﻿ 割缝筛管水平井注蒸汽热力参数分布规律数值模拟研究

1. 中国石油大学(华东)石油工程学院,山东青岛 266580;
2. 中国石化胜利油田分公司地质科学研究院,山东东营 257061;
3. 中国石油新疆油田分公司勘探开发研究院,新疆克拉玛依 834000

Numerical Simulation in Steam Injection Wells for Optimizing the Distribution of Thermal Parameters in Horizontal Wells with Slotted Liners
Chen Huijuan1, Li Mingzhong1, Wang Yiping2, Jiarela· Nurula3, Zhang Yanyu1
1. School of Petroleum Engineering,China University of Petroleum(Huadong),Qingdao,Shandong,266580,China;
2. Geological Science Research Institute,Sinopec Shengli Oilfield Company,Dongying,Shandong,257061,China;
3. Exploration and Development Research Institute,PetroChina Xinjiang Oilfield Company,Karamay,Xinjiang,834000,China
Abstract:To clearly understand the distribution patterns of thermal parameters during steam injection in horizontal wells completed with slotted liners and to establish a theoretical basis for the optimization of completion processes,a numerical model for the distribution of steam pressure,temperature and dryness in horizontal well while steam injection was developed according to the law of conservation of mass,momentum and energy.Next,the model was solved by iterating both steam pressure and dryness increments. On this basis,the case analysis was made to identify the distribution of thermal parameters of steam along horizontal wellbore and the impacts of slotted liner parameters on the patterns of distribution. The results show that after passing through a horizontal section of 300 m,the steam pressure,temperature and dryness were reduced by 5.8 kPa,0.035 ℃ and 0.128,respectively. When the width,length and density of slot were increased respectively from 0.2 mm to 0.4 mm,100 m to 140 m,and 200 slots/m to 360 slots/m,the steam absorption length would be reduced by 90 m,100 m and 70 m. Within the steam absorption length in the horizontal section,the steam pressures were decreased by 1.5 kPa,1.74 kPa and 1.38 kPa,whereas steam dryness increased by 0.03,0.06 and 0.056,respectively. Steam pressure,temperature and dryness display non-linear reduction in quadratic polynomial relationsalong the horizontal wellbore. Therefore,the increase in slot width,length and density will reduce the drop rate of steam pressures,increase the drop amplitude of steam dryness,and shorten the length of steam-absorption in horizontal section.
Key words: slotted liner    horizontal well    steam injection    steam pressure    steam temperature    steam dryness

1 数学模型的建立

1.1 基本假设

1)油层均质，水平方向无限大，注入的蒸汽在油层中沿着水平井径向进行一维稳态流动；2)割缝筛管水平井注汽管柱的管鞋位于水平段跟端；3)将长度为L的水平井均分为若干连续微元段，每一微元段包含一定数量的割缝，在同一微元段上蒸汽从井筒沿割缝等质量均匀地流入地层，而不同微元段蒸汽的流量不同；4)热量从井筒到筛管外环空及从筛管外环空到地层均为一维稳态传热；5)蒸汽在水平井筒内的流动为稳态流动；6)不考虑接箍散热，忽略蒸汽沿水平方向的热量传递。

1.2 质量守恒方程

 图1 割缝筛管完井水平井微元段示意 Fig.1 Schematic diagram of infinitesimal sectionin horizontal wells with slotted liner

1.3 能量守恒方程

vm=ismAh得:

1.4 动量守恒方程

1.5 未知物理量的求解

1) 湿蒸汽混合物密度。饱和湿蒸汽在水平井筒中的流动为气液两相流，其混合物密度的可采用Beggs-Brill方法[14]计算。

2) 微元段吸汽量。文献[15]根据R.L.Williams[16]等提出的蒸汽注入压力和注入速率之间的关系，建立了微元段吸汽量计算数学模型，利用该模型即可计算出微元段的吸汽量:

