一种新型天然气压缩因子数值计算方法

1、 收稿日期:20100612;改回日期:20100919基金项目:国家重大专项“南海深水油气勘探开发示范工程”(2008ZX05056002研究成果作者简介:管虹翔(1980,男,工程师,2006年毕业于西南石油大学机电专业,现从事油气田开发方面的生产科研工作。文章编号:10066535(201102008504一种新型天然气压缩因子数值计算方法管虹翔1,段国喜2,齐桃1,李伟1,李伟超1(1.中海油研究总院,北京100027;2.中海油天津分公司,天津300452摘要:天然气压缩因子是天然气重要的物性参数之一,传统计算方法对于高压天然气的计算存在较大误差。综合利用传统压缩因子图版与高压天然气

2、压缩因子实验数据进行拟合,得到了同时适用于中低压及高压范围的天然气压缩因子计算公式。计算显示在低压段平均误差为3.3%,在高压段平均误差为2.5%。将这一公式应用于气井压力的计算中,取得了较高的计算精度。关键词:压缩因子;天然气;常规气井;高温高压气井;计算方法中图分类号:TE31文献标识码:A引言目前使用较多的天然气压缩因子计算方法,包括Dranchk Abu Kassem 方法(DAK 12,Ha-nkinson Thomas Phillips 方法(HTP 3,Dran-chuk Purvis Robinson 方法(DPR 4,以及由石油大学李相方教授根据天然气压缩因子图版拟合的李相方

3、方法(LXF 。这些计算公式均是根据Standing 和KatZ 1942年提出的压缩因子图版5采用不同拟合方法拟合得到的6。在不同的对比压力及对比温度下,误差均较大。根据李相方教授的统计,各方法的最大误差均超过了55%7。近几年国内相继发现了一批高温高压天然气田8。原有压缩因子计算方法适用压力范围低的弊端逐渐暴露。石油大学郭绪强教授针对这一问题进行了相关试验,取得了丰富的高压天然气实验数据9。将郭绪强教授发表的高压天然气实验数据与传统天然气压缩因子图版10叠加,发现天然气压缩因子在高压阶段具有较强的延展性,表现出了较好的规律。利用三维绘图软件将数据进行处理,可以发现天然气压缩因子曲面较为复杂

4、。因此,本文利用传统压缩因子图版与郭绪强教授发表的高压天然气实验数据进行拟合,尝试找到高精度的能够同时兼顾高中低压范围的压缩因子计算方法。1公式拟合1.1分界线的确定天然气压缩因子具有较强的规律性。在低压段,压缩因子随对比压力的增大先降低后升高,在中高压段,压缩因子随对比压力的升高而增加。压缩因子的变化规律决定了无法使用一种函数形式对其进行统一的描述,因此尝试使用分段的方法进行描述。HTP 方法也使用了分段的方法进行描述,但是其给出的分界线是一个定值(p pr =5。这一分界线较好的保证了高压段的规律性,但是对于低压段,其规律性仍旧难以保障。因此本文根据图1中各曲线的拐点进行分割,其分界如图1

5、所示 。图1天然气压缩因子分界曲线对分界曲线进行数据回归,分界线上压缩因子86特种油气藏第18卷Z与对比压力ppr和对比温度T pr的关系如下式所示:Z=0.1547Tpr 51.7476Tpr4+7.875Tpr317.835Tpr 2+20.573Tpr8.8579(1p pr =1.266674Tpr4+11.683417Tpr339.764243Tpr 2+59.021716Tpr28.657098(2式中:Z为天然气压缩因子;p pr为对比压力,是实际压力与绝对压力的比值;T pr为对比温度,是实际温度与绝对温度的比值。1.2目标函数及系数的确定由天然气压缩因子图版可以看出,当温度一

6、定时,压缩因子Z值与对比压力p pr在低压段呈曲线关系,在高压段呈线性关系。通过计算对比,高压段采用线性函数,低压段采用二次曲线函数作为目标函数形式。Z低=a(Tprppr2+b(Tprppr+c(TprZ高=d(Tprppr+e(Tpr(3式中:a(T pr、b(T pr、c(T pr、d(T pr、e(T pr是关于T pr的函数,为相关式的系数。对压缩因子图版数据和实验数据按照对比温度T pr进行分组,利用公式(3进行回归(表1、2。 第2期管虹翔等:一种新型天然气压缩因子数值计算方法87对表1及表2数据进行拟合,可得到各系数与对比温度T pr 的关系式。a (T pr =0.1736T

