地埋熱交換器性能與土壤溫度恢復理論分析

Abstract

在地源熱泵系統(GSHPs)的使用中，常安裝地埋熱交換器(BHE)並藉由熱交換器與土壤間的熱交換使用地熱能源，而隨著人們環保觀念的提升，工商業發達提高了系統性能需求和安全或穩定性的重視。不同的土壤物理性質與熱交換器設計，將會有不同的系統或熱交換器性能表現與土壤溫度恢復能力。本研究將利用理論分析在井內以準三維熱傳模型得到地埋熱交換器內流體溫度解，以及視井外土壤為三維多孔介質，在線熱源假設下利用格林函數理論、映像法與變數變換方法得到地下水流動影響的土壤溫度解。首先將以先前研究之實驗數據驗證模型準確性，再建立三種土壤案例並以理論解得知各案例下系統連續操作24小時的流體出口溫度與熱傳率，藉此得知各案例的熱交器性能表現與有最差性能之案例為何，並以鑽井深度變化改善有最差熱交器性能案例狀況，除此之外，也以系統停機後土壤溫度變化了解各土壤案例與改善有最差熱交器性能案例後的土壤溫度恢復情況，最後以一個BHE設計案例探討BHE最佳間距與各種設計需求對BHE串並聯數目之影響。 在各土壤案例(Case1,Case2,Case3)中，Case3有較好的地埋熱交換器性能，並且有好的土壤溫度恢復能力，而Case1則有最差之BHE性能狀況與土壤溫度恢復能力。透過鑽井深度之變化改善最差之BHE性能情況(Case1)可以發現在最低單位長度之熱傳率時，鑽井深度50m、150m與300m時相較於最差之BHE性能情況總熱傳率分別提高92%、347%與535%，最高流體出口溫度則分別降低了2.4%、8.9%與14%。 鑽井深度愈長總長度之熱傳率愈高使流體出口溫度愈低，並可有效提高熱交換器性能，且在操作24小時後停機8小時內， Case1鑽井深度為原長25m，與更改Case1之鑽井深度為50m，150m以及300m時，靠近井壁處各鑽井深度之土壤溫度分別下降3.3°C，3.1°C，2.43°C與1.7°C，發現在靠近井壁時鑽井深度愈長土壤溫度恢復能力愈差，但距離井壁一定距離後鑽井深度變化對土壤恢復能力則沒有明顯的影響。在最後BHE設計案例中，藉由單根BHE影響之土壤升溫與溫度恢復圖可以了解在安裝多根BHE時最佳之BHE間距為何，並透過此最佳BHE間距得知流體出口溫度或是功率需求下的BHE串並聯數目，以供地源熱泵系統設計之參考。

In the use of ground source heat pump system(GSHPs), system is usually installed with borehole heat exchanger(BHE) to use geothermal energy by exchanging thermal energy between the device and ground. Because of the growth of environmental awareness, people definitely value the safety and stability of GSHPs, additionally, different soil property and design of system have different thermal performance of heat exchanger and ability of soil temperature recovery. In this essay, theoretical analysis will be used to obtain fluid temperature solution in heat exchanger based on quasi 3D heat transfer model, and three-dimensional soil temperature solution will be obtained by Green`s function theory, image method and change of variable. Besides, The temperature solution will be proof by experimental data from study. Three cases of soil will be used to understand the performance of BHE under each case, then the case which causes worst performance of heat exchanger will be found and improved by increasing the length of borehole, in addition, the soil thermal recovery will be discussed under each case of soil and length of borehole, finally, the case which is related to design of the BHE system will be discussed. The results show Case 3 has better performance of BHE and the ability of soil thermal recovery, Case 1 has the opposite. Under the case of soil which causes worst performance of BHE, the amount of heat transfer rate will be increased by 92%. 347% and 535% and outlet temperature will be decreased by 2.4%, 8.9% and 14% for each length of borehole 50m,150m and 300m, compared to length of borehole 25m. Increasing the length of borehole will improve the performance of BHE. After closing system, soil temperature will decrease by 3.1°C，2.43°Cand 1.7°C near borehole wall for each length of borehole 50m,150 and 300m, however the influence of borehole length on the ability of soil thermal recovery is small far from BHE. Finally, in the case of BHE design, from temperature distribution of soil thermal production and recovery the optimal spacing between BHEs can be known, additionally, the requirement of power and outlet temperature for the number of series and parallel design of BHE will be obtained.