臺灣博碩士論文加值系統

本文的主要目的是：（1）利用解析解及數值解方法，研究無窮邊界油層中壓力影響半徑之傳遞，並推導壓力影響半徑方程式；（2）利用所推導的壓力影響半徑方程式，估算有界地層之邊界影響時間，同時，探討典型曲線分析法所得之邊界影響時間與壓力影響半徑所估算之邊界影響時間之一致性，分析出壓力影響半徑係數。
由無窮邊界油層所推導之壓力影響半徑方程式得知，無因次壓力影響半徑的平方與無因次時間之間存有一線性關係。此線性關係即為壓力影響半徑係數。壓力影響半徑係數為一常數，其會隨著所定義的不同的壓力前鋒準則值（亦即，壓力前鋒上所定義之壓力降）而有所不同。當所定義的壓力前鋒準則值由0.1095變化到1.0E-9時，壓力影響半徑係數會從4.00變化到71.15。當井口以固定產率生產時，壓力影響半徑係數與產率大小無關。而當井口以變動產率生產時，若所定義的壓力前鋒準則值較大（大於0.001095）時，壓力影響半徑在地層內的傳遞會受到井口變動產率所影響。膚表因子與壓力影響半徑無關，而井口儲集效應僅會在生產早期影響壓力影響半徑在地層內之傳遞。
利用壓力影響半徑方程式，可以由壓力影響半徑係數以及幾何因子計算有界地層的邊界影響時間。幾何因子是考慮有界地層之幾何形狀以及井口之位置而新建立之參數，其可由有界地層之面積及離井口最近邊界之距離計算而得。本文建立了一些常見的有界地層系統之幾何因子表，可供工程使用。由有界地層之邊界影響時間研究中得知，典型曲線分析法之分離點所對應之邊界影響時間和利用壓力影響半徑係數為17.82所估算之邊界影響時間，兩者之結果最為一致。因此，由典型曲線分析法及壓力影響半徑估算法之邊界影響時間結果之一致性得知，壓力影響半徑係數應為17.82。

The purposes of this study are: (1) to estimate the propagation of the radius of investigation from a producing well in an infinite reservoir by using both analytical and numerical methods; and (2) to estimate the starting time of transient pressure affected by reservoir boundary, i.e., the boundary effect time in a bounded reservoir, and concurrently determine the radius coefficient in the linear relationship between the square of dimensionless radius of investigation and dimensionless time.
In an infinite reservoir, the square of the dimensionless radius of investigation is linearly proportional to the dimensionless time. The radius coefficient in the equation is the linear proportional constant, and varies with different criteria of pressure front defined, i.e., the amount of pressure change from the initial formation pressure at the pressure front of the pressure disturbance area. As the dimensionless pressure defined at the pressure front changed from 0.1095 to 1.0E-9, the radius coefficient varied from 4 to 71.15. The radius coefficient was independent of the level of the flow rate for a well producing at a constant flow rate. For a well producing with variable flow rates, the radius coefficient is not a constant for the case of larger pressure drops defined at the pressure front. The skin factor does not affect the result of the calculated radius of investigation. The wellbore storage volume will affect the propagation of the radius of investigation only at an early time, depending on the wellbore storage volume.
In a bounded reservoir, the dimensionless boundary effect time, i.e., the starting time of transient pressure affected by bounded reservoir, is a function of radius coefficient and geometry factor. The geometry factor is defined to consider the geometry shape of reservoir boundary and the location of the producing well. The values of geometry factor for various reservoir geometry shapes and well locations are derived. For a bounded circular reservoir with a well located at the center, the dimensionless boundary effect time is only a function of radius coefficient and independent on geometry factor. The results of this study show that the radius coefficient is 17.82 which is derived on the fact that the dimensionless boundary effect time estimated from the radius of investigation equation with radius coefficient of 17.82 is consistent with that from the deviated point of pressure type curves of infinite and finite reservoirs.

Abstract ------------------------------------------------------------------- i
中文摘要 ----------------------------------------------------------------- iii
Acknowledgements ----------------------------------------------------------- v
Contents ----------------------------------------------------------------- vii
List of Tables ------------------------------------------------------------ ix
List of Figures ----------------------------------------------------------- xi
Nomenclature ------------------------------------------------------------- xvi
Chapter 1 Introduction ----------------------------------------------------- 1
1.1 Research background ------------------------------------------------ 1
1.2 Study purposes ----------------------------------------------------- 3
Chapter 2 Literature Review ------------------------------------------------ 5
2.1 Radius of investigation and radius of drainage --------------------- 5
2.2 Literature review -------------------------------------------------- 6
Chapter 3 Basic theory ---------------------------------------------------- 15
3.1 Analytical solution of the diffusivity equation ------------------- 15
3.2 The radius of investigation equation ------------------------------ 17
3.3 The boundary effect time equation --------------------------------- 18
3.4 Numerical solution for estimating the radius of investigation and
boundary effect time ---------------------------------------------- 22
Chapter 4 Results --------------------------------------------------------- 27
4.1 Radius of investigation equation using an analytical solution with
a constant flow rate ---------------------------------------------- 29
4.2 Radius of investigation equation using an analytical solution with
variable flow rates ----------------------------------------------- 32
4.3 Radius of investigation equation using a numerical solution ------- 40
4.4 Effect of skin factor on radius of investigation ------------------ 48
4.5 Effect of wellbore storage on radius of investigation ------------- 49
4.6 Boundary effect time of a bounded circular reservoir -------------- 52
4.7 Boundary effect time of a bounded square and rectangular reservoir - 62
Chapter 5 Discussions ----------------------------------------------------- 71
5.1 The radius of investigation equation ------------------------------ 71
5.2 The boundary effect time equation --------------------------------- 76
Chapter 6 Conclusions ----------------------------------------------------- 83
6.1 Conclusions ------------------------------------------------------- 83
6.2 Suggestions of future work ---------------------------------------- 85
References ---------------------------------------------------------------- 87

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