本研究的目的是推導並計算地層反應函數（包含：壓力反應函數與產率反應函數），利用生產井或測試井的生產或測試資料可以推求地層的壓力反應函數與產率反應函數，而不需要事先知道地層參數即可預測（或計算）未來的壓力變化與生產率變化。
壓力反應函數與產率反應函數都是從流體擴散方程式的解析解推導而來，在一個特定的儲油層中，可以由生產時的產率與井底流壓資料來推導或計算出壓力反應函數與產率反應函數。利用已求得的壓力反應函數，可以在規劃未來的生產率下，計算或預測未來的壓力變化；或利用已推求的產率反應函數，可以在規劃未來的壓力變化下，計算或預測未來的生產率。在這些計算或預測之中，並不需要使用到任何的地層參數。本研究所推導的方程式與計算流程都經過模擬資料的驗證而證明其正確性，並了解壓力反應函數與產率反應函數受到井孔儲集效應、膚表因子與邊界效應的影響。在案例分析中，由壓力反應函數與產率反應函數可以計算井孔儲集效應結束時間與邊界效應開始時間，並且成功利用壓力反應函數預測未來生產時的壓力變化與利用產率反應函數預測未來生產時的生產率變化。

The purpose of this study is to derive and calculate a formation response function, including the pressure response function (PRF) and rate response function (RRF). These formation response functions can be used to predict the pressure and rate behavior of a producing or testing well without knowledge of reservoir parameters.
The pressure response function equation and rate response function equation are theoretically derived from an analytical solution of the diffusivity flow equation. The pressure response function and rate response function for a specific reservoir also can be derived from knowning wellbore pressure and flow rate information by using trial and error procedures, respectively. Once calculated, the pressure response function can be used to calculate future wellbore pressures for given flow rates. And the rate response function can be used to calculate future flow rates for knowing wellbore pressures. In these calculations or predictions, no reservoir and fluid parameters are necessary. The derived equations and the calculation methodology have been verified in this study by using reservoir simulation data. In these studies, the pressure response function and rate response function have been used to analyze the data with wellbore storage, skin factor, and boundary effect. In the case studies, the ability to calculate the time of ending of wellbore storage and the beginning of boundary effect are demonstrated. It is also shown that pressure response function and a rate response function could be used to calculate future wellbore pressures and flow rates, respectively.

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