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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Energy Res.</journal-id>
<journal-title>Frontiers in Energy Research</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Energy Res.</abbrev-journal-title>
<issn pub-type="epub">2296-598X</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">824421</article-id>
<article-id pub-id-type="doi">10.3389/fenrg.2022.824421</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Energy Research</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Technical Performance Optimization of a Novel Geothermal Hybrid Power Generation System</article-title>
<alt-title alt-title-type="left-running-head">Zhou et al.</alt-title>
<alt-title alt-title-type="right-running-head">Geothermal Hybrid Power Generation System</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhou</surname>
<given-names>Ying</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Qin</surname>
<given-names>Jiyun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<uri xlink:href="https://loop.frontiersin.org/people/1577290/overview"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Hu</surname>
<given-names>Eric</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Qinglei</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
</contrib>
</contrib-group>
<aff id="aff1">
<sup>1</sup>
<institution>China Institute of FTZ Supply Chain</institution>, <institution>Shanghai Maritime University</institution>, <addr-line>Shanghai</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>School of Mechanical Engineering</institution>, <institution>The University of Adelaide</institution>, <addr-line>Adelaide</addr-line>, <addr-line>SA</addr-line>, <country>Australia</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1021988/overview">Idiano D&#x27;Adamo</ext-link>, Sapienza University of Rome, Italy</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1031506/overview">Nallapaneni Manoj Kumar</ext-link>, City University of Hong Kong, Hong Kong SAR, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1464013/overview">Ephraim Agyekum</ext-link>, Ural Federal University, Russia</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Jiyun Qin, <email>qin.jiyun@foxmail.com</email>
</corresp>
<fn fn-type="other">
<p>This article was submitted to Process and Energy Systems Engineering, a section of the journal Frontiers in Energy Research</p>
</fn>
</author-notes>
<pub-date pub-type="epub">
<day>09</day>
<month>05</month>
<year>2022</year>
</pub-date>
<pub-date pub-type="collection">
<year>2022</year>
</pub-date>
<volume>10</volume>
<elocation-id>824421</elocation-id>
<history>
<date date-type="received">
<day>30</day>
<month>11</month>
<year>2021</year>
</date>
<date date-type="accepted">
<day>07</day>
<month>01</month>
<year>2022</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2022 Zhou, Qin, Hu and Zhang.</copyright-statement>
<copyright-year>2022</copyright-year>
<copyright-holder>Zhou, Qin, Hu and Zhang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>Geothermal Aided Power Generation (GAPG) technology is a geothermal hybrid power system that geothermal energy has been integrated into the fossil fired plant to preheat the feedwater, and displace the extraction steam of fossil fired plant. In such a power system, the heat exchange process between extraction steam and geo-fluid occurs in a heat exchange between. When the geo-fluid in the heat exchanger quench to lower temperature for heat transfer purpose, silica scaling would occur in the heat exchanger system. The performance of the GAPG plant would be influenced by the configuration of the heat exchanger and silica scaling in the heat exchanger. For a GAPG plant, it has two possible configurations for a heat exchanger system: series arrangement and parallel arrangement. The different configuration also impacts on the technical performance of the GAPG plant. The silica scaling in the heat exchanger system would harm the performance of the GAPG plant. In this study, a GAPG power system from a 300&#xa0;MW power plant is used as a case study to understand the impact of displacement selections and heat exchanger arrangement on the performance of the GAPG plant. It was found that there is no silica scaling occurring in heat exchangers system if geo-fluid is used to displace to high-grade extraction steam only. Furthermore, the Parallel arrangement is better than the Series arrangement in terms of the additional power output. Moreover, the GAPG plant has protentional to reduce carbon dioxide emissions by 13%.</p>
</abstract>
<kwd-group>
<kwd>geothermal aided power generation</kwd>
<kwd>configuration</kwd>
<kwd>power system</kwd>
<kwd>silica scaling</kwd>
<kwd>displacement selection</kwd>
</kwd-group>
</article-meta>
</front>
<body>
<sec id="s1">
<title>Introduction</title>
<p>With rapid economic development, the consumption of electricity has supplied an increasing share of the world&#x2019;s total consumption of energy (<xref ref-type="bibr" rid="B10">Christina et al., 2020</xref>). Coal is the most widely used fuel to produce electricity (<xref ref-type="bibr" rid="B10">Christina et al., 2020</xref>). However, with the increasing awareness of the negative environment impacts from carbon dioxide, which is emission from coal fired power plants, the use of other kinds of energy resources to produce electricity has become more attractive (<xref ref-type="bibr" rid="B16">Hargreaves and Jones, 2020</xref>). Renewable resources, such as geothermal energy, solar energy and wind energy, are receiving growing attention for the production of electricity purpose (<xref ref-type="bibr" rid="B16">Hargreaves and Jones, 2020</xref>). However, some of the renewable energy resources such as solar and wind energy have the disadvantage of being intermittent nature. Compared with other renewable energy such as solar and wind energy, geothermal energy has the advantage of being non-intermittent.</p>
<p>For the low to medium temperature geothermal resources in the range of 90&#xb0;C&#x2013;300&#xb0;C, from the thermodynamic points of view, the thermal efficiency of a geothermal alone power plant is capped by the temperature of the geothermal fluid entering geothermal power plants (<xref ref-type="bibr" rid="B35">Zhao et al., 2021</xref>). On the other hand, fossil fuel power plants are presently still the backbone of electricity production, which have relatively high thermal efficiency as the combustion temperature is much higher (<xref ref-type="bibr" rid="B30">Seyfettin, 2021</xref>). Therefore, a hybrid power plan is a practical way to efficiently use geothermal energy and reduce emission from electricity production (<xref ref-type="bibr" rid="B15">Hao et al., 2021</xref>).</p>
