mass flows entering andleaving both condensers. Steady-state values of the waterlevels showed that the secondary condenser absorbed thefluctuations in the operating conditions originated by thereduction of the working fluid’s mass flow rate.

The mass flow rate of the steam entering and the waterleaving these components is represented in Figure 8. Sim-ilar trends among the water levels and mass flows in thecondenser may be observed between Figure 7a and Fig-ure 8a, and Figure 7b and Figure 8b, where both variablespresent the same pattern but the water level response isslightly shifted in time.

It is worth noting the buffering effect that the hotwell ofthe condensers has in the cycle, as it smears out the fluc-tuations (see Figure 8). This effect is specially observablein the primary condenser as the water level is larger andhence the static pressure changes are smoothed, reducing

the variation in the mass flow rate of water leaving thehotwell.

5 ConclusionsThe dynamic modeling of the components integrating anoffshore combined heat and power plant was presented inthis work. Preliminary results on disturbance rejectionshow that the developed models produce reasonable re-sults on the transient behaviour of the studied system.

The offshore platform in Johan Castberg field was se-lected as case study to test the validity of the models de-veloped. A steady-state design procedure accounting forthe need of high efficiency while keeping a reduced weightwas briefly presented, pointing out the demanding restric-tions in offshore facilities. A dynamic model of the se-lected design was developed under the Modelica environ-ment, utilizing the ThermoPower library to develop themodels of the components integrating the steam Rankine

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cycle. A discretized condenser was programmed in or-der to accurately calculate the superheating conditions thatwere expected at the outlet of the back-pressure turbine.

The dynamic model of the combined heat and powerplant was validated for steady-state design and off-designconditions obtained by the software Thermoflex. A pre-liminary evaluation of the developed models’ capabilityto produce reasonable results under transient conditionswas carried out by means of a reduction in the power de-mand of the combined heat and power plant, which wasimplemented by simultaneous step changes in the exhaustgas mass flow rate and temperature. The dynamic per-formance of relevant variables during the dynamic opera-tion was shown and analyzed, showing that these modelscould be utilized for assessing that, with a suitable controlstrategy, the CHP plant would be able to produce the de-manded heat at the required temperature even if changesto the nominal operation conditions of the power plant oc-curred. In addition, it was verified that limiting conditions,e.g. maximum temperature in the steam turbine, are notreached during unsteady performance, which is a valuableinformation for the operator of the plant.

The proposed assessment methodology has been ap-plied for an offshore facility where restrictions are harderthan in on-shore power plants. However, it is readily ap-plicable to any waste heat recovery application where per-formance under transient conditions needs to be analyzed.

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A. Benato, L. Pierobon, F. Haglind, and A. Stoppato. Dynamicperformance of a combined gas turbine and air bottoming cy-cle plant for off-shore applications. In: Proceedings of theASME 2014 12th Biennial Conference on Engineering Sys-tems Design and Analysis, 2014.

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N. Mazzi, S. Rech, and A. Lazzaretto. Off-design dynamicmodel of a real organic rankine cycle system fuelled by ex-haust gases from industrial processes. Energy, 90(1):537–551, 2015.

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R. M. Montañés, S. Ó. GarDarsdóttir, F. Normann, F. Johnsson,and L. O. Nord. Demonstrating load-change transient per-formance of a commercial-scale natural gas combined cyclepower plant with post-combustion co2 capture. InternationalJournal of Greenhouse Gas Control, 63:158–174, 2017.

L. O. Nord and O. Bolland. Steam bottoming cycles offshore -challenges and possibilities. Journal of Power Technologies,92(3):201–207, 2012.

L. O. Nord and O. Bolland. Design and off-design simulationsof combined cycles for offshore oil and gas installations. Ap-plied Thermal Engineering, 54(1):85–91, 2013.

Norwegian Ministry of Petroleum and Energy. Emis-sions to Air. http://www.norskpetroleum.no/en/environment-and-technology/emissions-to-air/, 2017. [Accessed: 2017-05-15].

L. Pierobon, A. Benato, E. Scolari, F. Haglind, and A. Stoppato.Waste heat recovery technologies for offshore platforms. Ap-plied Energy, 136(1):228–241, 2014a.

L. Pierobon, E. Casati, F. Casella, F. Haglind, and P. Colonna.Design methodology for flexible energy conversion systemsaccounting for dynamic performance. Energy, 68(1):667–679, 2014b.

S. Quoilin, R. Aumannb, A. Grill, A. Schuster, V. Lemort, andH. Spliethoff. Dynamic modeling and optimal control strat-egy of waste heat recovery organic rankine cycles. AppliedEnergy, 88(1):2183–2190, 2011.

L. Riboldi and L. O. Nord. Lifetime Assessment of CombinedCycles for Cogeneration of Power and Heat in Offshore Oiland Gas Installations. Energies, 10(6):744, 2017.

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http://www.norskpetroleum.no/en/environment-and-technology/emissions-to-air/



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