并行算法在射孔产能研究应用

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并行算法在射孔产能研究应用

并行算法在射孔产能研究中的应用. 天然气工业,1999;19 (6):63～65

摘　要　文章根据射孔完井的渗流特点,利用有限元方法建立了三维单相稳定渗流的数值模型,数值模拟考虑了孔深、孔径、孔密、孔的相位、污染程度和厚度、压实程度和厚度等射孔参数对油气井产能的影响。有限元方程的求解是在曙光1000 大型并行机上利用区域分解法进行的,针对计算模型进行了并行算法加速比的研究,给出了不同计算结点的并行加速比,结果表明并行算法的计算速度与串行算法的计算速度明显提高;通过各种射孔方案的计算,给出了各种射孔参数对油气井产能影响的曲线,这些成果对于油气田设计射孔方案具有一定的指导意义。

主题词　射孔　射孔参数　并行计算机　有限元法　产能预测

目前,油气田上射孔完井是较为广泛的一种完井方式,射孔参数(孔深、孔径、孔密、孔的相位、污染程度和厚度、压实程度和厚度等) 对油气井产能的影响是一个重要的研究课题。利用数值方法来研究射孔产能的机理起于60 年代〔1〕,较全面地考虑各种射孔参数对油气井产能的影响始于80 年代〔2〕。由于射孔完井采油气时形成的渗流场非常复杂,这就要求人们把渗流区域剖分得很细,才能满足计算精度。由于受计算机内存和计算速度的限制,人们在建立

计算模型时,总是要作一些假设或简化。这次我们在曙光1000 上,利用目前普遍使用的区域分解法〔3〕来求解有限元方程组,取得了比较好的结果。通过各种方案的计算,给出了各种射孔参数对油气井产能影响的曲线,这些成果对于设计射孔方案具有一定的指导意义。

计算模型

1. 数学模型

按照射孔完井渗流场的特点,数学模型采用三维单相稳定渗流方程:

式中: p 为地层压力,MPa ; K 为地层渗透率, ;μ为地层原油气粘度mPa ;Γ1 为已知压力边界;Γ2 为已知流量边界(当q 等于0 时,为不渗透边界) ; n 为Γ2 的法线方向;Ω 为渗流区域。

2. 有限元方程的建立

在三维问题中最基本的单元是四面体单元,记为( e) ,它的四个顶点为有限元剖分的结点,其编号设为 i 、j 、k 、m ,根据里茨变分原理可得第 i 个结点的有限元方程:

同理可写出其他结点的有限元方程,就形成了有限元方程组。

3. 渗流区域的剖分

把三维渗流区域直接剖分成四面体单元,不仅难以绘出醒目的图示,而且会使输入的信息数量太大,因此在实际上都采用组合单元,最常用的是六面体单元,每个六面体组合单元又可剖分成五个四面体单元(有两种不同的剖分形式)〔4〕。只要输入组合单元的信息,可由计算机自动剖分成基本四面体单元进行计算(可按两种剖分形式计算系数矩阵取每个系数的平均值) 。

六面体组合单元的剖分也是有计算机自动完成的,剖分的原则是: ①在平面上以井为中心,径向剖分,夹角为10°。再以井为中心,做不同半径的同心圆剖分,在射孔的顶端比较密,向外向内变得比较疏(图1 - a) ,共有30 层; ②在垂向上,以ΔZ 为步长进行剖分(图1 - b) ; ③根据射孔的设计,在每个射孔处以孔为中心,用四个不同半径的同心圆进行加密剖

分(图1 - b) 。这样就把整个渗流区域剖分成不同大小的六面体组合单元。file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2D6.tmp.jpgfile:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2E7.tmp.jpg

(a)平面上的剖分图                   （b）射孔加密剖分图

图1 　平面上的剖分和射孔加密剖分示意图

有限元方程组的并行求解方法

有限元方程组的求解是在曙光1000 并行机上进行的。根据渗流区域剖分的特点,每一层同心圆上的剖分结点是相同的,比较适合区域分解法的并行算法。具体步骤如下。

有限元方程组形成一个N ×N 的大型稀疏系数矩阵如下:

file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2E8.tmp.jpg

由于系数矩阵很大，本文模型的剖分结点为36×30 ×20 = 21 600 ,再加上射孔处的加密结点,若按16 个射孔计算加密结点数为16 ×32 ×30 = 15 360 ,则系数矩阵是一个36 960 ×36 960 的矩阵。为了减少计算机内存和计算结点之间的信息传递,在实际形成系数矩阵时,本文仅储存非零元素,用两个指示数组来确定元素的具体位置,用一个N ×1 的一维数组来储存与每个结点有关的结点数;用一个N ×22 的二维数组来储存与每个结点有关的具体结点号,这两个数组可在形成系数矩阵时同时形成。一般剖分成六面体组合单元每个结点周围有26 个结点,但通过四面体建立基本单元后,实际上只有18个结点与其有关,在射孔处有些结点周围有33 个结点,实际有关的结点也仅有22 个结点,所以,系数矩阵变成了一个N ×22 的矩阵。

