pdf download - · pdf filesystems based on a combined moving boundary and discretized...

DYNAMIC MODELING AND SIMULATION OF GEOTHERMAL HEAT PUMPSYSTEMS BASED ON A COMBINED MOVING BOUNDARY

AND DISCRETIZED APPROACH

Roozbeh Sangi, Pooyan Jahangiri, Freerk Klasing, Rita Streblow and Dirk Mueller

Institute for Energy Efficient Buildings and Indoor Climate, E.ON Energy Research Centre,RWTH Aachen University, Aachen, Germany

ABSTRACTThe major goal of this study is to demonstrate thefeasibility of the dynamic modeling and simulationof both conventional and direct exchange geothermalheat pump applications particularly with regard to per-formance evaluations. Therefore, in this research, dy-namic models for the simulation of geothermal heatpump systems with the working fluid propane for theapplication in building-scale energy systems have beendeveloped based on the Moving Boundary approachand the challenges of dynamically evaluating thesekind of energy systems have been hereby met. Ad-ditionally, the performance of both horizontal (slinky-coil) and vertical (borehole) geothermal heat exchang-ers, which have been modeled based on the Conven-tional Discretized approach, for such systems has beenevaluated. Since these two modeling approaches arenot compatible with one another, the coupling of themoving boundary model with the discretized model istherefore another challenge and of great importance.On the basis of a case study, the complete conven-tional and direct exchange geothermal heat pump sys-tems with vertical and horizontal heat exchangers havebeen simulated and energetically and exergetically an-alyzed.

INTRODUCTIONA geothermal heat pump system consists of a con-ventional heat pump coupled with a ground heat ex-changer where water or a water-antifreeze mixture ex-changes heat with the ground. Although existing heatpump systems can already reach an annual coefficientof performance (COP) of over 4, there is still a sub-stantial potential to tap.A direct exchange geothermal heat pump system is ageothermal heat pump system in which the refrigerantcirculates through tubing placed in the ground. Directexchange geothermal heat pumps offer higher efficien-cies at even lower installation costs compared to con-ventional geothermal heat pumps. In addition, directexchange ground collectors require less space in thesoil. However the correct dimensioning of this typeof application is not yet very well investigated. Cur-

rently, only numerical simulations may offer a suit-able tool for the tailor-made design of such applica-tions and can make long term predictions of the per-formance. Therefore, with the aid of dynamic mod-eling and simulation, which is a convenient and low-cost engineering tool for the performance evaluationof HVAC systems, the feasibility of modeling suchcomplex thermo-hydraulic systems in the modelinglanguage Modelica has been proved and the potentialof different designs for them has been demonstrated.Possible optimizations of the system can then be easilyidentified by means of a first and second law thermo-dynamic analysis, which provides detailed informa-tion on losses and the efficiency of each component.

DYNAMIC MODELINGTwo conventional ways of characterizing heat pumpmodels are, firstly, by means of the physical approachof the model:

• Thermodynamic/physical approach: based onthe geometry of the heat pump and general lawsof physics (heat and mass transfer)

• Black box approach: completely empirical

• Grey box approach: intersection of physical andblack box approach

and secondly, depending on the dynamic representa-tion of the system [Blervaque et al., 2012]:

• Rated performances: part-load performance iscalculated by a temperature-rated full-load andsteady-state operation

• Quasi-static: Time is considered as a sequenceof steady states

• Dynamic: Transient and steady state phases areboth represented in a simulation.

Since no measurements for validation of the heat pumpsystem is available, the physical approach must be re-lied on. Furthermore, we are interested in trackingthe dynamics of the system. Dynamic simulationshowever are, depending on the system’s complexity,

Proceedings of BS2015: 14th Conference of International Building Performance Simulation Association, Hyderabad, India, Dec. 7-9, 2015.

- 1555 -

much more computational intense than static or quasi-static simulations. Therefore, the main emphasis lieson finding transient formulations of the system’s com-ponents, including the refrigerant, that can be solvedwithin an acceptable time.

Modeling and simulation environmentIn this study, the dynamic models have been devel-oped in the modeling language MODELICA, and theMODELICA Standard Library version 3.2 have beenapplied to simulate the hydraulic and thermal behav-ior of the system. The translation of a Modelica modelis performed in the simulation environment Dymola,version 2013 [Dassault Systems, 2011].

