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\hyphenation{pi-pe-li-ne pi-pe-li-nes  Wej-he-ro-wo per-for-med po-wer dec-rea-sed des-cri-bed ex-chan-ger ef-fi-cien-cy met-hod}
\journal{Journal of Power Technologies}
%\linenumbers
\begin{document}
\begin{frontmatter}

%\author{Maciej Cholewiński*}
%\author{Łukasz Tomków}

%\address{Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland,\\ * tel. +48668426564, maciej.cholewinski@pwr.edu.pl}

\title{Modelling of a nuclear combined heat and power station supplying heat to the remote municipal customers - the case of Poland}

\begin{abstract}
%\begin{linenumbers}
Nuclear power plants are considered as a source of cheap, clean and reliable source of electric power for both industry and household sector. This paper focuses on technical investigations of implementing a cogeneration unit in the cooperation with a typical PWR (Pressurized Water Reactor). Three heat extraction possibilities were analysed and modeled in order to identify the most favorable one based on different criteria. The investigated possibilities of heat extraction were the by-pass of a turbine, steam bleeding and partial removal of heat from the network of regenerating heat exchangers.\\
The working conditions of a municipal heat network, such as a pressure drop and the heat loses, were calculated and adapted to metropolitan area of Tricity (Poland). The annual demand was analysed considering the current development of heating network. The operational parameters of power plant were based on Asco Nuclear Power Station in Spain. It was observed that it is possible to obtain the significant increase of weighted utilisation factor after the application of some of the heat extraction methods.
%\end{linenumbers}
\end{abstract}
\begin{keyword}
Combined heat and power (CHP) technologies \sep  District energy systems \sep Nuclear power \sep Energy production
\end{keyword}
\end{frontmatter}
\twocolumn
\section{Introduction}
\label{intro}
Cogeneration is widely applied in the conventional coal-fired and gas-fired power stations in order to enhance the useful output from the conversion of a fuel chemical energy. These plants are known as the combined heat and power plants (CHP). The alternative for the conventional CHP processes is fission. In a nuclear power stations large amounts of a low temperature heat energy are produced as a by-product, most of which is currently wasted in condenser. The application of this potential for a district heating system and thus the formation of a nuclear combined heat and power plant (NCHP) may be an economic solution.\\ 
Works on NCHP were performed as early as in the 1950s. In 1957 the construction of Ågesta nuclear power plant started. After commission it produced 10 MWe and provided 100 MWt to Stockholm suburb district heating network \cite{dahlgren}. Small NCHP reactors were developed in USSR and then Russia \cite{samoilov,horak,kuznetsov}. Similar research on new technologies were performed in Japan \cite{imamura}, Canada \cite{paquette} and other countries \cite{csik,marques}.\\
Economical and technical analyses were performed by several research teams. Safa described a system to transport heat from nuclear power over long distances \cite{safa}. Bergroth analysed the application of large NCHP based on Loviisa Nuclear Power plant \cite{bergroth}. UK energy system has been analysed in the context of nuclear heating \cite{jones}. Le Pierrès et al. described the system to transport heat from nuclear power station on the distance of 35~km \cite{lepierres}. Initial analysis of heating application of a new Polish nuclear power station was performed \cite{minkiewicz}. The analysis of inclusion of a nuclear power plant in Polish energy mix was considered \cite{wyrwa}. Another research has shown a possible positive impact of NCHP application on the environment of Warsaw \cite{baurski}. Hanuszkiewicz et al. analysed the application of gas-cooled nuclear as the source of heat for cogenerating cycle \cite{hanuszkiewicz}.\\
Heat can be used not only for a district heating, but also for other purposes \cite{majumdar}. It was proposed to apply a nuclear generated steam to produce ethanol \cite{forsberg}. Konishi suggested to use a nuclear heat for water desalination \cite{konishi}, which was further described in IAEA report \cite{iaea2}. High temperature heat can find applications in chemical and oil industry \cite{kupitz}. Chen et al. suggested to integrate a nuclear source of heat and power with electrolysis device \cite{chen}. The application of a nuclear power for other purposes than electric energy production poses several problems connected with a dynamics of a reactor \cite{taylor}, similarly to the integration of nuclear and renewable power \cite{ruth,piera}. Hong et al. analysed the optimal share of renewable and nuclear power in a power system \cite{hong}. Nian et al. analysed total carbon emissions during the life cycle of a nuclear power plant \cite{nian}.\\
Polish efforts to build a nuclear power station date back to 1971 when the decision has been made by Polish government to start a nuclear energy program. The location next to Żarnowieckie Lake was selected in 1979. In this paper the application of a planned power plant as the source of heat for Tricity (Gdańsk-Gdynia-Sopot conurbation) regional heat network is investigated.
