以監測井之溫度時間序列推算溫泉區地層之現地熱傳導係數

Abstract

受壓含水層之溫泉井如同一般地下水井，隨著季節性的降雨補注會造成水壓上升，當井內水壓高過地表高程時，會有自湧現象的發生。井下高溫深層水因自湧上升時，會造成井體增溫，隨著溫泉自湧的持續，井中水溫會趨於穩定，當自湧現象結束時，井中水溫會因為地層熱傳導效應，逐漸下降至自湧前的初始溫度為止，此期間稱為熱恢復期(Temperature Recovery：TR)。熱恢復期溫泉觀測井之溫度時間序列，可利用地層熱傳導數學模型加以模擬，而地層熱傳導係數也可以透過熱恢復期溫泉觀測井現地實測之水溫數據，進行率定的工作。 溫泉井自湧現象受限於降雨及含水層地質等條件的影響，不確定性甚高，其發生之時間與位置無法事先預知，因此，即時且連續之水溫及水位資料觀測難以完整獲得。本研究提出除了溫泉自湧的觀測以外，可藉由抽水試驗方式，使溫泉井下高溫深層水上升，並於井中架設光纖量測系統進行溫度量測，當停止抽水後，水溫下降進入熱恢復期，利用井中的不同深度水溫時間序列變化數據，再透過熱傳導數值模擬以及參數優選模式，可進行各深度地層熱傳導係數之率定，以及相關地層岩性之判識。 由於溫泉井的深度少則幾十公尺，多則數百甚至超過上千公尺，井深遠大於井管的尺寸，當溫泉井水位及流速變動微小時，則井體熱損失主要由井體通過井壁，以熱傳導的方式傳向地層，所以可以將其近似為徑向一維圓柱熱傳導模型。熱傳導數值模擬模式之參數優選，則採用粒子群聚演算法(Particle Swarm Optimization, PSO)，該法係源於人類觀察鳥類覓食行為所發展出來的最佳化演算法工具，粒子群聚演算法具有簡單易行、收斂速度快、設置參數少等優點，已廣泛的被採用於多變量系統分析參數優選的議題研究上。 本研究蒐集國外兩組文獻中的數據：德國黑森林及北海鑽井，來說明所提出地層熱傳導模式與熱傳參數率定的方法，其結果與文獻現地試驗分析結果相當吻合；並進一步在2019年7月23-25日於礁溪溫泉區奇利丹溫泉井觀測井進行現地抽水試驗來產生井內熱源，並量測井中水溫之時間序列變化。現地試驗以空壓機打氣方式(Air-lift)，使井管內水體存在密度差異造成流動，井底高水壓將水體補充至上部，藉此讓井管內部溫度上升。當整口井管內的水溫達到穩定後，停止抽水，井體內部水位與溫度將逐漸回復至初始背景值，光纖纜線將全程於井下不同深度進行溫度量測，取樣時間設定為10分鐘一筆，溫度解析度則為±0.1℃。透過本研究試驗，在沒有自湧的時期，以抽水來使深層熱水往上流，然後利用此溫度差可推求各地層分層之熱傳導係數，而抽水試驗熱恢復期溫度量測時間的調整，則應該考量避免受到溫泉業者抽水影響的干擾。 研究結果顯示：礁溪溫泉奇利丹井不同深度之熱傳導係數，推測分成三層：深度0-50 m熱傳導係數2.57-2.89 W/m℃，推測岩性為砂層；深度55-65 m熱傳導係數1.11-1.68W/m℃，推測岩性為泥層；深度70-100 m熱傳導係數4.04-5.72 W/m℃，推測岩性為礫石層，所得出的數值與當地工程經驗相符。本研究在礁溪溫泉進行現地熱傳導係數研究，此方法經確立後將也可應用於其他溫泉區。

As with typical groundwater wells, hot spring wells drilled into a confined aquifer experience increases in water pressure following seasonal precipitation, and consequently, upwelling occurs. The well temperature then increases as high-temperature deep water rises; as upwelling continues, the water temperature within the well becomes stable. When upwelling ends, the well temperature gradually decreases to the prior level due to thermal conduction in strata; this process is known as temperature recovery (TR). The temperature time series of hot-spring observation wells during TR can be simulated using a mathematical model of stratum thermal conduction; the thermal conductivity (TC) coefficients in strata can be calibrated according to water temperatures that are actually measured at observation wells during TR. The time and location of upwelling at hot spring wells are highly uncertain because the phenomenon is affected by conditions including precipitation and aquifer geology. To address this problem, this study proposed an alternative of hot spring upwelling observation. Using a pumping test, the proposed method allowed the high-temperature deep water at the well bottom to rise. An optical fiber measuring system was installed in the well to measure water temperatures. After the pumping was stopped, water temperature decreased and entered the TR stage. Researchers could then obtain time series data of water temperatures at different depths, simulate TC values, and construct a parameter optimization model to calibrate the TC coefficient at each stratum and determine relevant stratum properties. The depth of a hot spring well can span from dozens of meters to hundreds or even thousands of meters. When changes in water level and flow rate within a well are small, heat energy passes through the well wall and transfers to other strata through thermal conduction, causing heat loss. A unidimensional cylinder model can be used to simulate the thermal conduction process. For the parameter optimization of the simulation model, particle swarm optimization (PSO) was adopted. This algorithm was inspired by foraging birds. PSO is simple with a fast convergence rate, and it requires few parameters. The algorithm has been widely applied to research on parameter optimization in multivariate system analysis. Data from two nondomestic studies concerning the Black Forest in Germany and North Sea well drilling were extracted to verify the proposed stratum thermal conduction model and TC parameter calibration method. The verification results were consistent with the on-site results in the studies. The authors also performed an on-site pumping test between July 23 and July 25, 2019 in an observation well of Cilidan, a hot spring located in Jiaoxi in Yilan County, Taiwan. The test was conducted to generate heat in the well and measure temporal variations in water temperature. The experiment was performed using an air-lift compressor to create differences in density in water in the well casing and cause fluid flow. The high water pressure at the well bottom forced the water to fill up the well, and the temperature of the well casing increased. Pumping was stopped after the water in the well casing reached a stable temperature, after which the water level and temperature in the well resumed their initial background values. During the process, optical fibers were employed to measure temperatures at various depths; the sampling frequency was set to every 10 min, with the temperature resolution being ±0.1°C. In the experiment, when upwelling was absent, the researchers could pump water up so that deep water rose; the resulting temperature differences enabled the computation of TC coefficients at various strata. Notably, temperature measurements during the TR of the pumping test should be adjusted to avoid interference caused by water pumping of hot spring resorts. The experimental results are as follows. In the Cilidan hot spring well, the TC coefficients could be divided into three levels as follows: (1) At a depth of 0–50 m, the TC coefficients were 2.57–2.89 W/m°C; accordingly, the lithology of this stratum mainly comprised sand. (2) At a depth of 55–65 m, the TC coefficients ranged between 1.11 and 1.68 W/m°C; hence, this stratum was speculated to be a mud layer. (3) At a depth of 70–100 m, the TC coefficients were 4.04–5.72 W/m°C, and the lithology indicated the presence of gravel. These values correspond with expectations from previous findings on on-site constructions. This study confirmed that the on-site TC coefficient experiment conducted in Jiaoxi can be performed in other hot spring areas.