Medium modelThe design and simulation of heat pumps or power cy-cles require an accurate representation of the workingfluid. The selected refrigerant in this study is propane,which will be used for the application in both conven-tional and direct exchange geothermal heat pump sys-tems. A medium model for the refrigerant propane en-titled Propane Fast developed by [Sangi et al., 2014]has been used in this research.

Advanced transient modeling of two phase flowThis sub-section will give an overview of two commondynamic modeling approaches for two phase flows andexplain the challenges and difficulties that occur whena two phase fluid model is used for simulation. Addi-tionally, a low order model based on a moving bound-ary formulation as well as the implementation of thismodel will be explained.The motivation for introducing this relatively-newmoving boundary method, also known as lumped pa-rameter model, has its origin mainly in the obser-vation of a greatly varying physical behavior in thesub-cooled, the two-phase and the superheated regionin two-phase heat exchangers [Jensen, 2003]. Theheat transfer coefficient for example, can differ signif-icantly from the superheated region to the two-phaseregion. In each region however, it may be relativelyconstant. In case of utilizing the finite volume method,this circumstance has two consequences:

• The spacial discretization needs to be high sothat the ratio of two phase and single phase canbe represented accurately.

• The simulation will slow down each time onefluid volume switches from single phase to twophase or vise versa, as the solver reduces its timestep time accordingly when the state variableshave large transients.

Moving Boundary MethodTo derive a low order model that can overcome thechallenges that were pointed out in the previous sub-section, the devision into the three regions sub-cooled,two-phase and superheated was therefore a natural se-lection. The idea of this approach is to model each

region as a Control Volume (CV) that has variableboundaries and average properties and track the lengthof the different regions dynamically [Jensen, 2003].In this way, the occurrence of discontinuities can beavoided and the number of state variables is kept small,which allows large simulations to be run on any com-puter.The description of the direct exchange geothermal heatexchanger using a moving-boundary formulation fol-lows the approach presented by [Li and Alleyne, 2010]for refrigeration systems, [Zapata et al., 2013] for so-lar thermal once through cavity receivers and [Bonillaet al., 2012] for direct steam generating solar thermalpower plants. The fluid and wall energy balances aswell as the mass balance for the fluid result in threeequations for each region. A moving boundary modelassumes the momentum balance to be negligible sincethe frictional pressure drop and the gravitational pres-sure drop are very small (or non existing), compared tothe pressure drop of other components like the com-pressor or the expansion valve, for conventional re-frigeration systems with compact evaporators and con-densers.

A

A

A

m

h

ρB

B

B

m

h

ρ

wT ( )w BT z( )w AT z

Az

Bz

p, h

Figure 1: Illustrastion of a fluid volume

Under the assumption of a one-dimensional flow andwith the nomenclature presented in Figure 1 the gen-eral fluid mass and energy balances with variableboundaries A and B yield equation (1) and (2). Thewall mass balance is superfluous, however the wall en-ergy balance can also be simplified and results in equa-tion (3).

Ad

dt

zB∫zA

ρdz +AρAdzA

dt−AρB

dzB

dt

= mA − mB (1)

Ad

dt

zB∫zA

ρhdz −A(zB − zA)dp

dt

+AρAhAdzA

dt−AρBhB

dzB

dt= mAhA − mBhB + q(zB − zA) (2)


- 1556 -

Awρwcw(zB − zA)dTw

dt

+Awρwcw(Tw(zA)− Tw)dzA

dt

−Awρwcw(Tw(zB)− Tw)dzB

dt= qw(zB − zA) (3)

Based on these simplified mass and energy balances,Differential Algebraic Equations (DAEs) can be foundfor all three regions. The derivation of these DAEsis not part of this study, since this has already beendone by many other authors. This work follows theapproach of [Bonilla et al., 2012], who describes anobject-oriented library of switching moving bound-ary models for two-phase flow evaporators and con-densers, as well as [Zapata et al., 2013], who describesa method for the dynamic simulation of the heat ex-change in a solar thermal once through cavity receivercoupled with a switching approach that allows the ap-plication of the moving boundary method for a greatvariety of boundary conditions.In the most general case, an evaporator has threeprevalent regions. As the evaporator’s operating con-dition is not always subcooled liquid at the inlet andsuperheated vapor at the outlet, it is necessary to pro-vide further models that describe their behavior. Alsoit is necessary to have a consistent description duringthe transition from one model to another.