\section{Methods}
\label{sec:1}
\subsection{Localisation}
\label{sec:1.1}
For the purpose of this paper NCHP will be assumed to be located on the site of formerly constructed Żarnowiec Power Station. This localisation was considered as one of the most advantageous during the survey of possible Polish nuclear power plant locations \cite{lokalizacja}. The site is in the proximity of large water reservoirs (Baltic Sea and Żarnowieckie Lake) and an existing energy storage infrastructure (Żarnowiec Pumped Storage Power Station).\\
\begin{figure*}
\begin{centering}
  \includegraphics[width=7.5cm]{fig1a}~\includegraphics[width=7.5cm]{fig1b}
\end{centering}
\caption{Location of the plant. Left - aerial photo of the proposed plant and its surroundings. Right - map showing the proposed route of heat pipeline.}
\label{fig:1}
\end{figure*}
The area which will be supplied with heat by the proposed NCHP is inhabited by approximately  800,000 people. This number includes the citizens of Gdańsk, Sopot, Gdynia, Wejherowo and Rumia, which are the major urban areas in the region. A proposed pipeline starts at the power station and ends in Gdańsk passing through each mentioned town. The route of the pipeline was chosen in order to minimize interference with the protected area of Tricity Landscape Park and the existing constructions.  The site and the proposed route of the pipeline are shown in figure \ref{fig:1}. \\
The distance from the power station site to Gdańsk city center is approximately 62 km. In order to obtain the total length of the pipeline, the length of the compensators has to be considered. It was assumed that an U-shaped compensator with the displacement of 10 m is placed every 200 m. This gives the total number of 310 compensators and the total pipeline length of 68.2~km.
\subsection{Heat demand}
\label{sec:1.2}
The assumptions of heat usage per person are based on a current data for Gdańsk (total population – approx. 460 000). The annual usage of heat according to \cite{pwc} in 2010 was approx. 2.22 TWh (8000 TJ of heat). According to the same report in 2030 (date of planned connection to the electrical grid of first polish NPP) a heat consumption will increase by 15\%. Therefore an anticipated value at the time of scheduled power station commission time is 2.56 TWh. Assuming steady structure of the heating systems and consumer preferences in other locations, a heat demand indicator of 5.53 MWh per capita per year was adopted. This value has to be multiplied to include the remaining region population, as shown in Table \ref{cities}, yielding an annual heat demand of 4.82~TWh (17.4 PJ).\\
\begin{table*}
\caption{Calculated heat demand in cities}
\label{cities}
\begin{tabular}{p{0.25\linewidth}p{0.14\linewidth}p{0.17\linewidth}p{0.18\linewidth}p{0.18\linewidth}}
\hline\noalign{\smallskip}
City & Population & Estimated heat demand in 2030 & \% of a total heat network load&Instantaneous heat flow\\
\noalign{\smallskip}\hline\noalign{\smallskip}
$-$ & $-$ & MWh p.a. & $\%$&MJ\slash s \\
Wejherowo \& Reda & 75 967 & 420 212 & 8.7 &28.3\\
Rumia & 47 500 & 262 747 & 5.5 &76.4\\
Gdynia & 248 000 & 1 371 813 & 28.5&76.4\\
Sopot & 38 000 & 210 197 & 4.3&11.8\\
Gdansk & 462 000 & 2 555 556 & 53.0&143.2\\
\noalign{\smallskip}\hline
\end{tabular}
\end{table*}
\begin{centering}
\begin{figure*}
\begin{centering}
  \includegraphics[width=15cm]{fig5}
\end{centering}
\caption{Heat demand and proposed power load of heat network}
\label{fig:5}
\end{figure*}
\end{centering}
Heat consumption varies over the year as shown in Figure \ref{fig:5}. In this figure the aggregated heat demand is compared with the several scenarios of available heat production of the power plant. Such arrangement allows the need for additional peak heating power from other sources needed to meet the demand to be assessed.\\
The availability of 8016 hours (31 days of NPP down time) was assumed. Every refueling stage of nuclear reactor should be launched by summertime, when heat demand is low. In order to achieve the proper operational parameters (low heat losses, high efficiency of auxiliaries) heat network should work under a steady thermal load during all year. Calculating the demand and supply for heat power, it was assessed, that the power of 250 $MW_{th}$ could be an optimal value. It covers 41.5\% of annual heat demand. The operation of nuclear power plant force the operational parameters of heat network to be as steady as possible.