<p>The concept of a hybrid geothermal power plant was first presented in the late 1970s by DiPippo (<xref ref-type="bibr" rid="B12">DiPippo et al., 1978</xref>). It was pointed that there are three kinds of hybrid power systems (<xref ref-type="bibr" rid="B27">Kingston Reynolds Thom and Allardice Ltd, 1980</xref>; <xref ref-type="bibr" rid="B11">DiPippo et al., 1981</xref>). The first choice is integrating geothermal fluid into the boiler for superheating, the second choice is using geothermal fluid to preheating feedwater to the boiler, and the third choice is to compound these two choices. Comparing these three choices, DiPippo found that the second choice has the advantages of easy control over than other two choices. In the present study, the second choice is termed geothermal aided power generation (GAPG) technology.</p>
<p>The GAPG technology is a method of integrating geothermal energy into a conventional regenerative Rankine cycle (RRC) power plant technology (<xref ref-type="bibr" rid="B15">Hao et al., 2021</xref>). In such a technology, geothermal energy carried by the geothermal fluid is used to displace extraction steam from the steam turbine by preheating feedwater to the boiler. Therefore, the displaced extraction steam is then can be expended further in the steam turbine. The GAPG plant can be operated both for power-boosting and fuel-saving purposes by adjusting the mass flow rate of feedwater entering the boiler (<xref ref-type="bibr" rid="B21">Kolb, 1998</xref>).</p>
<p>The major thermodynamic advantage of the GAPG technology is that the efficiency of geothermal to power efficiency is no longer capped by the temperature of the geothermal fluid, but the combustion temperature of the plant. Thermodynamic analysis shows that the GAPG technology has an overall improvement in the utilisation of low to medium temperature geothermal resources (<xref ref-type="bibr" rid="B20">Khalifa, 1978</xref>; <xref ref-type="bibr" rid="B19">Khalifa et al., 1978</xref>). Kestin et al. found that, for geothermal fluid at 200&#xb0;C, a GAPG plant can theoretically produce 4% more electricity than the original RRC plant and 60% more work than a geothermal alone power plant (<xref ref-type="bibr" rid="B18">Kestin et al., 1978</xref>). Buchta analysed a GAPG plant modified from a 200&#xa0;MW power plant, and geothermal energy is used to displace extraction steam to low-pressure feedwater heaters, it was found that even for the geothermal fluid temperature at 90&#xb0;C, the geothermal to power efficiency can achieve to about 10% (<xref ref-type="bibr" rid="B7">Buchta, 2009</xref>; <xref ref-type="bibr" rid="B8">Buchta and Wawszczak, 2010</xref>). For a 500&#xa0;MW power plant, GAPG technology can increase electricity production by up to 19% (<xref ref-type="bibr" rid="B39">Zhou et al., 2014</xref>). However, it was found that the thermodynamic of the GAPG plant over other kinds of geothermal alone power plant is dependent on the distance between the geothermal well and RRC power plant (<xref ref-type="bibr" rid="B23">Liu et al., 2016</xref>). Except thermodynamic advantages, it was also pointed that GAPG plants have advantage of lower cost of electricity than other kinds of geothermal alone power plants (<xref ref-type="bibr" rid="B3">Battye et al., 2010</xref>; <xref ref-type="bibr" rid="B5">Borsukiewicz-Gozdur, 2010</xref>).</p>
<p>Besides geothermal resources, solar thermal energy can also be used for preheating purpose, this kind of renewable preheating power system is termed as Solar Aided Power Generation (SAPG) technology (<xref ref-type="bibr" rid="B40">Zhou et al., 2015</xref>). Previous studies found that this kind of SAPG power system still has thermodynamic and economic advantages over solar alone power plants (<xref ref-type="bibr" rid="B36">Zhao et al., 2016a</xref>; <xref ref-type="bibr" rid="B37">Zhao et al., 2016b</xref>; <xref ref-type="bibr" rid="B38">Zhao et al., 2016c</xref>; <xref ref-type="bibr" rid="B32">Waqar et al., 2017</xref>; <xref ref-type="bibr" rid="B33">Zhang et al., 2017</xref>; <xref ref-type="bibr" rid="B34">Zhang et al., 2019</xref>). However, due to the intermittent nature of solar resources, a storage system is needed for the SAPG system (<xref ref-type="bibr" rid="B25">Qin et al., 2017</xref>; <xref ref-type="bibr" rid="B24">Qin et al., 2018</xref>; <xref ref-type="bibr" rid="B26">Qin et al., 2022</xref>). Compared with GAPG and SAPG plant system, the GAPG power system can be operated without thermal storage system, and can overcome the disadvantage of the intermittent nature for the SAPG power system (<xref ref-type="bibr" rid="B31">Sudhakar et al., 2018</xref>; <xref ref-type="bibr" rid="B22">Kumar, 2019</xref>; <xref ref-type="bibr" rid="B2">Agyekum et al., 2021a</xref>; <xref ref-type="bibr" rid="B1">Agyekum et al., 2021b</xref>).</p>
<p>In a GAPG plant, the additional power is not generated directly from the geothermal heat but from displaced/saved extraction steam. Therefore, displacement of extraction steam at different stages leads to different technical benefit (<xref ref-type="bibr" rid="B15">Hao et al., 2021</xref>). This means that the geothermal to power efficiencies of a GAPG plant might be dependent on the displacement stage selection. Previous studies pointed that there are two possible heat exchanger arrangements for the GAPG plant, which were series arrangement and parallel arrangement (<xref ref-type="bibr" rid="B20">Khalifa, 1978</xref>; <xref ref-type="bibr" rid="B19">Khalifa et al., 1978</xref>). In the series arrangement, the heat exchanger is arranged in series with the feedwater heater system of the Rankine cycle power plant. In the parallel arrangement, the heat exchanger is arranged in parallel with the feedwater heater system of the Rankine cycle power plant. It was found that series arrange had the advantages of being easy to control. However, there is a lack of study on the performance of the GAPG plant with different heat exchanger arrangements for a given displacement selection.</p>
