3本文为中国石油科技项目“低、特低渗透油气藏有效开发技术研究”
(编号:06202A 202201)的部分研究成果。 作者简介：吴晓东,1959年生，教授，博士，博士生导师；长期从事油气田和煤层气开发研究工作。地址:(102249)北京市昌平区中国石油大学石油天然气工程学院。电话:(010)89734626。E 2mail :
考虑储层伤害影响的水平气井产能
3
吴晓东1 安永生1 李凡华2
(1.中国石油大学石油工程教育部重点实验室 2.中国石油勘探开发研究院开发所)艾雅法拉火山
30年后 吴晓东等.考虑储层伤害影响的水平气井产能.天然气工业,2008,28(7):78280.
摘 要 随着“西气东输”工程的启动，越来越多的水平井在气藏开发中得以应用，但是由于气藏的低渗透性使得钻井过程中产生的储层伤害比常规油藏严重得多。基于坐标变换方法，将储层各向异性空间转
换为各向同性空间，利用坐标变换后水平井储层伤害区域同垂直压裂井近井地带渗流特征的相似性，推导出了新的表皮因子计算模型，并将其应用于水平气井产能公式。计算结果分析表明：储层伤害区域渗透率的损失程度对水平气井产能的影响远比储层伤害深度要严重。该方法充分考虑各向异性影响，计算简便快捷，能够广泛应用于气藏水平井开发的早期评估以及水平气井的产能预测。
主题词 气井 生产能力 各向异性 表皮系数 地层损害
一、引 言
随着我国“西气东输”工程的启动，水平井开发气藏因其生产压差小和控制泄气面积大的优势而获
得广泛应用。目前国内外学者对气藏水平井产能的计算进行了大量研究[123]，并在现场取得了一定的应用效果。但是大部分理论公式的推导都只考虑了各向同性气藏条件，并采用Hawkins 公式对储层伤害产生的表皮因子进行计算，这显然不能适用于各向异性气藏。 基于以上情况，提出采用坐标变换方法将各向异性空间转换为各向同性空间对水平气井产能进行计算的方法，并利用坐标变换后水平气井储层伤害区域同垂直压裂井近井地带渗流特征的相似性，推导出了新的表皮因子计算模型。
二、考虑储层伤害影响的水平气井
查找iphone产能计算
1.各向异性气藏的处理方法 如图1所示，假设在均质、各向异性等厚气藏中部有1口长L 的水平井，井筒半径为R w ，气藏厚度为H ，泄气半径为R eh ，气藏顶底边界均不渗透，水平井与x 轴夹角为φ。x 、y 、z 方向渗透率分别为K x 、
K y 、K z ，其中K x =K y >K z
。
图1 水平气井位置示意图
根据坐标变换理论，引入转换因子T 将原各向异性渗透率空间转换为等价的各向同性空间。
T =a 0
0b 0
c
(1)其中:a =
K y K z /3K x K y K z b =K x K z /3K x K y K z c =
K x K y /
3
K x K y K z
这样，在直角坐标系(x ,y ,z )外，就引进了一个
新的直角坐标系(x ′,y ′,z ′)。在新的坐标系中，各方向渗透率均相等，即K =3
K x K y K z 。同时，空间中
的几何关系也随之发生了改变:
H ′=c ・H
(2)L ′=L/c (3)R eh ′=R eh /
c
(4)
φ′=φ
(5) 2.储层伤害表皮因子计算模型 假设水平井井轴方向与x 轴方向平行，那么井
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87・开发及开采 天 然 气 工 业 2008年7月
筒截面所在的y z坐标系和y′z′坐标系有如下关系[4]:
y z =
I ani1/30
0I ani
-2/3
・
y′
z′
(6)
其中:I ani=K x
K z =
K y
K z
根据Peaceman对于各向异性储层流体流向井筒的处理方法，在各向异性空间中，井筒周围的等压线为同心椭圆(井壁处长轴与短轴之比等于1)。变换到各向同性空间后，井筒周围等压线变成一系列共焦同心椭圆，等压线越远离井筒，形状越接近于圆。由于储层伤害一般与流速直接相关，因此可以
认为储层伤害区域的分布类似于井筒周围压力场分布(图2)。
图2 坐标变换前后储层伤害区域对比图
显然，经过坐标变换后，水平井储层伤害区域特征与垂直压裂井近井地带渗流特征相同(图22b)，因
此只要计算出井筒壁面和储层伤害边界两个共焦同心椭圆的长半轴，就可以利用垂直压裂井表皮因子计算公式对其进行求解。
在工程上，可以通过岩心实验，测定实际钻井压差下钻井液的滤失速度以及污染带的渗透率，并根据钻井时间和各向异性系数推算储层伤害区域最大侵入深度。为了计算简便，笔者假设各向异性气藏中，储层伤害区域长半轴为R dh，渗透率为K s，忽略储层伤害区域内渗透率变化情况(图22a)。
因此，在y z平面内，两点坐标已知，分别为(R w, 0)和(R dh,0)，井筒壁面方程为:
y2+z2=R2w(7) 将式(6)带入式(7)，得到y′z′平面内井筒壁面方程:
z′2
R2w(I ani2/3)2+
y′2
