| Summary: | 博士 === 國立成功大學 === 資源工程學系碩博士班 === 96 === The purpose of this study is to utilize the convolution and deconvolution to analyze the pressure testing data, including obtaining source functions with various boundary conditions from simulations and using source functions to study the characteristics of source functions of a producing well in the different types of reservoirs.
The solution of flowing fluid in the reservoir (or solutions of the diffusivity equation) can be represented by the relationship among the pressure, flow rate, and source function. With such relationship, in applying either convolution or deconvolution, the third unknown function can be obtained if the other two are known. The pressure drop can be obtained by convoluting flow rates and source functions. If the pressure drop and flow rates are known, the source functions can be derived by deconvoluting the other two.
The source function is dependent on the boundary conditions of the reservoir, including the inner and outer boundary conditions. The inner boundary conditions investigated in this study include wellbore storage effects, skin effects, and partial penetrations. The outer boundary conditions studied are no flow boundary for a closed boundary reservoir, such as a finite reservoir, and water influx to a reservoir from an aquifer, such as water drive. The source function, changing with time, for wellbore storage effects is characterized by a horizontal line at a very early time stage. Then this coincides to the source function of the infinite surface cylinder, for the well without wellbore storage in an infinite reservoir, after the end of wellbore storage effects. The source functions with damage effects, i.e. positive skin factors, are almost the same. For a negative skin factor, the source function is a horizontal line at an early time that subsequently coincides with the infinite line source or infinite surface cylinder source functions. The source functions from wells with various penetration ratios are higher than the infinite surface cylinder source function, and then coincide to the infinite surface cylinder source function at a later time.
The source functions for different external reservoir radii become horizontal lines at a late time or while the outer boundary is affected. The source function of the partially-penetrated well in the center of a reservoir with water coning is consistent with the source function of the partial penetration at an early time. Later, the source function for water coning is lower than the infinite surface cylinder source function. At a late time, when the water breaks through the wellbore, the source function is dependent on the reservoir permeability. The value of the source function for edgewater drive is lower than the infinite surface cylinder source function at a later time. Then the source function for a well producing water has higher value than it does for the infinite surface cylinder source function at a late time stage. The value of the source function for bottomwater drive coincides to the partially-penetrated source function at an early time, and then decreases dramatically at a late time. Finally, when the water breaks through the well, the source function suddenly becomes higher than the infinite surface cylinder source function.
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