本研究目的為：（1）推求單口生產井受井眼條件（Wellbore conditions）及無流動邊界（No-flow boundary）影響之源函數及其特性，井眼條件包含有不同的井眼儲集體積（Wellbore storage volume）、膚表因子（Skin factor）及部分穿孔完井（Partially penetration）；而外邊界條件則為生產井與儲集層外圍無流動邊界之間距離的大小；（2）研究相互干擾之多口生產井，在不同的相對距離、不同方位及不同產率下，生產井自身產率之源函數及地層總產率之源函數及其特性。根據所得源函數特性及其對應之井眼條件及無流動邊界範圍，可提供井壓測試分析時，選擇分析模式之參考；另外，也可直接使用源函數推算壓力變化（若已知產率）或估算產率（若已知井眼壓力）。
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驗證。利用模擬可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驗證。再設定各種井眼條件、無流動邊界及多口生產井之數值模式，推求單井及干擾井之源函數。
由研究結果可知，不同的井眼條件會影響源函數之初期行為：（1）井眼儲集體積，會使得源函數（曲線）初期為一水平線，之後再與無限圓柱表面源函數（解析解）重疊（註：無限圓柱表面源函數為有限大的井眼在無限大的儲集層中，於定產率生產的條件下所得之解析解）；（2）源函數不受膚表因子影響；（3）部分穿孔完井之源函數值在初期會大於無限圓柱表面源函數，隨後再與之重疊。無流動邊界範圍大小會改變源函數之晚期曲線行為；地層邊界越小，所得之源函數越早偏離無限圓柱表面源函數，且後期會呈一水平直線。
在多口生產（含觀測）井的源函數推求中，源函數與鄰近井之間的相對距離及產率有關，但與其方位無關。井與井之相對距離越近，觀測井之源函數受影響的時間越快，曲線愈早偏離無限圓柱表面源函數；而鄰近井之生產率越大，其偏離的程度越大。
本研究也進行源函數之頻譜分析，將時間領域之源函數轉換至頻率領域，研究其頻域上的變化特徵。在三種基本解析源函數（無限線源函數、無限點源函數及無限圓柱表面源函數）之頻域特性上，若源函數在時域之初期重疊，則頻域之高頻區會呈現此重疊，反之，若源函數在時域之後期重疊，則此重疊會於低頻區呈現。轉換本研究之各個源函數至頻域領域，並與三種基本源函數比對可知，井眼條件於頻域之源函數型態與三種基本源函數之特性類似，且時域之源函數值越向上方偏離者於頻域之資料點亦會向上方偏離。在無流動邊界中及多井干擾試驗中，頻域之源函數型態恰巧為時域之曲線逆時鐘轉180度。因此，頻譜分析也提供另一種分析模式來預測地層及生產井的特性。

The purpose of this work is to obtain the source functions and to study their characteristics for the following cases: (1) a producing well’s pressure/flow rate affected by wellbore conditions and no-flow boundary. Wellbore conditions include wellbore storage volume, skin factor and partial penetration. The the outer boundary condition is the distance to the outer no-flow boundary from wellbore. The characteristics of source function derived in this study can be used to determine its corresponding wellbore conditions and the distance to the no-flow boundary from well for choosing the model in well-testing analysis. From source function, the wellbore pressure drop can be estimated if flow rates are given, or flow rates can be calculated if wellbore pressure drop is given. (2) a well’s pressure/flow rate affected by other producing well. The characteristics of source function of the well affected by the different distance, position and producing rate of the interference well are also investigated, under multi-well distribution.
A basic numerical simulation model is built to calculate the bottom hole pressure if production rate is given, or to calculate the flow rate if pressure is specified. The results of pressure from numerical model are checked with analytical solution. The souce function, from deconvolution of pressure and flow rates from numerical model, is verified with the analytical source function from literature. Then the source functions, for a well with different wellbore conditions, outer no-flow boundary, and for the multiple producing interference wells, can be calculated from the results of numerical model.
For a producing well with wellbore storage volume, the curve of source function is horizontal at the early time and then coincide with the infinite cylinder surface source function which is an analytical source function of constant terminal rate with finite wellbore in an infinite size reservoir. Basically, source function will not affected by skin factor. For a producing well completed with partial penetration, the value of source function will be higher than infinite cylinder surface source function at the early time and coincide with the source function at later time. In a reservoir with outer no-flow boundary, the source function has a characteristic of horizontal line at later time.
For the case of multiple producing wells in a reservoir, the source function is affected by the production rates of nearby well and the distance between is wells. The closer the distance of nearby well, the sooner the source function be affected. The higher the producing rate of nearby well, the more the deviating from analytical infinite cylinder surface source function will be.
In this study, we also conduct the frequency analysis of source function. The source function is transformed from time domain to frequency domain. The characteristics of source function in frequency domain are studied. We investigate the characteristics of three basic analytical source functions including infinite line source function, infinite point source function and infinite cylinder surface source function. If source functions are the same or coincide at the early stage in time domain, the corresponding source function will be the same or coincide at high frequency in frequency domain. In contrast, if source functions are coincide at the late time in time domain, the corresponding source function will be coincide at low frequency in frequency domain.
The source functions derived in this study are transformed to frequency domain, and then compared with three basic analytical source functions. The characteristics of source functions with different wellbore conditions are similar to the three basic analytical source functions in frequency domain. The high source function value in time domain, will correspond the high source function in frequency domain. In the cases of no-flow outer boundary and the well interfered by other producing well, the characteristics of source function in frequency domain is the total difference from these in time domain. Thus, the result from frequency analyze can be provided some characteristics of reservoir and producing well for selecting model for pressure analysis.

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