\begin{centering}
\begin{figure*}
\begin{centering}
  \includegraphics[width=15cm]{fig6}
\end{centering}
\caption{Diagram of heat demand showing assumed load of the heat network}
\label{fig:6}
\end{figure*}
\end{centering}
\subsection{Power station model}
\label{sec:1.3}
The models of cycles were developed in Aspen Hysys. It is based on the operational parameters of Asco Nuclear Power Station using two PWR reactors. Only a single reactor loop was modeled as the heat source of district heating system. The employed equation of state is Peng-Robinson. \\
Power cycle of a modeled power plant consists of two thermally connected loops. Primary loop receives heat from a reactor and moves it to a steam generator. Working fluid of the primary loop is water pressurized to 15.7~MPa. Pressure losses occurring in the loop are included at the steam generator model and were assumed as 0.5~MPa. They are countered with the application of a coolant pump. The major issue connected with this loop is to keep working fluid in liquid state during whole operation. It is done by properly adjusting coolant mass flow and pressure. Failure to meet this requirement might result in water vaporization on the reactor rods. This leads to an uncontrolled heat release and the danger of rod melting and safety layer perforation. Fortunately, due to the application of a modern reactor no Chernobyl-class accident would occur \cite{iaea}.\\
Secondary loop is a Rankine cycle with a steam generator serving as a heat source. In the case of modeled plant steam expansion is performed in a 2-stage high pressure turbine and a 6-stage low pressure turbine. Part of the flow from each stage is rerouted to the network of heat exchangers including reheater and the series of regenerators. Normal operational pressure of steam generator is 66.5~MPa and of condenser is 7~kPa. Steam in the steam generator and in the reheater is superheated to approximately 281\degree C. Total mass flow of steam entering the steam generator is approximately 5850~t/h. 1.4\% of initial steam flow is used to provide power to turbopumps. Expected electric power produced by the power station is 1013~MW. Reactor heat duty is 3088~MW.\\
The model includes adiabatic pressure drop blocks to account for pressure losses occurring in the piping of the plant. Multistream heat exchangers were modeled as the combination of mixer and heat exchanger blocks. Similarly to the actual power station, some amount of steam was allowed to be condensed in the turbines. The schematic diagram of the power station is shown in figure \ref{fig:3}. Its operational parameters are presented in table \ref{tab:oppar}. $p$ is the pressure at given point, $T$ - temperature, $\dot{m}$ - mass flow and $x$ - vapour fraction.
\begin{figure*}
\begin{centering}
 \includegraphics[width=15cm]{fig3}
\end{centering}
\caption{Diagram of a power station without modifications}
\label{fig:3}
\end{figure*}
\begin{table*}
\caption{Operational parameters of a power station}
\label{tab:oppar}
\begin{tabular}{ccccc|ccccc}
\hline\noalign{\smallskip}
Point & $p$ & $T$ & $\dot{m}$ & $x$ &Point & $p$ & $T$ & $\dot{m}$ & $x$\\
\noalign{\smallskip}\hline\noalign{\smallskip}
- & $kg \slash cm^2$ & $\degree C$ & $tonne \slash h$ & - & - & $kg \slash cm^2$ & $\degree C$ & $tonne \slash h$ & - \\
I & 152 & 289.5 & 43000 & 0 & 4 & 15.1 & 261 & 4190 & 1\\
II & 152 & 325 & 43000 & 0 & 5 & 0.07 & 41.7 & 3195 & 0.87\\
1 & 83.1 & 227 & 5857 & 0 & 6 & 0.07 & 41.7 & 4190 & 0\\
2 & 66.5 & 281 & 5857 & 1 & 7 & 83.1 & 145.9 & 4190 & 0\\
3 & 16.1 & 201 & 5042 & 0.91 & 8 & 83.1 & 197.6 & 5857 & 0\\
\noalign{\smallskip}\hline
\end{tabular}
\end{table*}
\subsection{Modeling of district heating system}
\label{sec:1.4}
In the case of models with heat extraction for district heating system a third loop representing the heat pipeline was added. It connects power station with a metropolitan area. Series of heat exchangers representing every major city is included in this loop and connected with pipelines were modeled as pipe block. A district heat system was modeled as parallel, therefore the pipeline consists of the supply and return pipes. To provide heat for customers the part of the flow is routed from the supply pipe to an exchanger and then moved to the return pipe. The flow through each exchanger were adjusted so the removal of heat causes a similar temperature drop. Pumps were also included to counter pressure losses. The diagram of the network is shown in Figure \ref{fig:heatnet}.The details on the calculation of heat and pressure losses are presented in subsection \ref{sec:hpm}. In this paper three mechanisms of heat supply to the district heating system are presented. The goal of each of them is to provide needed heat while minimizing interference with normal operational parameters of the power station.