<p>In addition, a GAPG plant faces the specific problem of silica scaling in heat exchangers, which would not be allowed for the safe operation of the plant (<xref ref-type="bibr" rid="B29">Setiawan et al., 2019</xref>). In the GAPG technology, with the geothermal fluid from (production) well head for preheating purpose, the temperature of the geothermal fluid would be dropped. Then, the dissolved silicon dioxide might precipitate from the geothermal fluid, and the silica scaling would then occur in the heat exchangers of the GAPG plant. The precipitation rate of silicon dioxide is mainly dependent on the geothermal fluid temperature and silica concentration in the fluid. Therefore, when determining the displacement selection, the potential silica scaling problem in the heat exchangers must be considered.</p>
<p>In the present study, the silica scaling process in heat exchangers with different displacement selections has been considered for studying the impact of displacement selections and heat exchanger arrangement on the performance of the GAPG plant.</p>
</sec>
<sec id="s2">
<title>Geothermal Aided Power Generation</title>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> presents a schematic diagram of a regenerative Rankine cycle power plant. In such a power system, some steams are extracted from the steam turbine through various stages to the feedwater system of the power plant. In the feedwater heater system, the extraction steam is used to preheat the feedwater of the boiler. By doing this, the overall efficiency of the RRC power plant could be increased but it would lead to a decrease in the net power output per kilogram of the steam flow through the boiler.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Schematic diagram of a typical 300&#xa0;MW regenerative Rankine cycle power plant with seven feedwater heater (FWH) and one deaerator.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g001.tif"/>
</fig>
<p>The GAPG plant is based on the RRC power plant. In such a plant, the geothermal energy carried by the geothermal fluid enters a heat exchanger, also termed geo-preheater, sub-system to displace extraction steam for feedwater preheating purpose. The extraction steam replaced by geothermal energy, sometimes termed as saved steam, could then expand further in the lower stages of the steam turbine to generate (more) power. After the feedwater of the RRC power plant is preheated by the geothermal fluid, the geothermal fluid is sent back to the geothermal (injection) well. In order to integrate geothermal energy into the power plant, there are two kinds of arrangement for the heat exchanger sub-system, i.e. the parallel and the series arrangements.</p>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> shows the schematic diagram of a GAPG plant with the parallel heat exchanger arrangement. As shown in <xref ref-type="fig" rid="F2">Figure 2</xref>, in a parallel GAPG plant each high pressure FWHs of the RRC power plant (FWH1 to FWH3 in <xref ref-type="fig" rid="F2">Figure 2</xref>) would potentially have one geo-preheater to transfer of the geothermal heat to the feedwater. Namely, each geo-preheater is in parallel with the displaced FWH. The FWHs that could be displaced by geothermal fluid depends on the geothermal fluid temperature. If the temperature of the geothermal fluid can be used to displace FWH1 in <xref ref-type="fig" rid="F2">Figure 2</xref>, the temperature of the geothermal fluid at point G1 must be higher than the temperature of the feedwater at point 1. In this arrangement, shown in <xref ref-type="fig" rid="F2">Figure 2</xref>, the valves A to C require to be adjusted according to the geothermal fluid flow rate to make sure the feedwater temperatures at the exit of each FWH remain unchanged.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Schematic diagram of parallel GAPG plant feedwater heater system.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g002.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> shows the schematic diagram of the series arrangement of the heat exchanger or geo heater arrangement. As shown in <xref ref-type="fig" rid="F3">Figure 3</xref>, in the series arrangement, there is only two heat exchangers required to preheat feedwater. The geo-preheater 1 is used to displace FWH1 to FWH3 (high pressure FWHs) and the geo-preheater 2, if allowed, is used to displace FWH5 to FWH8 (low pressure FWHs). Similarly (to the parallel arrangement), the Valves A-C, should be adjusted according to the flow rate and the temperature of the geo-fluid at point G1, to make sure the temperature of the feedwater at ws1 remain unchanged.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Schematic diagram of Series GAPG plant feedwater heater system.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g003.tif"/>
</fig>
<p>In a GAPG plant, besides the temperature of geo-fluid, there is another factor that would determine which stage of FWH cloud be displaced, that is silica scaling. As the geothermal fluid transfers heat (to feedwater) in geo-preheaters, its temperature drops. When the temperature of geothermal fluid drops, the dissolved silicon dioxide in the geothermal fluid would precipitate from the fluid. the precipitation rate of silicon dioxide is a function of the temperature and silica concentration of the geothermal fluid (<xref ref-type="bibr" rid="B4">Bhuana et al., 2009</xref>) (<xref ref-type="bibr" rid="B31">Sudhakar et al., 2018</xref>). The precipitation of the silicon dioxide would cause the silica scaling in the heat exchanger and pipelines, which could not be allowed to occur for the safe operation of the plant. Therefore, determining or selecting the right FWH(s) to be displaced, according to the temperature and SiO2 concentration of the geo-fluid, would help to minimize/reduce silica scaling.</p>
</sec>
<sec id="s3">
<title>Simulation Model of the GAPG Plants</title>
<p>To calculate the performance of the GAPG plant, a simulation model has been developed. The simulation model consists of two parts. The first part is used to calculate the GAPG plant&#x2019;s technical performance, and the second part is used to simulate the silica scaling process that occurred in the geo-preheater.</p>
<sec id="s3-1">
<title>Simulation Model of GAPG Plant</title>
<p>For a GAPG plant, the simulation of the GAPG plant is actually simulating the energy and mass balance of the FWH system, in which the Matrix Method is often used (<xref ref-type="bibr" rid="B17">Huang et al., 2019</xref>). In this paper, the Matrix Method is used to simulate the extraction steam&#x2019;s mass flow rate variations after geothermal energy integration. Then, the power output of steam turbine can be calculated by using new calculated mass flow rate.</p>