Switching algorithm for the moving boundary ap-proachAs indicated previously, when one zone appears or dis-appears, it must be switched between different modelequations for the different modes. In total, there aretwelve switching possibilities with the correspondingswitching criteria for the evaporator or condenser. Allswitching criteria involve an expression for the spe-cific enthalpy at the crossing boundary. For disappear-ing zones the length is also taken into account. Thresh-olds can be chosen for each condition and should benon zero, otherwise the solver might get trouble solv-ing the DAEs.After switching from one mode to another, the wholesystem must be reinitialized, since it is not cer-tain, especially if a zone disappears, that both regionlength and specific enthalpy converge simultaneouslytowards their respective switching references. Justswitching between the model equations would then re-sult in wrong calculations and the pseudo-equationswould introduce a non-conservative behavior, whichis not desired and unacceptable for performance eval-uations. To avoide that, all state variables shoul bereinitialized in a conservative way.

Thermodynamic model of the heat pumpA vapor compression heat pump cycle must at leastconsist of the the four following basic components:

evaporator, compressor, condenser and expansionvalve. Figure 2 shows the general model of this cy-cle. Each component is coupled internally throughfluid connectors that equalize the outputs of one modelwith the inputs of another model.

Controller

Heat transfer from brine water or soil

Heat transfer to distribution system

Compressor

work

Figure 2: Components of the heat pump cycle

Control strategies for the evaporatorThe valve is controlled with a simple proportional-integral (PI) controller. Therefore, two methods havebeen investigated: the first control strategy takes theevaporator outlet pressure as a reference, while thesecond strategy acts on changes in the temperature dif-ference between the inlet and the outlet of the evapo-rator. After evaluating the suitability for the purposedapplication, the second strategy was chosen for con-trolling the heat exchanger. The reason for this de-cision is the fact that evaluating the temperature dif-ference over the evaporator ensures the presence of asuperheated region at all times. This circumstance isessential for a safe operation of the compressor. Alsothe two phase length can be maximized even under dy-namic conditions. A pressure controller however cannot overcome these challenges and the set point mustbe chosen according to the prevalent temperatures inevaporator. In this case, a change in temperature of 1K on the source-side of the evaporator may actuallychange the flow situation on the sink-side from almostcompletely flooded to almost completely superheated.This behavior is not desired and can reduce the effi-ciency of the heat exchanger.

Geothermal field modelIn this research, a model for a field of closed loopborehole heat exchangers and a model for horizon-tal slinky-coil heat exchanger including the model forthe surrounding soil has been developed. Only threeheat ports are necessary for these models. The sideconnector is connected to the undisturbed soil temper-ature, the bottom heat port is connected to the con-stant geothermal heat flow from the earth core andthe top connector is connected to the surface tempera-ture, which basically varies with the ambient tempera-ture and the radiation from the sun. For a brine waterheat pump the fluid connectors are simply connectedto the heat pump model. In case of a direct expansionheat pump, the whole system becomes a little bit morecomplicated and the models have to be modified, asthe moving boundary heat exchangers are used for this


- 1557 -

purpose. Here the entire internal interface of the de-veloped geothermal model has been replaced with theheat exchanger model presented in Figure 2.

Coupling of the moving boundary model with thediscretized modelSince the moving boundary model has variable cellsizes and adjacent cells of other models have, incase of a discretized approach, fixed sizes, the cou-pling of the moving boundary model with the dis-cretized model therefore is of great importance. Math-ematically, these methods were described by utiliz-ing ”min()” and ”max()” functions that return thesmallest or largest value of an array. In this way, it ispossible to obtain an explicit set of equations, which isalso continuous when the moving boundary crosses afixed boundary.

RESULTS AND DISCUSSIONBased on a case study described in the next section,a dynamic simulation for a conventional brine wa-ter heat pump has been performed and the resultshave been presented and analyzed. Furthermore, thethree technologies of brine water heat pump, directexchange slinky-coil heat pump and direct exchangeborehole heat pump have been analyzed from a ther-modynamic point of view.