3) 摩擦力做功。为反映注入蒸汽在割缝筛管内的实际流动，笔者提出一种新的计算摩擦力做功的方法。其具体思路是：将微元段分为若干个更小微元段，每一小微元段上流体热物性参数相同，计算每一小段的摩擦力做功，然后将其进行迭加，从而求出该微元段总的摩擦力做功。

j排割缝的质量流量isl(j)为：

4) 井筒热损失。割缝筛管完井水平井井筒结构如图2所示。

 图2 割缝筛管完井水平井井筒结构示意图 Fig.2 Schematic diagram of the casing program with a slotted liner in a horizontal well

2 模型的求解

1) 已知水平井跟端的蒸汽压力、温度、干度和质量流量，以水平井筒跟端为起点，将整个水平段分为N段，每段的长度为dl=L/N

2) 估算dl长度内的干度变化Δx和压降变化Δp作为迭代计算的初始值，依次计算出该段平均压力和平均温度；

3) 采用Beggs-Brill方法确定该段平均压力及温度下湿蒸汽混合物物性参数和流动参数；

4) 利用式(17)计算地层的吸汽量，利用式(22)和式(23)计算蒸汽与筛管之间的摩擦力和摩擦力做功；

5) 利用式(15)计算出该段压力梯度dp/dl，进而得到dl长度的压降Δp′；

6) 利用式(24)计算出微元段内井筒热损失，在此基础上，利用式(13)计算该微元段蒸汽的干度及干度变化Δx′；

7) 将计算得出的Δp′、Δx′和第2)步中估算的Δp、Δx进行对比，如果|Δp－Δp′|≤δ且|Δx－Δx′|≤δ，则认为计算结果合理；否则，令Δpp′，Δxx′，返回步骤2)重新计算；

8) 重复步骤2)—7)，计算每一微元段上蒸汽的压力、温度和干度分布，直至各微元段的累加长度大于等于水平井筒的总长度。

3 实例分析

3.1 蒸汽热力参数分布规律

 图3 蒸汽热力参数沿水平井筒的分布 Fig.3 Distribution of thermal parameters of steam along the horizontal wellbore

3.2 割缝筛管参数的影响

 图4 不同割缝宽度下蒸汽热力参数沿水平井筒的分布 Fig.4 Distribution of thermal parameters of steam along the horizontal wellbore under different slot widths

 图5 不同割缝长度下蒸汽热力参数沿水平井筒的分布 Fig.5 Distribution of thermal parameters of steam along the horizontal wellbore under different slot lengths

 图6 不同割缝密度下蒸汽热力参数沿水平井筒的分布 Fig.6 Distribution of thermal parameters of steam along the horizontal wellbore under different slot densities

4 结 论

1) 蒸汽的压力、温度和干度从水平井跟端到趾端逐渐降低，但蒸汽压力和温度的降低幅度越来越小，而干度降低幅度却越来越大，三者沿井筒均呈二次多项式的非线性分布规律。

2) 随着割缝宽度、割缝长度和割缝密度的增大，蒸汽压力和蒸汽温度沿水平井筒下降幅度变缓，蒸汽干度下降幅度增大，水平井吸汽长度降低。因此，在现场采用割缝筛管完井水平井开采稠油时，应选择合理的割缝筛管参数，以提高水平井吸汽长度。

3) 文中所建模型考虑的是蒸汽在地层内的稳态流动，建议继续研究考虑蒸汽在地层内不稳态流动的水平井井筒热力参数计算模型。

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#### 文章信息

Chen Huijuan, Li Mingzhong, Wang Yiping, Jiarela· Nurula, Zhang Yanyu

Numerical Simulation in Steam Injection Wells for Optimizing the Distribution of Thermal Parameters in Horizontal Wells with Slotted Liners

Petroleum Drilling Techniques, 2015, 43(03): 109-115.
http://dx.doi.org/10.11911/syztjs.201503020