\begin{centering}
\begin{figure*}
\begin{centering}
  \includegraphics[width=15cm]{heatnet}
\end{centering}
\caption{Diagram of the district heating network}
\label{fig:heatnet}
\end{figure*}
\end{centering}
\subsubsection{By-pass of a single turbine stage}
Common solution applied to extract heat for a district heating system is the application of a back pressure turbine. This leads to the decrease of a produced electric power, the gain being the increase of condensation temperature and pressure. In the case of a power station modeled by us the amount of extracted heat is small when compared to the enthalpy carried by the flow of working fluid through the turbine. Therefore it would be unjustified to remove the entire turbine section down to a condenser. It is proposed to bypass only the single stage of the turbine in which the temperature of working is sufficient to supply district heat exchanger.\\
In the light of these assumptions it was decided to bypass stage~4 of the turbine located in its low pressure section. During the normal operation of the power station dry steam entering this stage has a temperature of 162\degree C and a pressure of approximately 0.51~MPa. It is expanded to approximately 0.2~MPa obtaining a temperature of approximately 121\degree C and a vapor fraction of~0.97. These parameters are optimal to supply the district heat exchanger with heat. We assumed that the district heat exchanger replacing the turbine stage will cause a pressure loss of 0.12~MPa and remove the amount of heat required to supply the previously assumed part of demand. Intermediate expansion pressures $p_{ex}$ of subsequent stages were calculated so that a criterion described with formula \ref{eq:interpres} was met. In this formula $n$ is a stage number.
 \begin{equation}
\label{eq:interpres}
p_{ex_{n}}=\sqrt{p_{ex_{n-1}}\cdot p_{ex_{n+1}}}
\end{equation}
Entire steam flow which normally would enter the turbine stage is passed through the district heat exchanger. Except for the difference in a pressure of exiting working fluid and the further expansion pressures, the rest of the system remains the same.
\subsubsection{Steam bleeding}
The next proposed solution is steam bleeding. In this case only the part of the working fluid flow (known as a bleed steam) is rerouted to a district heat exchanger after exiting the high pressure section of a turbine. Bleed steam gives away heat at the heat exchanger and experiences a pressure loss and partial condensation. Alternatively, in the case of a low heat demand it can be moved to a pressure reduction station. After heat removal it is injected to further stage of low pressure section of the turbine and is further expanded.\\
The major difference between normal and cogenerating operation is a lower steam flow to some stages of the turbine. This causes a decreased electric power production and a lower heat input to the regeneration heat exchangers. Expansion pressures and other operational parameters remain the same. We assumed that the bleed steam after mixing with an expanded steam coming from a turbine stage 6 will be injected to a turbine stage 7. We expect that a condensing pressure in the district heat exchanger will be similar to an inlet pressure of this stage.
\subsubsection{Regeneration heat utilisation}
Our final proposal is to obtain the part of heat from the network of regenerating heat exchangers and use it to supply the district heating network. In this case smaller amount of heat will be supplied to the steam generator. The operational parameters of the turbines will remain the same. However, thermal efficiency of electricity production will still suffer as either more heat would have to be supplied by the reactor or less working fluid would have to flow in the secondary loop in order to maintain proper outlet parameters from the steam generator. To reduce interference with the reactor operation the latter option will be chosen. \\
The amount of heat obtained from regenerating heat exchangers is limited by the amount of heat supplied by streams extracted from the turbines and their parameters, especially temperature. In the case of our solution heat is removed from the line of return streams connecting regenerating heat exchangers. In each heat exchanger occurs the mixing of the flow from a previous one with a steam extracted from a next stage of the turbine. Therefore the flow and the available amount of heat increases with each heat exchanger at the cost of decreasing temperature. Large amount of low-temperature heat can be efficiently used to preheat the stream coming from district heating network.
\subsection{Heat pipeline model}
\label{sec:hpm}
Calculations of a heat pipeline were performed on the basis of PN-EN 13941+A1:2010: \textit{Design and installation of preinsulated bonded pipe systems for district heating} standard. The pipeline is constructed in a non-canal technology of pre-insulated distribution lines. Its cross-section is shown in figure \ref{fig:4}. This pipeline technology was chosen in order to minimize heat losses during the pipeline operation \cite{babiarz}. Heat power in a calculated heat network was chosen in order to obtain rated conditions during all seasons of the year. It guarantees the steady mass flows and reduces additional heat looses during a summertime when a heat demand is low \cite{jachura}. Dimensions of the lines were matched to obey the local recommendations (average velocity of a water between 2 and 3~m/s).