Description of the case studyTo demonstrate the feasibility of the developed ap-proaches in this research, a case study has been set upand a complete heating system of a one-family houseequipped with a brine water heat pump has been inves-tigated. Since the emphasize on this research is placedon the thermo-hydraulic part of the system, the heatdistribution system has been idealized and a theoreti-cal heat demand profile has been generated. Figure 3shows the overall system. As it can be seen, the casestudy contains four main sub-systems, which are ex-plained in the following paragraphs.

Heat demand profileThe theoretical heat demand profile has been gener-ated with a single-family house model and weatherdata for a location near Hamburg. Already-developedhouse and weather models have been used for this pur-pose. The Test Reference Year (TRY) is 2010, and thefollowing assumptions have been made:

• The room temperature is held constant at 21◦C

• Negative heat flows in summer are neglected.

Buffer storageThe buffer storage has been idealized by means of alumped heat capacity. The stratification, observable ina real system, has been thereby completely neglected.This simplification is feasible as the major dynamicbehavior that is introduced by a buffer storage is its in-ertia. The storage capacity has been chosen to be 1000liters. The circulating pump on the hot side of the heat-

ing system is controlled continuously according to theheat demand.

Heat pump modelA heat pump model has been developed within thisstudy. The compressor is controlled by an On-Off con-troller, which evaluates the set point temperature andshows a hysteresis behavior. In this case, the compres-sor power is 1000 W. Also the heat exchanger dimen-sions have been chosen in a way that realistic valuesfor their terminal temperature difference occurred un-der steady state conditions. The controller set pointtemperature difference for the evaporator was set to2.5 K.

Soil modelThe soil model used in this part of this research is thethe soil with slinky coil heat exchanger described inthe geothermal field model section and the dimensionshave been chosen according to [VDI 4640 2, 2010].

Simulation results of the case studySimulation results of the case study for a conventionalbrine water heat pump system have been presentedin Figure 4. The heating demand and the heat pumppower, the flow and return temperatures of the heat-ing water cycle and the maximum temperature in theheat pump (after the compressor), the flow and re-turn temperatures for the geothermal field, the con-denser pressure, the evaporator pressure, the two phasezone length of the condenser and the two phase zonelength of the evaporator have been depicted in the cor-responding graphs.The compressor is either switched on or off, as can beseen by the block structure of the power signal. This iscaused by the hysteresis behavior of the On-Off con-troller.The temperature after the compressor (black line in thesecond graph) fluctuates as a result of the dynamic op-eration of the heat pump. The flow temperature dif-fers from the refrigerant temperature at the inlet of thecondenser by approximately 15 K at almost all timesduring operation. The refrigerant temperature after thecompressor decreases by around 5 K after the shut-down of the heat pump. As the recirculation pumpis also connected to the controller signals of the heatpump, a constant temperature difference of approxi-mately 3 K between flow and return is maintained. Tosum up, the flow temperature (red line in graph B) fluc-tuates around the set point of the heat pump.In the next graph C, the flow and return temperature ofthe collector field has been portrayed. The water tem-perature of the evaporator outlet is also influenced bythe dynamic behavior of the heat pump. During oper-ation, the controller is capable to maintain a constanttemperature difference of around 5 degrees betweenflow and return. After the shut down of the heat pump,the flow temperature converges towards the averagetemperature of the evaporator. Notable are the peaks


- 1558 -

Soil model Heat pump model Buffer storage Heat demand

On-Off

Control

T

Control

ΔT

Co

ntro

l

ΔT

Figure 3: Illustration of the overall system of the case study

during the shut down, which can be explained by thedecrease of the evaporator pressure (graph E) originat-ing from the chosen control strategy of the evaporator.At the beginning, the water at the inlet of the evapora-tor has the same temperature as the initialization tem-perature of the geothermal field, but its temperatureslowly decreases due to the heat extraction.

In the condenser, the pressure is predominantly de-termined by the flow and return temperatures of theheating system. This value varies between 12 and 20bars. The pressure in the evaporator however is influ-enced actively through the controller of the expansionvalve. This maintains a certain temperature differencebetween in and outlet of the heat exchanger at the re-frigerant side.

