【摘要】：本文從分析天然氣不穩(wěn)定滲流數(shù)學模型入手。利用擬壓力函數(shù)和擬時間函數(shù)將非線性的天然氣滲流方程化簡為線性的方程,然后利用“擬穩(wěn)態(tài)”階段的特點,將不穩(wěn)態(tài)滲流方程化簡為穩(wěn)態(tài)方程,再求解穩(wěn)態(tài)方程得到天然氣井的產能方程,最后對產能方程進行分析計算,并且分析對比了另外三種改善的氣井產能方程。根據(jù)擬函數(shù)的定義,本文給出了常規(guī)儲層、壓敏儲層擬壓力函數(shù)和普通擬時間、物質平衡擬時間函數(shù)的計算方法和計算結果。在直角坐標圖中展示了擬壓力函數(shù)曲線、壓敏擬壓力函數(shù)曲線、采出程度與物性參數(shù)(μgcg)關系曲線、采出程度與擬時間函數(shù)關系曲線。針對圓形均質氣藏偏心氣井的不穩(wěn)定滲流模型,利用Laplace變換和Bessel函數(shù)加法定理求解,然后通過漸近分析得到了晚期擬穩(wěn)態(tài)產能方程,計算分析了偏心距對氣井產能的影響。計算結果表明:偏心距的存在使得邊界影響提前,平面徑向流動持續(xù)時間相對變短,無量綱壓力導數(shù)后期產生上翹,這種上翹類似于單一直線斷層的影響,但本質上是不同的,在壓力導數(shù)曲線上不能產生半徑向流直線段;對于給定的儲層,大偏心距的井產量遞減相對較快,在彈性開采條件下,擬穩(wěn)態(tài)生產階段的中后期偏心距大的井彈性產量其實是小的,只是在末期相對大些。針對矩形均質壓敏氣藏不穩(wěn)定滲流模型,利用點源函數(shù)結合Newman乘積方法給出了其解析解式,通過重新定義壓敏擬壓力函數(shù)和壓敏擬時間因子,應用漸近分析給出了晚期擬穩(wěn)態(tài)產能方程。計算結果表明:隨著滲透率敏感性的增加,定流量生產過程中井壁壓力下降增大,定流壓生產則井產量下降幅度增加,表明滲透率的下降引起地層滲流阻力相對增大。本文的研究結果可用于產能分析和預測,為天然氣井的生產方案設計提供基礎數(shù)據(jù)。
[Abstract]:In this paper, the mathematical model of gas unstable seepage is analyzed. The nonlinear natural gas seepage equation is simplified to linear equation by using quasi pressure function and quasi time function, and the unsteady seepage equation is simplified to steady state equation by using the characteristic of "quasi steady state" stage. The productivity equation of natural gas well is obtained by solving the steady-state equation. Finally, the productivity equation is analyzed and calculated, and the other three improved gas well productivity equations are analyzed and compared. According to the definition of quasi function, this paper gives the calculation methods and results of the pseudo pressure function, the general pseudo time function and the material balance pseudo time function of conventional reservoir, pressure sensitive reservoir and general pseudo time function. The pseudo pressure function curve, pressure sensitive pseudo pressure function curve, recovery degree and physical property parameter (渭 gcg) curve and extraction degree and quasi time function curve are shown in the Cartesian coordinate diagram. In view of the unstable percolation model of eccentric gas wells in circular homogeneous gas reservoirs, Laplace transform and Bessel function addition theorem are used to solve the problem, and then the late quasi-steady productivity equation is obtained by asymptotic analysis, and the effect of eccentricity on gas well productivity is calculated and analyzed. The calculation results show that the existence of eccentricity makes the boundary effect advance, the duration of plane radial flow is relatively shorter, and the dimensionless pressure derivative produces upwarping at the late stage, which is similar to the effect of a single linear fault, but it is different in nature. For a given reservoir, the production decline of the well with large eccentricity is relatively fast, and under the condition of elastic exploitation, the radial flow line can not be produced on the pressure derivative curve. The elastic production of wells with large eccentricity in the middle and late stage of quasi-steady production is small, but relatively large at the last stage. In view of the unstable percolation model of rectangular homogeneous pressure-sensitive gas reservoir, the analytical solution of point source function combined with Newman product method is given. By redefining the pressure-sensitive quasi-pressure function and pressure-sensitive pseudo-time factor, The late quasi steady state productivity equation is given by asymptotic analysis. The calculation results show that with the increase of permeability sensitivity, the wellbore pressure decreases and the well production decreases with the constant flow pressure production, which indicates that the decrease of permeability leads to the relative increase of percolation resistance. The results of this paper can be used for productivity analysis and prediction, and provide basic data for the production scheme design of natural gas wells.
【學位授予單位】：中國地質大學(北京)
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：TE328

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