7、 pr 4+1.3481T pr 33.8363T pr 2+4.7201T pr 2.1017(4b (T pr =0.2154T pr 31.4096T pr 2+3.106T pr 2.3266(5c (T pr =0.0107T pr 3+0.0673T pr 20.1412T pr +1.0987(6d (T pr =0.0799ln (T pr +0.1016(7e (T pr =0.789ln (T pr +0.1276(8选取压缩因子图版和实验数据中对比温度及对比压力,利用公式(3计算压缩因子。在低压段平均误差为3.3%,在高压段平均误差为2.5%,公式具有较高的精确度(表3。

8、 由表3可以看出,在对比温度为1.05时,本文计算方法与其他计算方法一样误差较大,最大误差达到了60%。从压缩因子三维图可以看出,对比温度在1.05 1.10之间时,Z 值曲面表现出了较强的扭曲性,这也是造成各方法预测精度均较低的主要原因。因此,需要对对比温度在1.05 1.10之间的数据重新进行回归,其系数关系式如下:a (T pr =4.076T pr 4.5034(9b (T pr =2.9681T pr +2.9204(10c (T pr =0.4617T pr +0.5033(11当对比温度在1.05 1.10之间时,系数a (T pr 、b (T pr 、c (T pr 选择式(9

9、 (11计算,当对比温度大于1.1时,系数a (T pr 、b (T pr 、c (T pr 选择式(4 (6计算。经修正,压缩因子计算精度大为提高,但其最大误差仍有25%(表4。2适用条件及实例计算2.1适用性分析本文提出的计算方法(GHX ,同时适用于中 低压与高压的天然气井计算,仅在对比温度低于1.1时(为超低温气井精度较低,在其他对比温度条件下,具有较高的精度,平均误差为1.7%。对比目前常用的几种天然气压缩因子计算方法,在典型对比温度与压力条件下,几种方法计算误差见表5。从表5可以看出,本文计算方法除在极个别条件下,均具有比较高的计算精度,具有较好的稳定性,适用于常规天然气井及高温高

10、压气井。并且本文在拟合过程中考虑了郭绪强教授实验获得的340个高压天然气压缩因子数据(对比压力最高达88特种油气藏第18卷20.71,对高压天然气井计算也具有较好的代表性。 2.2实例计算某气田射孔深度为3394m,测试日产气为14.2104m3/d,井口压力为40.9MPa,测试井底流压为50.3MPa,属异常高压天然气田。利用Pipesim软件建模,从井口压力反算求得井底流压为49.23MPa,误差为1.07MPa。分析认为,软件中使用的压缩因子计算公式为一般压力下的计算公式,对于高压天然气计算存在较大误差,影响了计算的结果。利用本文求得的压缩因子计算公式进行计算,结合软件计算的摩阻损失等

11、数据,井底流压为50.4MPa,误差仅0.1MPa,精度远高于软件中默认的计算方法。说明本文提出的压缩因子计算公式具有较高的精确度。3结论本文根据压缩因子图版与收集到的高压压缩因子实验数据,拟合出了同时适用于中低压与高压的天然气压缩因子计算公式,取得了精度较高的计算结果。但是同时也应看到,在对比温度较低时(1.05T pr1.10,本文方法以及其他计算方法均不能较好计算压缩因子,因此在今后的工作中应加强这一方面的研究。参考文献:1汪周华,等.酸性天然气压缩因子实用算法对比分析J.西南石油学院学报,2004,26(1:4750.2Dranchuk P M,AbouKassem J H.Calcu

12、lation of ZFactors for natural gases using equations of stateJ.JCdn Pet Tech,1975,14(3:3436.3Hankinson R W,Thomas L K,et al.Predict natural saspropertiesJ.Hydr proc,1969,48(4:106108. 4Dranchuk P M,Purvis R A,Robinson D B.Computer cal-culation of natural gas compressibility factors using theStanding

13、and KatZ correlationJ.Inst of Pet Tech Se-ries,1974,1(1:74108.5唐蒙.天然气压缩因子的计算J.石油与天然气化工,1987,16(1:6668.6李相方,等.高压天然气偏差系数的高精度解析模型J.石油大学学报,2001,25(6:4546.7李相方,等.天然气偏差系数模型综合评价与选用J石油钻采工艺,2001,23(2:4246.8郭绪强,等.特高压力下天然气压缩因子模型应用评价J.石油大学学报,2000,24(6:3638.9郭绪强,等.特高压天然气压缩因子的实验测定J.高校化学工程学报,1999,13(5:393397.10何更生

14、.油层物理M.北京:石油工业出版社,2005:108.编辑孟凡勤and laboratory data by employing statistical analysis,empirical equation and relative permeabilitymercury penetration analysisThe type and composition of water production are determinedThe study result indicates that the distribution of gas and water dis-plays"gr

