本研究目的為使用數值模式，研究液裂處理（Hydraulic Fracturing）生產井之源函數及其特性。於數值模式中設定不同裂縫傳導度、液裂長度及不同液裂寬度來推求源函數。研究結果（源函數）可用於現場液裂處理後，判斷液裂之長度、寬度及裂縫性質，並可供壓力分析時模式篩選之參考。
本研究首先建立基本數值模擬模式，設定已知產率，計算井底壓力隨時間之變化，與文獻之壓力解析解比對而驗證模式之正確性。再利用模擬所得之壓力及產率資料經反迴旋積分計算源函數，並與文獻之源函數解析解比對，而驗證源函數計算方程式之正確性。然後，設定各種傳導模式（包含有限傳導及無限傳導）、裂縫長度及寬度，由數值模擬模式運算井壓隨時間之變化資料後，計算得源函數。另外，並以膚表因子取代裂縫長度而計算所對應之源函數。
本研究的結果為：在無因次源函數（S（tD））中，（1）液裂井之無因次源函數於時間早期會向下偏離無限表面圓柱源函數，於後期會與無限表面圓柱源函數重合。（註：無限表面圓柱源函數為在無限大的儲集層中的有限大的井眼半徑，於定產率生產的條件下所得之解析解）；（2）當無因次裂縫傳導係數（FCD）為一固定值時，液裂寬度不影響無因次源函數而液裂長度越長時，其無因次源函數與無限表面圓柱源函數重合之時間越晚；（3）無因次裂縫傳導度越大源函數於時間早期偏離無限表面圓柱源函數之程度越大，也會越晚重合無限表面圓柱源函數；（4）源函數之擬合與否與流體之流態相關，與無限表面圓柱源函數重合時，其流態為放射流（Radial Flow）；（5）無因次裂縫傳導度為20π時，其源函數行為與無限傳導之源函數相同，故於源函數推求中，若無限傳導度大於或等於20π，則可視為無限傳導液裂井之源函數。
在無因次源函數S（tDxf）中，（1）由解析解模式所得之無限傳導液裂井之無因次源函數與數值模式推求之結果完全擬合；（2）當無因次裂縫傳導係數（FCD）為定值時，裂縫寬度不影響源函數之行為；而裂縫長度越長，其無因次源函數會往tDxf小的地方延伸；（3）當無因次裂縫傳導係數（FCD）變小時，無因次源函數於初期會向上偏離無限傳導液裂井之無因次源函數，其偏離程度隨係數越小而增加；（4）無因次裂縫傳導係數（FCD）越小，其無因次源函數與無限傳導液裂井之無因次源函數重合時間越晚（5）無因次裂縫傳導度為20π時，其源函數行為與無限傳導之源函數完全相同，故於源函數推求中，若無限傳導度大於或等於20π，則可視為無限傳導液裂井之源函數。
本研究也進行負膚表因子取代液裂長度可行性分析，將液裂長度轉換為負膚表因子，使用數值模式進行運算，研究其壓力行為上與實際設置液裂於數值模式上之差異，並比較其源函數差異。由研究結果得知，若欲研究液裂晚期之壓力變化，則可以負膚表因子取代液裂來施作數值模擬。若欲觀察裂縫初期之壓力變化，則於數值模擬上不可以負膚表因子取代設置裂縫。

The purpose of this work is to derive source functions for a hydraulic fracturing well and to study their characteristics. In the study, different fracture lengths, different fracture widths and different fracture conductivities are used in the simulation runs to obtain source functions, which can be used in the interpretation of well pressure test data.
A basic numerical simulation model is set up to calculate the bottom hole pressure with a given production rate. The result of pressures from the model is validated with analytical solution from literature. The sources functions, from deconvolution of pressure and flow rate from numerical model, are verified with the analytical source functions shown in literature. Then simulation studies are conducted for a vertical fracturing well with different fracture lengths and different fracture widths. The results from these simulation runs are used to derive source functions. Also, we use the relationship between hydraulic fracture length and skin factor in numerical model; and then calculate the source function for a vertical well with skin factor.
There are two types of fracture well source functions used in this study, i.e., dimensionless source function S(tD), in terms of dimensionless time with well radius, and the dimensionless source function S (tDxf), in terms of dimensionless time with fracture half length. In the source function S(tD) in terms of well radius, we obtain the following results: (1) the fracture length will affect the shape of source function. As the fracture length is longer, the value of source function becomes smaller comparing with infinite cylinder surface source function (ISCSF) at early time. And the source function of fracture well will be close to ISCSF at later time; (2) the fracture width does not affect the source function for a dimensionless fracture conductivity(FCD); (3) for the larger dimensionless fracture conductivity, the source function will apart away from ISCSF in early time and will be close to ISCSF at later time; (4) when the flow regime from a producing fracture well becomes radial flow, the source function of the well is close to ISCSF.
In the source function S(tDxf) in terms of half fracture length we obtain the following results: (1) the fracture width does not affect source function under the same dimensionless fracture conductivity; (2) for the smaller dimensionless fracture conductivity , the value of source function will become larger at early time; (3) the smaller the dimensionless fracture conductivity is the later the dimensionless source function S(tDxf) will be close to the infinite conductivity fracture well source function; (4) when the dimensionless fracture conductivity is larger than 20π, the behavior of source function is the same as source function of infinite conductivity fracture.

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