<p>For a GAPG plant with 8 FWHs (including three high pressure FWHs, one deaerator, and four low pressure FWHs), and extraction steam to all high pressure FWHs has been displaced by geothermal energy, the Matrix for FWH system can be expressed as:<disp-formula id="e1">
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<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mn>6</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
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</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mn>8</mml:mn>
</mml:msub>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:math>
<label>(1)</label>
</disp-formula>Where, <inline-formula id="inf1">
<mml:math id="m2">
<mml:mrow>
<mml:msub>
<mml:mi>q</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kJ/kg) is the decrease of extraction steam specific enthalpy in the <italic>i</italic>th FWH; <inline-formula id="inf2">
<mml:math id="m3">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3c4;</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kJ/kg) is the increase of the feedwater specific enthalpy in the <italic>i</italic>th FWH; <inline-formula id="inf3">
<mml:math id="m4">
<mml:mrow>
<mml:msub>
<mml:mi>r</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kJ/kg) is the decrease of the drained steam specific enthalpy from the (<italic>i-1)</italic>
<sup>th</sup> FWH in the <italic>i</italic>th FWH; and <inline-formula id="inf4">
<mml:math id="m5">
<mml:mrow>
<mml:msub>
<mml:mi>y</mml:mi>
<mml:mi>i</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the each stages of extraction steam mass flow rate. <inline-formula id="inf5">
<mml:math id="m6">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mi>Q</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kJ/s) is the geothermal energy input of <italic>i</italic>th FWH; and <inline-formula id="inf6">
<mml:math id="m7">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mi>m</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> (kg/s) is the boiler mass flow rate. The <inline-formula id="inf7">
<mml:math id="m8">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mi>Q</mml:mi>
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</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is equal to <inline-formula id="inf8">
<mml:math id="m9">
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mover accent="true">
<mml:mi>Q</mml:mi>
<mml:mo>&#x2d9;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mstyle>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>The extraction steam flow rates of each extraction steam at each FWHs with various geothermal energy integration could be calculated by <xref ref-type="disp-formula" rid="e1">Eq. 1</xref>.</p>
<p>In a GAPG plant, the increased power output after geothermal input can be termed as geothermal power output. Therefore, the power efficiency for the whole GAPG plant can be given as:<disp-formula id="e2">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi>&#x3b7;</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mtext>&#x394;</mml:mtext>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>B</mml:mi>
<mml:mi>o</mml:mi>
<mml:mi>i</mml:mi>
<mml:mi>l</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>r</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:math>
<label>(2)</label>
</disp-formula>Where <inline-formula id="inf9">
<mml:math id="m11">
<mml:mrow>
<mml:mtext>&#x394;</mml:mtext>
<mml:msub>
<mml:mi>W</mml:mi>
<mml:mi>e</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the increased power output after geothermal integration; and <inline-formula id="inf10">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi>Q</mml:mi>
<mml:mrow>
<mml:mi>G</mml:mi>
<mml:mi>e</mml:mi>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the geothermal energy input.</p>
</sec>
<sec id="s3-2">
<title>Prediction of the Silica Deposition</title>
<p>In a GAPG plant, the silicon dioxide becomes supersaturated as the geo-fluid flows up and quenches to a lower temperature (<xref ref-type="bibr" rid="B9">Chan, 1989</xref>). Polymerization happens when the concentration of silica is supersaturated and polymerization proceeds to silica (<xref ref-type="bibr" rid="B14">Gunnarsson and Arn&#xf3;rsson, 2005</xref>). The silica scaling takes place in geothermal wells, well pipes, and heat exchanger in the GAPG plant. In geothermal fluid, the rates of silica deposition and polymerization is determined by the PH and salt concentration of geothermal fluid, the residence time, and temperature of geothermal fluid (<xref ref-type="bibr" rid="B14">Gunnarsson and Arn&#xf3;rsson, 2005</xref>). The rate of silica deposition can be controlled by adjusting PH through the addition acid of by adding salt (<xref ref-type="bibr" rid="B14">Gunnarsson and Arn&#xf3;rsson, 2005</xref>). However, adding salt might still have a negative effect on the pipes of power system and environment of geothermal wells. In the present paper, it is assumed that the solubility of silicon dioxide is only controlled by the temperature of the geothermal fluid and the silica scaling occurs in the heat exchanger system of the GAPG system.</p>
<p>In order to optimise the displacement selections of the GAPG plant with different silica concentrations, the net precipitation rate of silicon dioxide should be calculated. The approaches taken to calculate the silica precipitation and deposition rate of silicon dioxide are quite complex and poorly understood (<xref ref-type="bibr" rid="B6">Brown and Bacon, 2009</xref>). A simplified approach using experimental data from Brown and Bacon is used in the present paper to calculate the deposition rate of silicon dioxide.</p>
<p>The precipitation rate of silicon dioxide is mainly determined by the kinetics of amorphous silica in the geothermal fluid. For a geothermal fluid at temperatures ranging from 0 to 300&#xb0;C, the kinetics of amorphous silica precipitation have been determined by the study of Rimstidt and Barnes (<xref ref-type="bibr" rid="B28">Rimstidt and Barnes, 1980</xref>). The reversible reaction of silicon dioxide is shown as:<disp-formula id="equ1">
<mml:math id="m13">
<mml:mrow>