\begin{figure*}
\begin{centering}
 \includegraphics[width=15cm]{fig4}
\end{centering}
\caption{Model of pipeline heat loss calculations}
\label{fig:4}
\end{figure*}
Thermal conductivity of insulation (per length unit) $R_i$ is calculated using formula \ref{eq:heat1}.
\begin{equation}
\label{eq:heat1}
R_i=\frac{1}{2\cdot\pi\cdot\lambda_i}\cdot\ln\frac{D_{i}}{d_{pe}}
\end{equation}
$D_{i}$ is there an external diameter of insulation, $m$, $\lambda_{i}$ - thermal conductivity coefficient of insulation material, equal to 0.028 $W$\slash$mK$, $d_{pe}$ is an external diameter of steel pipe in meters.\\
To compute thermal conductivity of a soil (per length unit) $R_g$ formula \ref{eq:heat2} is used.
\begin{equation}
\label{eq:heat2}
R_s=\frac{1}{2\cdot\pi\cdot\lambda_s}\cdot\ln\frac{4\cdot Z_{c}}{D_{c}}
\end{equation}\\
$D_{c}$ is there an external diameter of a shell in meters, $\lambda_{s}$ - thermal conductivity coefficient of a soil, estimated for wet ground as 2 $W$\slash$mK$, $Z_c$ is the depth of a pipeline foundation equal to 2 $m$.\\
Thermal conductivity between two lines (interaction between supply and return) of a pipeline (per length unit) $R_h$ is found with formula \ref{eq:heat3}.
\begin{equation}
\label{eq:heat3}
R_h=\frac{1}{4\cdot\pi\cdot\lambda_s}\cdot\ln\left(1+\left(\frac{2\cdot Z_{c}}{C}\right)^2\right)
\end{equation}
$C$ is the distance between line axles given in meters.\\
Heat loss coefficients for both supply (formula \ref{eq:heat4}) and return (formula \ref{eq:heat5}) lines were calculated.
\begin{equation}
\label{eq:heat4}
U_1=\frac{R_s + R_i}{\left(R_s+R_i\right)^2-R_h^2}
\end{equation}
\begin{equation}
\label{eq:heat5}
U_2=\frac{R_h}{\left(R_s+R_i\right)^2-R_h^2}
\end{equation}
Heat losses of a pipeline $q$ (per length unit) were calculated using equation \ref{eq:heat6}.
\begin{equation}
\label{eq:6}
q=\left(U_1-U_2\right)\cdot\left(t_{1av}+t_{2av}-2\cdot t_s\right)
\end{equation}
$t_{1av}$ is an average temperature of a medium in a supply line estimated as 135\degree C, $t_{2av}$ - average temperature of a medium in a return line expected as 70\degree C and $t_{s}$ - average temperature of a soil, assumed as 8\degree C.
\begin{table*}
\caption{Geometry and flow velocity of pipelines}
\label{tab:1}
\begin{tabular}{rcccccc}
\hline\noalign{\smallskip}
Line & Pipeline type & $D_c$ & $D_i$ & $d_{pi}$ & $C$ & $w$\\
\noalign{\smallskip}\hline\noalign{\smallskip}
\multicolumn{1}{c} - & - & $m$ & $m$ & $m$ & $m$ & $m$\slash$s$ \\
NPP $\Leftrightarrow$ Wejherowo & DN700 & 1 & 0.976 & 0.695 & 1.5 & 2.52\\
$\rightarrow$ Wejherowo & DN200 & 0.355 & 0.347 & 0.2101 & 0.855 & 2.40\\
Wejherowo $\Leftrightarrow$ Rumia & DN650 & 1 & 0.976 & 0.6458 & 1.5 & 2.67\\
$\rightarrow$ Rumia & DN150 & 0.28 & 0.272 & 0.1603 & 0.78 & 2.58\\
Rumia $\Leftrightarrow$ Gdynia & DN650 & 1 & 0.976 & 0.6458 & 1.5 & 2.51\\
$\rightarrow$ Gdynia & 3 x DN200 & 0.355 & 0.347 & 0.2101 & 0.855 & 2.61\\
Gdynia $\Leftrightarrow$ Sopot & DN550 & 0.8 & 0.778 & 0.5462 & 1.3 & 2.34\\
$\rightarrow$ Sopot & DN150 & 0.28 & 0.274 & 0.1603 & 0.78 & 2.06\\
Sopot $\Leftrightarrow$ Gdansk & DN500 & 0.71 & 0.688 & 0.4954 & 1.21 & 2.62\\
$\rightarrow$ Gdansk & DN500 & 0.71 & 0.688 & 0.4954 & 1.21 & 2.63\\
\noalign{\smallskip}\hline
\end{tabular}
\end{table*}
Geometric parameters of the pipes are shown in table \ref{tab:1}. In the table $d_{pi}$ is an internal diameter of steel pipe. Parameters for supply and return line are equal. Pipeline section to Gdynia was divided into 3 DN200 lines to follow the guidelines suggesting the ratio between the inner dimension of a branch and the main one (close to 1:3). Heat transfer parameters are presented in Table \ref{tab:2}.