During operation, the two-phase zone in the condenseris relatively large and accounts for approximately 90% of the total length. Directly after the shout down,the super heated region disappears almost completely.A totally different behavior is observable for the evap-orator. Here, strong fluctuations of the two-phase zonelength occur. During operation, this lengths is around90 % of the evaporator length. Despite the fact thatthe pressure in the evaporator deceases by around 0.5bar, the two-phase zone length remains constant forthe whole simulation. This can be explained by thecontrol strategy which aims to achieve a good wet-ting of the evaporator wall. As soon as the heat pumpshouts down, the temperature in the whole evapora-tor rises abruptly. The refrigerant evaporates almostcompletely and consequently the pressure increases.Choosing a pressure control introduces less pressuredynamics to the heat exchanger but is not as flexibel

as the chosen control strategy in terms of varying op-eration temperatures for the evaporator.These simulation results appear to be plausible withregard to the dynamic operation of heat pump heatingsystems.

Thermodynamic analysisThe first and second laws of thermodynamics havebeen applied to the overall heat pump system of thecase study and each component has been investigatedboth energetically and exergetically. Figure 5 showsthe general system setup for the conventional groundsource heat pump investigated in the case study aswell as a horizontal and a vertical direct exchange heatpump. The boundaries of the two-cycle heat pumphave been chosen according to the figure. Here, foreach of the three heat pump systems, the heat demandis fixed to 3 kW and consequently the compressorpower is adjusted.For the two-cycle heat pump, the same heat pumpmodel from the case study has been used. The onlydifference is a fixed soil temperature of 10 ◦C. Alsothe buffer storage is not considered in this analysissince for all three systems it has been assumed thatthe heat distribution is not changed. One further as-sumption, to obtain a more realistic situation, is thatthe return temperature of the ground source collectorhas already reached 5 ◦C.It would not be fair to compare two technologies withthe assumption that both only have the same amountof heat available from the soil. This would automati-cally affect the more efficient technologies adversely.In order to be able to yet compare the three systems, ithas been assumed that the outlet temperature from the


- 1559 -

0510 4567204060800

2000

4000

Wee

k1W

eek2

0

50100101520 0

50100

Power [W] Temperature [°C] Temperature [°C] Pressure [bar] Pressure [bar] Length [%] Length [%]

Cond

ense

r pre

ssur

e

Evap

orat

or p

ress

ure

Two-

phas

e zo

ne le

ngth

cond

ense

r

Two-

phas

e zo

ne le

ngth

eva

pora

tor

Wat

er te

mpr

eatu

re e

vapo

rato

r out

let (-

) and

inlet

(-)

Wat

er te

mpr

eatu

re co

nden

ser o

utlet

(-),

inlet

(-) a

nd co

mpr

esso

r out

let (-

)

Heat

dem

and

(- -)

and

heat

pum

p po

wer (

-)A B C D E F G

Figure 4: Simulation results


- 1560 -

TSoil = 10°C

1 2

4 3

C

D

E

BA

PComp

PPump

QDemand

.

TSoil = 10°C

1 2

4 3

BAQDemand

.

PComp

TSoil = 10°C

1 2

4 3

BAQDemand

.

PComp

dp

Heat pump model from the case study

two-cycle heat pump horizontal one-cycle heat pump vertical one-cycle heat pump

Figure 5: Boundaries for the exergy analysis

soil is approximately the same for all three systems.This of course requires a different size of the groundsource collector or the borehole heat exchanger.For a brine water heat pump it is totally sufficient toknow the inlet and outlet conditions for the groundsource heat exchanger when it comes to exergy anal-ysis. For the direct exchange systems, an assumptionfor the wall temperature has to be made so that a com-ponent wise analysis is still possible. Therefore, thewall temperature has been assumed to be constant (inthis case 5 ◦C).The vertical one-cycle heat pump has the same setupas the horizontal one. The only difference is that a con-stant pressure increase between the inlet and the out-let of the borehole heat exchanger has been assumed.This pressure drop of 0.2 bar corresponds to a boreholedepths of 100 m.In order to compare the two-cycle application with theone cycle application, all boundary conditions are thesame for both systems. The ambient temperature hasbeen chosen to be at −5◦C and the ambient pressure is1 bar. The undisturbed soil has the same temperatureof 10◦C for all applications.In this thermodynamic analysis three approacheswhere followed: The first one only evaluates the rel-ative irreversibilities and the system efficiency on theheat pump basis, the second one considers all compo-nents of the system and the third one takes into ac-count that the soil has an exergy content too, which isregarded as fuel.For all three cases and different boundaries, the ex-ergy efficiency and the coefficient of performance havebeen shown in Figure 6. Most noticeable here is thefact that the direct applications are slightly better than