<mml:mi mathvariant="normal">Si</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mi mathvariant="normal">2</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi mathvariant="normal">&#x2b;2</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi mathvariant="normal">2</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mi mathvariant="normal">1</mml:mi>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2194;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi mathvariant="normal">4</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">Si</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mi mathvariant="normal">4</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="normal">aq</mml:mi>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>For this reversible reaction, H4SiO4 (aq) is the precipitation of silicon dioxide. The net precipitation rate can be expressed as (<xref ref-type="bibr" rid="B4">Bhuana et al., 2009</xref>):<disp-formula id="e3">
<mml:math id="m14">
<mml:mrow>
<mml:msubsup>
<mml:mtext>r</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mtext>k</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mtext>Q</mml:mtext>
<mml:mo>/</mml:mo>
<mml:mtext>K</mml:mtext>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>mol</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>L</mml:mtext>
<mml:mo>.</mml:mo>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:math>
<label>(3)</label>
</disp-formula>Where the k<sub>&#x2b;</sub> is the forward rate constant, K is the equilibrium constant and Q is the activity quotient. The Q/K is the degree of saturation (S).</p>
<p>Q is then calculated by<disp-formula id="e4">
<mml:math id="m15">
<mml:mrow>
<mml:mtext>Q</mml:mtext>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac bevelled="true">
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mtext>O</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:math>
<label>(4)</label>
</disp-formula>Where, <italic>a</italic>
<sub>
<italic>i</italic>
</sub> is the activity of species <italic>i</italic>. In the mathematical model, <inline-formula id="inf11">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mtext>i</mml:mtext>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is calculated as the silica concentration. As SiO<sub>2</sub> and H<sub>2</sub>O are present as a solid and a liquid, then <inline-formula id="inf12">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf13">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mtext>O</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mtext>&#xa0;</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula> can be calculated as &#x201c;1.&#x201d;</p>
<p>Rimistidt and Barnes provide a method to calculate k<sub>&#x2b;</sub> and K as a function of the geothermal fluid temperature (<xref ref-type="bibr" rid="B28">Rimstidt and Barnes, 1980</xref>). The forward rate constant k<sub>&#x2b;</sub> and the equilibrium constant are given by:<disp-formula id="e5">
<mml:math id="m19">
<mml:mrow>
<mml:mi>log</mml:mi>
<mml:mi>K</mml:mi>
<mml:mi mathvariant="normal">&#x3d;</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">b</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
<mml:mi>T</mml:mi>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mo>,</mml:mo>
</mml:math>
<label>(5)</label>
</disp-formula>
<disp-formula id="e6">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>logk</mml:mtext>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">2</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">b</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
<mml:mi>T</mml:mi>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">1</mml:mi>
</mml:msub>
<mml:mi mathvariant="normal">&#x2b;</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mi mathvariant="normal">2</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
<mml:mo>/</mml:mo>
<mml:mi mathvariant="normal">T</mml:mi>
</mml:mrow>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:math>
<label>(6)</label>
</disp-formula>
</p>
<p>Rimistidt and Barnes provide the a<sub>1</sub>, a<sub>2</sub>, b<sub>1</sub>, c<sub>1</sub>, c<sub>2</sub> which is shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Temperature functions of the rate constants for silica-water reactions (<xref ref-type="bibr" rid="B28">Rimstidt and Barnes, 1980</xref>).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">logk<sub>&#x2b;</sub> &#x3d; 1.174&#x2013;2.028 &#xd7; 10<sup>&#x2212;3</sup>T-4158/T</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">a<sub>2</sub> &#x3d; &#x2212;0.707, c<sub>2</sub> &#x3d; &#x2212;2598</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>From <xref ref-type="disp-formula" rid="e3">Eq. 3</xref> to <xref ref-type="disp-formula" rid="e6">Eq. 6</xref>, the net precipitation rate of silica with various geothermal fluid temperature and silica concentration can be expressed as follows:<disp-formula id="e7">
<mml:math id="m21">
<mml:mrow>
<mml:msubsup>
<mml:mtext>r</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mtext>b</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mtext>T</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mtext>c</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mtext>c</mml:mtext>
<mml:mn>2</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mtext>T</mml:mtext>
</mml:mfrac>
</mml:mrow>
</mml:msup>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mrow>
<mml:msub>
<mml:mtext>H</mml:mtext>
<mml:mn>4</mml:mn>
</mml:msub>
<mml:msub>
<mml:mrow>
<mml:mtext>SiO</mml:mtext>
</mml:mrow>
<mml:mn>4</mml:mn>
</mml:msub>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mn>10</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:msub>
<mml:mtext>a</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>&#x2b;</mml:mo>
<mml:msub>
<mml:mtext>b</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mtext>T</mml:mtext>
<mml:mo>&#x2b;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mtext>c</mml:mtext>
<mml:mn>1</mml:mn>
</mml:msub>
</mml:mrow>
<mml:mtext>T</mml:mtext>
</mml:mfrac>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>)</mml:mo>
</mml:mrow>
<mml:mfrac>
<mml:mrow>
<mml:mtext>mol</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mtext>L</mml:mtext>
<mml:mo>.</mml:mo>
<mml:mtext>s</mml:mtext>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
<mml:mo>.</mml:mo>
</mml:math>
<label>(7)</label>
</disp-formula>
</p>
<p>By using <xref ref-type="disp-formula" rid="e6">Eq. 6</xref>, the silica scaling process in the heat exchanger system of the GAPG plant can be simulated.</p>
</sec>
</sec>
<sec id="s4">
<title>Case Study</title>