\begin{centering}
\begin{table*}
\caption{Heat transfer parameters of pipelines}
\label{tab:2}
\begin{tabular}{rcccccc}
\hline\noalign{\smallskip}
line & $R_s$ & $R_i$ & $R_h$ & $U_1$ & $U_2$ & q\\
\noalign{\smallskip}\hline\noalign{\smallskip}
- & $m\cdot K\slash W$ & $m\cdot K\slash W$ & $m\cdot K\slash W$ & $m\cdot K\slash W$ & $m\cdot K\slash W$ & $W \slash m$ \\
NPP $\Leftrightarrow$ Wejherowo & 0.11 & 1.930 & 0.041 & 0.490 & 0.010 & 90.82\\
$\rightarrow$ Wejherowo & 0.193 & 2.852 & 0.074 & 0.329 & 0.008 & 60.60\\
Wejherowo $\Leftrightarrow$ Rumia & 0.110 & 2.347 & 0.041 & 0.407 & 0.007 & 75.65\\
$\rightarrow$ Rumia & 0.212 & 3.005 & 0.081 & 0.311 & 0.008 & 57.31\\
Rumia $\Leftrightarrow$ Gdynia & 0.110 & 2.347 & 0.041 & 0.407 & 0.007 & 75.65\\
$\rightarrow$ Gdynia & 0.193 & 2.852 & 0.074 & 0.329 & 0.008 & 60.60\\
Gdynia $\Leftrightarrow$ Sopot & 0.128 & 2.011 & 0.048 & 0.468 & 0.011 & 86.42\\
$\rightarrow$ Sopot & 0.212 & 3.047 & 0.081 & 0.307 & 0.008 & 56.60\\
Sopot $\Leftrightarrow$ Gdansk & 0.138 & 1.867 & 0.052 & 0.499 & 0.013 & 91.89\\
$\rightarrow$ Gdansk & 0.138 & 1.867 & 0.052 & 0.499 & 0.013 & 91.89\\
\noalign{\smallskip}\hline
\end{tabular}
\end{table*}
\end{centering}
To calculate pressure drop in pipe Darcy-Weisbach model was used. Darcy equation is used also to compute the friction factor \ref{eq:heat6}.
\begin{equation}
\label{eq:heat6}
\frac{\Delta p}{L}=f_d\cdot\frac{\rho}{2}\cdot\frac{w^2}{d_{pi}}
\end{equation}\\
$\Delta p\slash L$ is a pressure drop per length unit given in Pa/m, $f_d$ - Darcy friction factor, $\rho$ is density of the water in kg/m$^3$, $w$ - average flow velocity of water in a cross-sectional area in m/s.
\subsection{Comparison criteria}
The performance of each proposed NCHP solution was rated based on several criteria. The first one is reactor thermal power $P_{reac}$ marking the amount of nuclear fuel being used. The second is the net amount of electric power $P_{el}$ produced by a power station. Next two criteria are related - $Q_{hn}$ is the amount of heat supplied to district heating network and $\%D$ is the percentage of supplied annual demand. $\eta_{el}$ is electrical efficiency of the plant found with formula \ref{eq:elef}.
\begin{equation}
\label{eq:elef}
\eta_{el}=\frac{P_{el}}{P_{reac}}
\end{equation}
The next criterion is fuel utilisation factor $\eta_{us}$ calculated using equation \ref{eq:fuus}.
\begin{equation}
\label{eq:fuus}
\eta_{us}=\frac{P_{el}+Q_{hn}}{P_{reac}}
\end{equation}
In order to take into consideration the fact that thermodynamically and economically electric power is more valued than heat the coal equivalent of useful product $m_{coal}$ was chosen as the final criterion and is calculated with formula \ref{eq:eqcoal}.
\begin{equation}
\label{eq:eqcoal}
m_{coal}=\frac{P_{el}\cdot r_{el}+Q_{hn} \cdot r_{h}}{P_{reac}}
\end{equation}
$r_{el}$ and $r_{h}$ are there weighting factors based on coal use of a typical CHP. They are equal to 1 and 0.673 respectively. Obtained result gives the amount of coal in tonnes which is saved for each MWh of heat produced by a nuclear reactor.