一维指示数组　    　二维指示数组　　    系数矩阵

file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2E9.tmp.jpg       file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2EA.tmp.jpg          file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2EB.tmp.jpg

用超松弛迭代法求解有限元方程组,程序并行化采用部分重叠的区域分解法,具体做法如下:首先按30 层同心圆状剖分不同层上的结点,平均地加载到不同计算结点上。比如加载到4 个计算结点上,1～8 层加载到0 号计算结点上;8～15 层加载到1 号计算结点上;15～22 层加载到2 号计算结点上;22～30 层加载到3 号计算结点上;每迭代一次,就将重叠层上的计算结果相互传递,取算术平均值作下一次迭代的初值,计算中仅需传递重叠层和相邻层,如上

面重叠层(8 、15 、22 层) 和相邻层(7 、9 、14 、16 、21 、23层) 。表1 是不同计算结点数计算时的并行加速比(串行程序计算时间与并行程序计算时间之比) 对比表,表明随着计算结点的增多,计算速度明显加快。

表1 　并行计算加速比对比表

计算结点数	1	2	3	4	5	6	8	10	15	30
计算时间 (min) 计算加速比	78.9 1.00	51.6 1.53	35.9 2.20	29.1 2.71	25.7 3.07	22.4 3.52	19.2 4.11	15.9 4.96	13.3 5.93	11.0 7.17

射孔参数对油气井产能的影响

这次研究所选取的数据: 地层渗透率为0. 01file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2FB.tmp.jpg 、油气井半径( Rw) 为0. 1 m ;根据前人的研究经验影响半径(有限元计算的外边界) 取30 倍的油气井半径,即S Rw = 30 Rw ;影响半径处的地层压力与射孔内的压力差为4 MPa 。在以上假定条件下,我们研究了射孔参数的变化对油气井产能的影响。图中的产率比是计算的射孔产能与裸眼井稳定流产能的理论值之比。

图2 是在没有污染和压实的情况下,射孔密度为每米16 个孔,孔径为4 mm ,90°相位时射孔深度与孔径的变化对产能的影响曲线,从图中可看出,射孔深度和孔径对产能的影响都比较大。

图3 是在没有污染和压实的情况下,射孔密度为每米16 个孔,孔径为4 mm ,90°相位时射孔相位不同对油气井产能的影响曲线,图中表明0°相位产能最低,螺旋式90°相位产能最大。

file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2FC.tmp.jpgfile:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2FD.tmp.jpg

图2 　射孔深度和孔径对产能影响曲线            图3 　射孔相位对产能的影响曲线

file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2FE.tmp.jpg   file:///C:\Users\ADMINI~1\AppData\Local\Temp\ksohtml\wpsE2FF.tmp.jpg

图4   污染程度对产能的影响曲线              图5   压实程度对产能的影响曲线

图4 是不考虑压实,仅考虑污染的情况下,射孔密度为每米16 个孔,孔径为4 mm ,90°相位,污染深度为0. 3 m 时,不同污染程度对产能的影响曲线,图中Kd 代表污染区渗透率与原地层渗透率的比值。图中可看出,在射孔深度小于污染深度时,污染程度对产能的影响较大;而射孔深度大于污染深度时,污染程度对产能的影响较小。

图5 是不考虑污染,仅考虑压实的情况下,射孔密度为每米16 个孔,孔径为4 mm ,90°相位,压实深度为0. 004 m 时,不同压实程度对产能的影响曲线,图中Kc 代表压实区渗透率与原地层渗透率的比值。图中可看出,压实程度对产能的影响较大,这是因为压实区包围了整个射孔。

以上研究表明,利用并行算法求解地下渗流方程计算速度比串行算法的计算速度明显提高,因此,并行算法应该在射孔产能研究、油气藏数值模拟等研究中被推广应用。本文给出的各种射孔参数对射孔产能的影响结果对油气田设计射孔方案具有一定的指导意义。

ABSTRACT :The main reasons of the well slough occurred in the course of drilling under the complex geological conditions in east Sichuan region and several common types of well slou- gh (caused by high-angle formation ,by easy-to-hydrate formation , by ground stress and by engin -eering factors etc. )are analyzed in this paper. The anti-sloughing methods for east Sichuan region (i.e. using anti-sloughing drilling fluid,determining reasonable drilling fluid density and finding zone with smaller stress etc.)and the problem in preventing and treating well slough and research direction in future are introduced also.