<p>A GAPG plant, modified from a 300&#xa0;MW subcritical RRC power plant, was chosen to be the study case, which is shown in <xref ref-type="fig" rid="F1">Figure 1</xref>. The key parameters of the 300&#xa0;MW power plant are given in <xref ref-type="table" rid="T2">Table 2</xref>. As there is no existing GAPG plant, the validation of the GAPG plant is based on the real operation data. In this study, the simulated results of the Rankine cycle plant model have been compared with real operated data with the case study plant. The simulation results for the power output and mass flow rate to the boiler without geothermal input are 303&#xa0;MW and 241.5&#xa0;kg/s, while the real operation data are 300&#xa0;MW and 245.8&#xa0;kg/s. It can be seen that the comparison results of the GAPG plant show further agreement between the simulation model and reference data.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Key parameters of case study power plant (300&#xa0;MW subcritical power plants).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th colspan="10" align="left">Points in <xref ref-type="fig" rid="F1">Figure 1</xref>
</th>
</tr>
<tr>
<th align="left">Item</th>
<th align="center">Unit</th>
<th align="center">A</th>
<th align="center">B</th>
<th align="center">C</th>
<th align="center">D</th>
<th align="center">E</th>
<th align="center">F</th>
<th align="center">G</th>
<th align="center">H</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Pressure</td>
<td align="center">Bar</td>
<td align="char" char=".">54.41</td>
<td align="char" char=".">34.62</td>
<td align="char" char=".">15.76</td>
<td align="char" char=".">7.56</td>
<td align="char" char=".">4.86</td>
<td align="char" char=".">1.87</td>
<td align="char" char=".">0.632</td>
<td align="char" char=".">0.226</td>
</tr>
<tr>
<td align="left">Temperature</td>
<td align="center">&#xb0;C</td>
<td align="char" char=".">374.9</td>
<td align="char" char=".">313.2</td>
<td align="char" char=".">430.4</td>
<td align="char" char=".">326.3</td>
<td align="char" char=".">276.5</td>
<td align="char" char=".">174.9</td>
<td align="char" char=".">85.9</td>
<td align="char" char=".">61.6</td>
</tr>
<tr>
<td align="left">FWH outlet temperature</td>
<td align="center">&#xb0;C</td>
<td align="char" char=".">269</td>
<td align="char" char=".">240.2</td>
<td align="char" char=".">198.2</td>
<td align="char" char=".">169.1</td>
<td align="char" char=".">146.1</td>
<td align="char" char=".">113.7</td>
<td align="char" char=".">83.1</td>
<td align="char" char=".">58.8</td>
</tr>
<tr>
<td align="left">Drain steam temperature</td>
<td align="center">&#xb0;C</td>
<td align="char" char=".">245.9</td>
<td align="char" char=".">203.8</td>
<td align="char" char=".">174.7</td>
<td align="char" char=".">165.4</td>
<td align="char" char=".">119.3</td>
<td align="char" char=".">88.8</td>
<td align="char" char=".">64.4</td>
<td align="char" char=".">40.2</td>
</tr>
<tr>
<td align="left">Extraction flow rate</td>
<td align="center">kg/s</td>
<td align="char" char=".">16.00</td>
<td align="char" char=".">19.78</td>
<td align="char" char=".">9.70</td>
<td align="char" char=".">14.73</td>
<td align="char" char=".">10.42</td>
<td align="char" char=".">9.44</td>
<td align="char" char=".">7.34</td>
<td align="char" char=".">7.37</td>
</tr>
<tr>
<td colspan="10" align="left">Outlet steam parameters of boiler, and Steam turbine</td>
</tr>
<tr>
<td align="left">&#x2003;Item</td>
<td align="center">Unit</td>
<td align="center">Boiler</td>
<td align="center">Reheater</td>
<td colspan="2" align="center">HP turbine</td>
<td colspan="2" align="center">IP turbine</td>
<td colspan="2" align="center">LP turbine</td>
</tr>
<tr>
<td align="left">&#x2003;Pressure</td>
<td align="center">Bar</td>
<td align="char" char=".">167</td>
<td align="char" char=".">31.16</td>
<td colspan="2" align="center">34.62</td>
<td colspan="2" align="center">4.77</td>
<td colspan="2" align="center">0.052</td>
</tr>
<tr>
<td align="left">&#x2003;Temperature</td>
<td align="center">&#xb0;C</td>
<td align="char" char=".">537</td>
<td align="char" char=".">537</td>
<td colspan="2" align="center">312.8</td>
<td colspan="2" align="center">276.5</td>
<td colspan="2" align="center">33.6</td>
</tr>
<tr>
<td align="left">&#x2003;Flow rate</td>
<td align="center">kg/s</td>
<td align="char" char=".">241.5</td>
<td align="char" char=".">205.8</td>
<td colspan="2" align="center">225.6</td>
<td colspan="2" align="center">170.9</td>
<td colspan="2" align="center">146.8</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>According to <xref ref-type="fig" rid="F1">Figure 1</xref>, the 300&#xa0;MW subcritical RRC power plant has seven feedwater heaters and one deaerator. Four different displacement scenarios have been evaluated in the present study, which are given in <xref ref-type="table" rid="T3">Table 3</xref>.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Case study scenarios.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="left">Scenario No</th>
<th rowspan="2" align="center">Displaced FWHs</th>
<th colspan="2" align="center">Case study power plant</th>
</tr>
<tr>
<th align="center">Geo-fluid inlet temperature (<sup>o</sup>C)</th>
<th align="center">Geo-fluid outlet temperature (<sup>o</sup>C)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Scenario 1</td>
<td align="left">Displacing extraction steam to FWH1 to FWH3</td>
<td align="center">280</td>
<td align="center">180</td>
</tr>
<tr>
<td align="left">Scenario 2</td>
<td align="left">Displacing extraction steam to FWH5 to FWH8</td>
<td align="center">155</td>
<td align="center">45</td>
</tr>
<tr>
<td align="left">Scenario 3</td>
<td align="left">Displacing extraction steam to FWH1 to FWH 8</td>
<td align="center">280</td>
<td align="center">45</td>
</tr>
<tr>
<td align="left">Scenario 4</td>
<td align="left">Displacing extraction steam to FWH5</td>
<td align="center">180</td>
<td align="center">120</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>In Scenario 1, extraction steam to FWH 1 to FWH 3 has been displaced by the geothermal energy. In Scenario 2, the geo-fluid is used to displace extraction steam to FWH5 to FWH8. In Scenario 3, all FHWs have been displaced by the geo-fluid. In Scenario 4, it is assumed that the geothermal fluid from the Scenario 1 (180&#xb0;C) is used to displace extraction steam at points E only.</p>
<p>In the present study, the minimum temperature difference required for heat transfer in heat exchangers is assumed to be 10&#xb0;C. At the (production) well, silica is present as quartz, and the concentration of silica in the reservoir ranges from 500 to 700&#xa0;mg/kg SiO<sub>2</sub>, which is dependent on the temperature at the well head (<xref ref-type="bibr" rid="B13">Fournier and Rowe, 1966</xref>).</p>
</sec>
<sec sec-type="results|discussion" id="s5">
<title>Results and Discussion</title>