\section{Results}
\label{sec:2}
Figure \ref{fig:schembypass} shows the diagram of NCHP using heat from partially by-passed low pressure turbine. The differences of operational parameters are minor, except for the decrease of electrical power output. The mass flow of steam flowing through the district heat exchanger on the cold side is 3800 t\slash h. The temperature of district heating water increase from 70\degree C to 135\degree C. The mass flow of working fluid on the hot side is 3724 t\slash h. The temperature at point W1 is 161\degree C, then after passing through district heat exchangers it drops to 121\degree C. During the process most of heat exchange occurs in a condensing regime.\\
\begin{figure*}
\begin{centering}
 \includegraphics[width=15cm]{upust}
\end{centering}
\caption{Diagram of NCHP using heat from the by-passed turbine}
\label{fig:schembypass}
\end{figure*}
The diagram of NCHP using heat from bleed steam is shown in Figure \ref{fig:schembleed}. The mass flow of heating medium on the hot side of the district heat exchanger is 1468 t\slash h. The temperature drops between 261\degree C at point W1 and 78\degree C at point W2. The parameters on the cold side remain the same. The parameters of water entering steam generator also do not change. Similarly to previous solution large part of heat transferred to the district heating water come from steam condensation process.\\
\begin{figure*}
\begin{centering}
 \includegraphics[width=15cm]{bleed}
\end{centering}
\caption{Diagram of NCHP using heat from the bleed steam}
\label{fig:schembleed}
\end{figure*}
The schematic diagram of NCHP using heat extracted from the network of the regenerating heat exchanger network are shown in Figure \ref{fig:schemreg}. Mass flow of district water which enters the network of heat exchangers on the cold side is 3240~t\slash h. Temperature at the inlet is 70\degree C (point D1 on the diagram), at the outlet - 122\degree C (point D2). The increase of temperature is lower than in the case of two former methods. The parameters of flow on the hot side differ between individual exchangers.\\
The major operational parameter which changes when compared to the based model is the temperature of water entering the steam generator. It drops from 227\degree C to 205\degree C. In order to maintain the constant operational parameters of the reactor the mass flow in the point A was decreased from 5857 t\slash h to 5334 t\slash h. Other flows in the secondary loop were decreased proportionally.\\
\begin{figure*}
\begin{centering}
 \includegraphics[width=15cm]{regen}
\end{centering}
\caption{Diagram of NCHP using heat from the regenerating heat exchangers}
\label{fig:schemreg}
\end{figure*}
Table \ref{tab:res1} shows the comparison of analysed heat extraction varaints based on the criteria described before.
\begin{table*}
\caption{Comparison of NCHP variants}
\label{tab:res1}
\begin{tabular}{cccccccc}
\hline\noalign{\smallskip}
Variant & $P_{reac}$ & $P_{el}$ & $Q_{hn}$ & $\% D$ & $\eta_{el}$ & $\eta_{us}$ & $m_{coal}$\\
\noalign{\smallskip}\hline\noalign{\smallskip}
- & $MW$ & $MW$ & $MW$ & $\%$ & - & - & $t \slash MWh$ \\
No modification & 3088 & 1012 & 0 & 0 & 0.328 & 0.328 & 0.138\\
Turbine removal & 3088 & 840 & 270 & 44.9 & 0.272 & 0.359 & 0.139\\
Bleed & 3091 & 817 & 270 & 44.9 & 0.264 & 0.352 & 0.136\\
Regeneration & 2982 & 915 & 219 & 36.4 & 0.307 & 0.38 & 0.149\\
\noalign{\smallskip}\hline
\end{tabular}
\end{table*}
\section{Discussion}
\label{sec:3}
Obtained results show that it is possible to obtain environmentally and economically beneficial effect of application of NCHP. The reduction of electric power output, which accompanies every proposed solution, can correspond with increased utilisation factor. It is generally assumed that for acceptable loss for 6~$kWh_t$ is 1~$kWh_e$ All analysed methods of heat extraction have their advantages and drawbacks.\\
Turbine by-pass leads to a significant decrease of produced electric power and electrical efficiency. Supplied heat demand concurs with the assumptions. The system provides 44.9\% of annual heat demand, the assumed share was 41.5\%. Coal equivalent is marginally higher than in the case of normal operation. The removal of the turbine stage leads to changes in working pressures of the remaining turbines as well as the parameters of the regenerating heat exchangers. Even though, the regenerating network is able to provide working fluid with unchanged parameters to the steam generator. \\
Primary loop can therefore operate with the same parameters. The application of this solution may require the application of a pressure reducing station in order to avoid excessive condensation of working fluid leaving the district heat exchanger. Since the turbine stage chosen to be by-passed was selected based on the similarity of outlet and inlet parameters of the turbine stage and the district heat exchanger, exergy losses are smaller than in the case of next solution.\\
Bleed steam extracted right behind reheater has high parameters and exergy. It is mostly lost, even though after heat extraction it is further expanded in the low pressure turbine. This causes very high losses of electric power output and efficiency. Coal equivalent is actually lower than in the normal operation mode. The main advantage of this solution is small interference with existing design. Operating pressures remain unchanged and the thermodynamics of regenerating network is affected only slightly. This solution allows the assumed part of demand to be fully supplied.\\