SUBJECT HEADINGS:Sichuan basin,East,Complex structure,Anti-sloughing drilling fluid ,Technique

APPLICATION OF FULL 3 - D FRACTURINGDESIGN SOFTWARE TO ULTRA DEEP WELL FRACTURINGDESIGN

ABSTRACT:Because the pump pressure and temperature at the time that ultra deep well fra-    cturing operation is made are very high ,if fracturing engineer can not exactly predict the operating pump pressure and the temperature profile in fractures ,it is difficult to make a fracturing design suited to ultra deep formation ,leading to failure in the operation finally. In view of the. Character-

ristics of the ultra deep wells in Tarim DH oil field ,an optimum fracturing design for the three water injection wells has been made through accurately predicting the operating pump pressure,  understanding the temperature profile in fractures and mastering the fracture extending law by use of full 3 - D fracturing design software ( Terra Frac) and by combination with the results in reserv-  oir simulation. The field operation came to a successful conclusion and obtained an obvious augmented injection effect by use of the boosting pump fracturing unit and the premium and low-damage new organic fracturing fluid system suited to ultra deep formation..

SUBJECT HEADINGS :Ultra deep well , Three dimensional ,Fracturing design ,Pump pressure ,Temperature ,Fracture extension.

APPLICATION OF PARALLEL COMPUTATION METHOD IN PERFORATION PROD UCTIVITY RESEARCH

ABSTRACT:According to the seepage feature of perforation completion ,a 3 - D single phase and stable seepage numerical model has been established by use of finite element method. The influence of the perforation parameters (perforating depth , perforation diameter , shot density,perforation phase , degree of damage and thickness of the interval damaged ,as well as degree and thickness of compaction etc. ) on oil and gas well′s productivity was considered in numerical simulation. The solution of finite element equation was acquired by adopting parallel domain decomposition method in Dawn 1000. Taking aim at the computation method ,a study of the speedup ratio of parallel computation was made ,given out the parallel speedup ratio at different computing nodes. The results show that the computing rate of parallel method is obviously faster than that of serial one. Through the computations of various perforation plans , the curves reflecting the influence of various perforation parameters on the productivity of oil and gas wells have been given out , which is of a certain directive function for designing the perforation plans of oil and gas fields.

SUBJECT HEADINGS : Perforation , Perforating parameter , Parallel computation , Finite element method , Productivity forecast.

COUPLING ANALYSIS OF THE PRESSURE AND TEMPERATURE IN GAS WELL BOREHOLE

ABSTRACT:The distributions of the pressure and temperature in a wellbore are two important parameters in the management ,design and dynamic analysis of gas wells. In this paper ,a coup-

ling analysis model for the pressure and temperature in gas well borehole is established through overcoming the shortcomings of previous articles in the pressure and temperature calculation

and synthetically considering the interrelation between the pressure and temperature. This model is composed of pressure calculation model and temperature calculation one. For the pressure

calculation model , the effect of kinetic energy change is considered. For the temperature distri-

bution model ,it is assumed that the heat transfer in wellbore is steady-state one and that in the

adjacent formations is transient one , and the effect of the heat caused by friction on the distribute-

ion of the temperature in wellbore is considered also. The whole wellbore is first divided into seve

ral intervals before the distributions of the pressure and temperature are calculated ,and then ,the physical property parameters of each interval are acquired. Because these parameters are also the

functions of the pressure and temperature ,whereas the pressure and temperature are the unknown

numbers necessary to be acquired in the calculation ,thus ,it can be seen that the pressure and temperature are coupled with each other and it is necessary to use iterative method to solve them. The method for acquiring the initial value of the temperature in iterative calculation is given out in this paper. Finally ,the model is verified by use of the practical data from 6 wells in Sichuan gas fields ,which shows that the model is of a higher accuracy ;its calculation method is simple and it is easy to be operated , thus it can satisfy the engineering needs in the analysis and calculation of the pressure and temperature distributions in producing and testing wells..

SUBJECT HEADINGS :Gas well ,Borehole ,Pressure ,Temperature ,Thermal stability ,Heat transfer ,Coupling

MODULARIZED DESIGNOF THE TECHNOLOGI2 CAL PROCESS OF GAS GATHERING STATION

ABSTRACT:At present ,oil and gas production is mainly concentrated in the regions with complex topography and very harsh climate ( such as polar region , seas , oceans and desert etc. ) , thus there are great technical difficulties in the production ;the construction volume is tremendo-       us;a short construction cycle is required and the quality requirement is serious. Respectively,the technologies of oil and gas gathering and processing are many and diverse and there is an interr-  elation among each process. Therefore ,based on the principles of the systematology and cybern -etics ,a modularized design method for the technological process of gas gathering station is proposed. This design has a great adaptability and flexibility and is favourable to save time and to use mannual and material resources sparingly , thus , the design cycle can be curtailed. The refer-  ence standard and basic principle for the modularized design are expounded and a successful application of the modularized design method to the design of the technological process of the gas gathering station in Chuannan (south Sichuan) Mine District of Sichuan Petroleum Administration is introduced.

SUBJECT HEADINGS :Natural gas ,oil and gas gathering , Gas collecting station ,Technolog-

ical process ,Analysis ,Design