15、adual complementary"relationship,with relatively waterrich area in the northwest;the water produced from the forma-tion comprises condensate water,movable water and free water;formation water production can be controlled by controlling draw-down pressureThis study provides basis for management

16、of water production wells and selection of development zones in the gas fieldKey words:formation water;type of water production;distribution of gas and water;Sulige gas fieldPreliminary study on interwell communication and fracture development in theupper Shaximiao gas reservoir of the Xinchang gas

17、fieldWANG Xu,LI Zuyou,DENG Wenlong,YAN Xiaoyong,XU Guangpeng(Southwest OilGas Company,SINOPEC,Deyang,Sichuan618000,ChinaAbstract:Interwell communication is increasingly seen in the upper Shaximiao gas reservoir of the Xinchang gas field due to fractu-ring operationThis paper comprehensively analyzes

18、 earth stress,fracturing fracture monitoring,pressure drop in well block,time of interwell communication,and interwell azimuth relationship,generalizes that fracturing fracture development is the main reason for interwell communicationGas well fracturing can lead to sand production and plugging in a

19、djoining gas wellsOn this basis,three preventive measures of interwell fracturing communication are proposed:the orientation of earth stress and fracture development shall be fully considered when placing infill wells in a gas reservoir;the technology of perforation and fracturing shall be optimized

20、;and the adjoining wells shall be shut in to build up pressure when performing fracturing operationKey words:interwell communication;fracturing fracture;earth stress;sand production mechanism;Xinchang gas field;upper Shaximiao gas reservoirStudy and application of fracture propagation model of multi

21、ple sand fracturingLIU Chunlin1,2,WANG Rui3(1China University of Petroleum,Beijing102249,China;2Xian Shiyou University,Xian,Shaanxi710065,China;3Jidong Oilfield Company,PetroChina,Tangshan,Hebei063000,ChinaAbstract:In multiple sand fracturing process,the height of sand bank has certain influence on

22、fluid flow in fractures and subse-quent proppant settlementA pseudo3D model is built to predict fracture propagation in multiple sand fracturing process through nu-merical simulationThe model includes continuity equation,pressure drop equation,and fracture width and height equation of frac-turing fl

23、uid flowing in fracturesThe pressure drop equation is based on the plate flow theory and mechanic equilibrium principle, and its difference from conventional pressure drop equation is that it takes the effect of sand bank height on fluid flow into accountThe computation shows that multiple fracturin

24、g is more effective in increasing production than conventional fracturingField test shows that multiple fracturing is an effective reservoir stimulation method and has significant meaning to improving oil productionKey words:fracturing;multiple sand input;sand bank;fracture;pressure drop;Hua152block

25、 of the Changqing oilfield Productivity study of lowvelocity nonlinear flow in low permeability tight gas reservoirsSONG Hongqing1,HE Dongbo2,LOU Yu1,YI Huaijian1,ZHU Weiyao1(1University of ScienceTechnology Beijing,Beijing100083,China;2Research Institute of Petroleum Exploration and Development,Pet

26、roChina,Beijing100083,ChinaAbstract:Low permeability tight gas reservoirs are classified into three categories according to formation water occurrencesMathe-matical models are established for seepage flow in different reservoirs by taking account of slippage effect,stress sensitivity and threshold p

27、ressure gradient respectively and simultaneouslyProductivity formulas are derived for lowvelocity nonlinear flow in the three categories of low permeability tight gas reservoirsNumerical analysis shows that,compared with traditional Darcy flow,the productivity of low velocity nonlinear flow in low p

28、ermeability tight gas reservoirs is quite different under different flow regimesWhen producing pressure drop is big,stress sensitivity has greater effect on gas well productivityIn the production process of low permeability tight gas reservoirs,productivity equations corresponding to specific flow r

29、egime shall be chosen according to the water content of a gas reservoirLarge drawdown pressure and accelerated production shall be avoidedKey words:low permeability tight gas reservoirs;lowvelocity nonlinear flow;slippage effect;stress sensitivity;mathematical model;productivity equationNumerical si

30、mulation of the buried hill reservoir in the Sudeerte oilfieldWU Wei(Daqing Oilfield Company Limited,PetroChina,Daqing,Heilongjiang163712,ChinaAbstract:The influence of different fracture properties on buried hill reservoir development response has been simulated with a dual porosity dualpermeabilit

31、y model by using time variant techniqueThe trend of oil and water migration and remaining oil distri-bution is analyzed and predicted for buried hill reservoir under the condition of fracture influencePrediction of the development re-sponses of different well patterns and water injection schemes can