The extraction of heat from the network of regenerating heat exchangers leads to the best electrical efficiency among proposed solutions. Coal equivalent is significantly higher than in normal operation. Utilisation factor is also the highest. These advantages come with a cost. The amount of heat which can be reasonably extracted from the regenerating network is insufficient to cover the assumed heating target and amounts only to 36.4\%. Additional problem is the change of temperature of working fluid entering the steam generator. It is lower by 25\degree C than in the unmodified power station. This may require the changes in the design of the steam generator to ensure proper heat transfer and to avoid mechanical stresses.\\
When considering only thermodynamical efficiency the best solution seems to be the extraction of heat from the network of regenerating heat exchangers. However, the application of this method causes strong changes of operational parameters of the primary loop. The remaining methods do not offer significant gains of weighted utilisation factor.\\
The interference with the existing operational parameters may prolong the process of power station licensing. It would also require the costly redesign of power station components. However the observed gain of almost 8\% of coal equivalent in the case of the extraction of heat from the regenerating network may justify these actions. Since heat is commonly needed commodity this profit would be also obtained while commissioning of new power stations without the need to redesign.\\
It was assumed that the power station would supply only the base demand for heat, connected mostly with domestic hot water. Therefore operational parameters would be steady, without seasonal variations. The application of nuclear reactor as a heat source for district heating system offers the advantage of high availability. However, if the system was supposed to cover larger share of annual demand, the problems with waste heat would appear and utilisation factor would decrease.\\
Proposed method of long range heat distribution is simple and do not cause large heat losses. The application of more expensive high efficiency pipelines with additional insulation can further decrease the heat leaks. The major share of operating expenditures of the system is the energy needed to pump water through the long network. It was taken into consideration during the simulations. As shown, even with this additional energy it is still possible for positive effects to be obtained.\\
The application of proposed causes the reduction of environmental pressure. Presented coal equivalent is based sheerly on the energetic considerations. Saving coal leads to the reduction of emissions of carbon dioxide and other harmful gases. Actually the environmental effect is even more pronounced, as many of domestic and local heat sources are extremely inefficient and burn fuels more harmful than coal. They also lack any method of cleaning emissions. The replacement of these sources with clean heat from NCHP may significantly rise the quality of air. Another issue is the decrease of amount of waste heat released to environment and connected with this the reduction of changes especially to the local water bodies.\\
There is no significant increase of radiation risk. Heat exchange in the district heat exchanger occurs with the non-irradiated working medium from the secondary loop. Any irradiated contaminants present in the water from in primary loop are separated. In the extremely unlike case of simultaneous leak in both the steam generator and the district heat exchanger the consumers of heat are far away enough for the short-living products to decay. The risk would be more significant in the case of the application of boiling water reactor. An intermediate loop would be required.\\
\section{Conclusions}
It was observed that a technical potential of implementing cogeneration unit within PWR nuclear power plants exists. By reducing electric power of a nuclear power plant, district water can be warmed up to the network supply conditions and transferred to the remote commercial individual recipients. The possible locations for heat extraction were identified and assessed. The best solution seems to be the extraction of heat from the network of regenerating heat exchanger. However its application would require significant changes in the operational parameters of a power station.\\
In order to identify satisfying working parameters, a feasibility study of local heat demands is necessary in order to ensure steady operation of NCHP. Long distance water heat networks can achieve high efficiencies when pipelines are installed underground and rated operating conditions (such a mass flow and temperature profile) are met during the year, regardless of the season and weather. The application of NCHP can lead to the reduction of environmental impact and the reduction of emissions. Radiation risk is extremely low when applying PWR technology. 
\label{sec:4}
\section*{Acknowledgments}
The authors are grateful to Wroclaw Networking and Supercomputing Center for granting access to the computing infrastructure built in the project No. POIG.02.03.00-00-028/08 "PLATON - Science Services Platform".
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