the conventional type. This is because of the ab-sence of a recirculation pump. The vertical type iseven more efficient than the horizontal direct exchangeheat pump. In conclusion, the application of directexchange geothermal heat pumps is to be consideredpositively in terms of exergy efficiency and overallsystem performance.

CONCLUSIONSIn the course of this work a dynamic model of a com-plete heat pump system was developed in the object-oriented programing language Modelica. At first, amedium model for propane was implemented, whichproved to be stable, accurate and much faster than theother availabe media libraries. However, the simula-tion speed was still not good enough to simulate aclosed thermo-fluid cycle with standard componentsof the Modelica libraries. Hence, most attention waspaid to finding a transient and yet computational sim-ple model for the heat exchangers of the heat pump.Therefore, a two-phase flow model using the mov-ing boundary method in combination with a switch-ing approach was implemented and tested. With theaid of a coupling approach developed in this research,it was then possible to build a closed cycle model ofa heat pump system and connect it to other adjacentdiscretized components.

The developed Modelica component of the movingboundary heat exchanger is universally usable for dy-namic simulations with any two phase flows and canthus be used not only for the modeling of refriger-ant applications, but also for any kind of boiler orcondenser. Especially for the design of accurate con-trollers, the moving boundary approach offers a valu-


- 1561 -

Figure 6: Exergy efficiency and Coefficient of performance

able tool.On the basis of a case study, a complete heating systemwas simulated. Particularly, the dynamics introducedby the start-up and shut-down of the compressor couldbe reproduced. The simulation speed for this fully dy-namic heat pump model showed to be in an acceptablerange.Besides the dynamic simulations, the model was alsoused for a thermodynamic analysis of three heat pumpsystems. This thermodynamic analysis revealed thepotential of direct exchange geothermal heat pumpsover conventional ground source heat pump systems.Furthermore, it could be shown, for one particularcase, that vertical direct exchange heat pumps offer thepotential to be more efficient than horizontal direct ex-change systems.

ACKNOWLEDGEMENTThe authors gratefully acknowledge the financial sup-port provided by the BMWi (Federal Ministry forEconomic Affairs and Energy), promotional reference0327466A.

ReferencesBlervaque, H., Stabat, P., Filfli, S., Muresan, C., and

Marchio, D. 2012. Comparative analysis of air-to-air heat pump models for building energy simula-tion. In SimBuild 2012, Madison, Wisconsin, USA.

Bonilla, J., Yebra, L. J., Dormido, S., and Cellier, F. E.2012. Object-oriented library of switching mov-ing boundary models for two-phase flow evapora-tors and condensers. Proceedings of the 9th Inter-national Modelica Conference, 9:71–80.

Dassault Systems 2011. Dymola - multi-engineering modelling and simulation.http://www.3ds.com/products/catia/portfolio/dymola.

Jensen, J. M. 2003. Dynamic Modeling of Thermo-Fluid Systems - With focus on evaporators for re-

frigeration. PhD thesis, Technical University ofDenmark.

Li, B. and Alleyne, G. 2010. A dynamic model of a va-por compression cycle with shut-down and start-upoperations. International Journal of Refrigeration,33:538552.

Sangi, R., Jahangiri, P., Klasing, F., Streblow, R., andMller, D. 2014. A medium model for the refrigerantpropane for fast and accurate dynamic simulations.In Proceedings of the 10th International ModelicaConference.

VDI 4640 2 2010. Thermal use of the underground -ground source heat pump systems.

Zapata, J. I., Pye, J., and Lovegrove, K. 2013. A tran-sient model for the heat exchange in a solar ther-mal once through cavity receiver. Solar Energy,93:280293.


- 1562 -

pdf download - · pdf filesystems based on a combined moving boundary and discretized...

Documents