<p>In this study, the silicon dioxide precipitation in the geo-preheater system for four scenarios has been simulated. Based on the simulation results, the displacement selection with minimum silica scaling occurring would be selected. The technical performance of the optimal displacement selection with two heat exchanger arrangements has been compared.</p>
<sec id="s5-1">
<title>Silicon Dioxide Precipitation in the Geo-Preheater System</title>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> presents the variation of silicon dioxide precipitation rate for scenario 1. It can be found from <xref ref-type="fig" rid="F4">Figure 4</xref> that temperature at which silicon dioxide precipitation starts and the temperature at which its rate reaches maximum depend on the silicon dioxide concentration in the geothermal fluid. When the silicon dioxide concentration is 700&#xa0;mg/kg, the silicon dioxide begins to precipitate at about 162&#xb0;C, and the maximum precipitation rate occurs at around 140&#xb0;C. If the silicon dioxide concentration was to 550&#xa0;mg/kg, these two temperatures would be 136 and 116&#xb0;C, respectively. This trend provides a mechanism to decrease the precipitation of silicon dioxide in the Geo-preheater system.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Variation of silicon dioxide precipitation rate in the heat exchanger/geo-preheater system for scenario 1.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g004.tif"/>
</fig>
<p>For Scenario 1, the geo-fluid temperature at the inlet of the heat exchangers for the 300&#xa0;MW power plant is assumed to be 280&#xb0;C, and that at the outlet is 180&#xb0;C. Both temperatures i.e. 280&#xb0;C and 180&#xb0;C are well above the precipitation starting temperature, according to <xref ref-type="fig" rid="F4">Figure 4</xref>, even for the highest SiO2 concentration of 700&#xa0;ppm. In other words, precipitation of silicon dioxide or silica scaling would not occur in Scenario 1.</p>
<p>
<xref ref-type="fig" rid="F5">Figure 5</xref> presents the variations of precipitation rate in the Geo-preheater system of the GAPG plant for Scenario 2. For Scenario 2, the geothermal inlet temperature is 155&#xb0;C, and the geothermal outlet temperature is 45&#xb0;C. From <xref ref-type="fig" rid="F5">Figure 5</xref>, it can be found that when the geo-fluid with the concentration of silica at 650 and 700&#xa0;mg/kg, silicon dioxide begins to precipitate from geo-fluid when they enter the Geo-preheater system. When the concentrations of silica are 550 and 600&#xa0;mg/kg, about 90 and 80% of the Geo-preheater system are susceptible to fouling by silicon dioxide. This means that Scenario 2 is not suitable for the GAPG plant.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Variation of silicon dioxide precipitation rate in the heat exchanger system/geo-preheater for Scenario 2.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g005.tif"/>
</fig>
<p>The variations of precipitation rate of silicon dioxide in the Geo-preheater system for Scenario 3 is plotted in <xref ref-type="fig" rid="F6">Figure 6</xref>. For Scenario 3, the geothermal inlet and outlet temperatures are 280&#xb0;C and for 45&#xb0;C. As can be seen in <xref ref-type="fig" rid="F6">Figure 6</xref>, when the temperature decreases to about 160&#xb0;C, the geothermal fluid becomes saturated. This means that about 50% of the heat exchanger system is susceptible to fouling by silicon dioxide. This area is the heat exchanger system parallel with low-pressure heat exchanger system. This means that geothermal fluid with the concentration of silica at 550&#x2013;700&#xa0;mg/kg is also not suitable for the GAPG plant.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Precipitation rate as a function of temperature in the heat exchanger system/geo-preheater for Scenario 3.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g006.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F7">Figure 7</xref> presents the variation of silicon dioxide precipitation rate in the heat exchanger system for Scenario 4. In this Scenario, the geothermal temperature at the inlet is about 180&#xb0;C, which is higher than Scenario 2. However, it can be found that there is still about 30&#x2013;70% of the heat exchanger system is susceptible to fouling by silicon dioxide for the concentration of silica ranging from 550 to 700&#xa0;mg/kg. This means that Scenario 4 is also not suitable for the GAPG plant.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Precipitation rate as a function of temperature in the heat exchanger system for Scenario 4.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g007.tif"/>
</fig>
<p>From <xref ref-type="fig" rid="F4">Figure 4</xref> to <xref ref-type="fig" rid="F7">Figure 7</xref>, it can be concluded that the best displacement option for the GAPG plant is geo-fluid used to displace all high-pressure FWHs, due to the low silica scaling during the preheating process. Therefore, the technical performance of the GAPG plant with two structures for scenario 1 has been compared.</p>
</sec>
<sec id="s5-2">
<title>Comparison of Technical Performance of the Series and Parallel Arrangement</title>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> shows the Extra power output of the steam turbine after different geothermal fluid flow rate integration. <xref ref-type="fig" rid="F8">Figure 8</xref> shows that when the FWH1 to FWH3 are fully displaced by geothermal energy, the two kinds of GAPG plants have the same power output. When the extraction steam from FWH1 to FWH3 is fully displaced by the geothermal energy, the extra output of steam turbine is 38.9&#xa0;MW for both of the GAPG plants. When the extraction steam to all high pressure FWHs has been displaced, the power output can be increased by 13%. This means that if the GAPG plant has been operated for reducing boiler consumption. It has protentional to reduce the 13% of carbon dioxide emissions. However, when the extraction steam from FWH1 to FWH3 is partly displaced by the geothermal energy, the power output of the Parallel GAPG plant is higher than the Series GAPG plant. The reason is thought that in the Series GAPG plant, the lower pressure FWH is displaced firstly, this leads to the lower power output than the Parallel GAPG plant.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>The power output of geothermal energy of two kinds of GAPG plants with different geothermal fluid integration.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g008.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F9">Figure 9</xref> shows the power output percentage difference of two kinds of GAPG arrangements. As shown in <xref ref-type="fig" rid="F9">Figure 9</xref>, when 50&#xa0;kg/s geothermal fluid is integrated into two kinds of GAPG plant, the extra output of the Parallel GAPG plant is 29.3% higher than the Series GAPG plant. With the increase of geothermal fluid, the power output difference percentage decrease with the amount of geothermal energy integration.</p>