32、 guide oilfield infill modificationA modification plan of well pat-tern and water injection scheme has been proposed according to the geologic feature of the Sudeerte oilfield and has obtained good development resultKey words:fractured buried hill reservoir;dual media;numerical simulation;developmen

33、t modification;Sudeerte oilfieldA new computing method of gas compressibility factorGUAN Hongxiang1,DUAN Guoxi2,QI Tao1,LI Wei1,LI Weichao1(1CNOOC Research Institute,Beijing100027,China;2Tianjin Branch of CNOOC,Tianjin300452,China Abstract:Compressibility factor is one of the important parameters of

34、 natural gasTraditional computing method has big error incalculation of superhigh pressure natural gas This paper matches the traditional compressibility factor with the experimental data of superhigh pressure gas compressibility factor，and obtains a formula of compressibility factor for both mid lo

35、w and high pressure conditions The computation shows that the average error is 3 3% for low pressure interval and 2 5% for high pressure interval Gas well pressure has been calculated by applying this formula，and high calculation accuracy has been achieved Key words： compressibility factor； natural

36、gas； conventional gas well； high temperature high pressure gas well； computing method An approach to similarity method of experiment of remaining oil distribution after water flooding WANG Jin lin，TIAN Jin jie，WANG Jing bo，HUANG Bo，LIU Fu hai （ CNOOC Energy Technology Services Limited，Tianjin 300452

37、，China） Abstract： The similarity methods of physical simulation of oil displacement experiment generate many similarity criteria The requirement on model construction is relatively high and the realization is difficult According to the research on remaining oil distribution after water flooding and

38、development performance，this paper combines geometric method with equation method，recognizes that the real velocity （ movement velocity） of seepage flow is the same and the geometry changes in proportion when the major features of core and fluid are the same，thus obtained a relatively simple method

39、of similarity transformation This method effectively averts the difficulty brought by rigorously considering the similarity of geometric thickness，and needs not to select and combine different system parameters，thereby greatly reduced the difficulty of similarity transformation Key words： equality o

40、f velocity； similarity criteria； geometric method； equation method； Bohai SZ36 1 oilfield The effect of structural dip on gas injection response in condensate gas reservoir 2 CHEN Xiao fan1 ，YANG Cheng bo1， ，YANG Jian3 （ 1 State Key Laboratory of Oil Gas Reservoir Geology and Exploitation， Southwest

41、 Petroleum University，Chengdu，Sichuan 610500，China； 2 Star Petroleum Company，SINOPEC，Beijing， 100083，China； 3 Southwest Petroleum Company，SINOPEC，Chengdu，Sichuan 610081，China） Abstract： Structural dip is a critical factor affecting gas injection response Condensate gas reservoirs with different stru

42、ctural dip have different rules of oil / gas / water seepage flow and production characteristics， therefore different development strategies and measures are required Numerical simulation has been conducted to compare the effect of different structural dip on gas injection response based on fluid pa

43、rameters of the Dalaoba condensate gas reservoir to research into the rule of condensate oil recovery factor It is suggested that more injectors shall be placed in structural high and more producers shall be placed in structural low This will be helpful to improving the development effect of cyclic

44、gas injection for condensate gas reservoir Key words： condensate gas reservoir； gas injection； structural dip； anisotropy； condensate oil； recovery factor； numerical simulation； Dalaoba Structure 2 condensate gas reservoir Experimental study of formation damage in ultra low permeability sandstone re

45、servoirs 2 2 HE Wen xiang1， ，YANG Yi qian1， ，MA Chao ya3 ，ZHU Sheng ju1 （ 1 Yangtze University，Jingzhou，Hubei 434023，China； 2 MOE Key Laboratory of Oil and Gas Resources and Exploration Technoloy， Yangtze University，Jingzhou，Hubei 434023，China； 3 Changqing Oilfield Company，PetroChina，Yan an，Shaanxi

46、717606，China） Abstract： Formation damage during the process of water flooding has been analyzed for ultra low permeability sandstone reservoirs under different permeability conditions，and rational development strategies have been worked out The cores of ultra low permeability from the Geng 43 well b

47、lock and the Middle Baima block in the Changqing Oilfield have been taken as the samples to analyze formation sensitivity，Jamin effect，water lock effect and water injection damage The general law of formation damage in ultra low permeability reservoirs and its relationship with permeability has been

48、 generalized Measures of avoiding formation sensitivity damage and improving water quality have been proposed The study results will provide guidance for the development of similar oilfields Key words： sensitivity； water injection damage； ultra low permeability reservoir； water lock effect； Jamin effect； Geng 43 well block； Middle Baima well block Study on catalytic aquathermolysis and enhanced