<fig id="F9" position="float">
<label>FIGURE 9</label>
<caption>
<p>Comparison of two kinds of GAPG plant output with same amount of geothermal integration.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g009.tif"/>
</fig>
<p>
<xref ref-type="fig" rid="F10">Figure 10</xref> shows the power output difference of two kinds of the GAPG plant with different geothermal fluid input. <xref ref-type="fig" rid="F10">Figure 10</xref> indicates that when the flow rate of geothermal fluid is integrated into two kinds of GAPG plant from 50 to 100&#xa0;kg/s, the output difference increases from 1.1 to 2.1&#xa0;MW. After the geothermal fluid flow rate is 100&#xa0;kg/s, with the increase of geothermal fluid flow rate, the output difference of two kinds of GAPG plant decrease to 0.</p>
<fig id="F10" position="float">
<label>FIGURE 10</label>
<caption>
<p>Power output difference between two kinds of GAPG plants with the same amount of geothermal integration.</p>
</caption>
<graphic xlink:href="fenrg-10-824421-g010.tif"/>
</fig>
<p>
<xref ref-type="table" rid="T4">Table 4</xref> shows the hybrid efficiencies of two kinds of GAPG plant with different geothermal energy integration. The hybrid efficiency is defined as the total output of the steam turbine divided by the boiler fuel consumption and geothermal input. As shown by <xref ref-type="table" rid="T4">Table 4</xref>, with the same amount of geothermal thermal energy input, the two kinds of GAPG plant have almost the same hybrid efficiencies.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Hybrid efficiencies of two kinds of GAPG plant with different amount of geothermal energy integration.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Geothermal fluid flow rate (kg/s)</th>
<th align="center">50 (%)</th>
<th align="center">100 (%)</th>
<th align="center">150 (%)</th>
<th align="center">200 (%)</th>
<th align="center">250 (%)</th>
<th align="center">300 (%)</th>
<th align="center">350 (%)</th>
<th align="center">400 (%)</th>
<th align="center">428.7 (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Parallel GAPG plant</td>
<td align="char" char=".">46.3</td>
<td align="char" char=".">46.1</td>
<td align="char" char=".">45.8</td>
<td align="char" char=".">45.6</td>
<td align="char" char=".">45.4</td>
<td align="char" char=".">45.1</td>
<td align="char" char=".">44.9</td>
<td align="char" char=".">44.7</td>
<td align="char" char=".">44.6</td>
</tr>
<tr>
<td align="left">Series GAPG plant</td>
<td align="char" char=".">46.3</td>
<td align="char" char=".">46.0</td>
<td align="char" char=".">45.7</td>
<td align="char" char=".">45.5</td>
<td align="char" char=".">45.2</td>
<td align="char" char=".">45.0</td>
<td align="char" char=".">44.9</td>
<td align="char" char=".">44.7</td>
<td align="char" char=".">44.6</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="conclusion" id="s6">
<title>Conclusion</title>
<p>In a GAPG plant, geothermal fluid at different temperatures is used to displace different grade extraction steam to different stages of feedwater heater. Different displacement selections lead to different technical performances. As the rate of silica deposition is mainly dependent on the temperature of geothermal fluid, adjusting displacement selections can be used to control the silica scaling process that occurred in the heat exchanger system. Also, there are two configurations for the GAPG plant, Parallel, and Series configurations.</p>
<p>In this study, the silica scaling that occurred in the heat exchanger system for different GAPG plant&#x2019;s displacement selections is simulated to optimise displacement selections. The technical performance for the optimal displacement selections with two structures has been compared. To achieve this aim, a 300&#xa0;MW subcritical power plant GAPG plant has been used as a case study. Four different displacement selections are used as scenarios for assessment. The results indicate that:</p>
<p>When extraction steam to all high pressure FWHs has been displaced by geo-fluid, there is no silicon dioxide scaling occurred for the GAPG plant. In other words, for scenario 1, there is no energy loss caused by silica scaling with different silico dioxide concentrations in the geothermal fluid.</p>
<p>When extraction steam to all low pressure FWHs has been displaced by geo-fluid, it was found that there is at least 30% of heat exchanger system is susceptible to fouling by silicon dioxide.</p>
<p>Considering the silicon dioxide scaling in the GAPG plant&#x2019;s heat exchanger system, displacement of extraction steam to all high pressure FWHs is the best displacement selection for the GAPG plant.</p>
<p>When geo-fluid is used to partly displace the extraction steam of the power plant, the Parallel GAPG plant&#x2019;s geothermal power output is higher than that of the Series GAPG plant. When the geo-fluid flow rate is 100&#xa0;kg/s, there is a maximum power output difference which is 2.1&#xa0;MW. However, extraction steam has been fully displaced by the geo-fluid, two kinds of GAPG plants have the same geothermal output. Under this condition, the GAPG plant has protentional to reduce the emissions of Rankine cycle power plant by 13%.</p>
</sec>
</body>
<back>
<sec id="s7">
<title>Data Availability Statement</title>
<p>The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec id="s8">
<title>Author Contributions</title>
<p>YZ is responsible for the investigation, conceptualization. JQ contributes to conceptualization, methodology, formal analysis. EH contributes to contributes to data curation, formal analysis. QZ contributes to investigation and validation.</p>
</sec>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of Interest</title>
<p>The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<ack>
<p>This paper is supported by the National Natural Science Foundation of China (51875332).</p>
</ack>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s Note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
</sec>
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