R2w/(I ani1/3)2
=1(8)
引入Peaceman公式进行保角变换[5]:
z′=b・coshρ・sinθ0
y′=b・sinhρ・cosθ0
(9) 其中，椭圆的短半轴和长半轴分别为:
R u=b・coshρ
R v=b・sinhρ
(10) 联立公式(8)、(10)得到:
b=
R w
I ani1/3
I ani2-1(11) 将已知两点(R w,0)、(R dh,0)和b，代入公式(6)、(10)便可分别计算出y′z′平面内井筒壁面和储层伤害区域边界椭圆的长半轴，最终推导得到水平气井储层伤害表皮因子计算公式:
R u,w=R w I ani2/3(12) R u,dh=
R w
I ani1/3
I ani2-1cosh sinh-1
R dh
R w I ani2-1业务活动表
(13)
S=
K
K s
-1ln R u,dh+R
2
u,dh-R
2
u,w
R u,w
(14)式中:K=3K x K y K z
3.气藏水平井产能计算
坐标变换后的井筒半径采用Brigham方法计算:
R′w=
R w
2
1
I ani1/3
+I ani1/3(15) 分别将气藏各向异性空间转换到各向同性空间后的计算参数K、H′、L′、R eh′、R w′和S代入Joshi公式[6]就得到了新的考虑储层各向异性和储层伤害影响的气藏水平井产能计算公式:
Q h=
0.02714K H′(p2e-p2wf)(T sc+273)
μ
g Z(T+273)p sc ln
R eh′
Π+S
(16)式中:
Π=R eh′L′/2
A{1+1-[L′/(2A)]2}[H′/(2R w′)]H′/L′A=(L′/2)[0.5+0.25+(2R eh′/L′)4]0.5
三、计算结果与分析
假设各向异性气藏中一口水平井长500m，井筒半径0.12m，泄气半径2000m，储层厚度20m，储层温度80℃，气体地下黏度0.015mPa・s，气体压缩因子0.9，水平渗透率0.05μm2，垂向渗透率0.025μm2，原始地层压力15M Pa，井底流压10 M Pa。
图3、图4分别为由于不同伤害程度(储层伤害区域渗透率)和不同伤害深度(钻井液侵入深度)对表皮因子和水平气井产能的影响变化图。从图中可以看出，由于储层伤害程度和伤害深度增加，导致表皮因子增加、气藏水平井产能不断下降，而无论从产
・
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7
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第28卷第7期 天 然 气 工 业 开发及开采
能的损失程度和趋势来看，储层伤害程度对产能的
影响远比伤害深度要严重。因此，在钻井过程中应尽可能使用优质钻井液，减少由于近井地带渗透率降低所造成的产能损失
。
图3 表皮因子随伤害程度和伤害深度变化规律图
图4 水平气井产能随伤害程度和伤害深度变化规律图
四、结 论
(1)利用坐标变换后水平井储层伤害区域同垂
直压裂井近井地带渗流特征的相似性，推导出了新的表皮因子计算模型，并将其应用于水平气井产能公式。为各向异性气藏中水平井产能的计算提供了新的方法。
(2)实例计算表明，气藏水平井近井地带渗透率的伤害程度对产能的影响远比泥浆侵入深度要严重，在钻井过程中应尽可能使用优质钻井液，减少由于近井地带渗透率的降低所造成的产能损失。
符 号 说 明
Q h 为水平气井产能,104m 3;H 为气藏有效厚度,m ;K x 、K y 、K z 分别为气藏x 、y 、z 方向渗透率,μm 2;H ′、L ′、R eh ′、φ′分别为新坐标系下的气藏厚度、水平井长度、泄气半径和水平井与x ′轴的夹角;K s 为储层伤害区域渗透率,μm 2;R eh 为水平气井动用半径,m ;R w 为水平气井井筒半径,m ;R dh 为储层伤害区域半轴,m ;S 为储层伤害表皮因子，无因次;L 为水平井长度,m ;p e 为地层压力,MPa ;p wf 为井底流压,MPa ;μg 为气体平均黏度,mPa ・s ;Z 为平均压缩因子，无因次;T 为储层温度,℃;T sc 为地面温度,℃;p sc 为地面压力,MPa 。
参 考 文 献
[1]陈志海，马新仿，郎兆新.气藏水平井产能预测方法[J ].
天然气工业,2006,26(2):982100.
[2]黄世军，程林松，赵凤兰，等.薄互层油藏中阶梯水平井
产能评价模型研究[J ].西南石油大学学报,2007,29(3):
60265.
[3]李晓平，刘启国，赵必荣.水平气井产能影响因素分析
[J ].天然气工业,1998,18(2):53256.
[4]B ESSON J.Performance of slanted and horizontal wells
on an anisotropic medium[C]∥European Petroleum Con 2ference ,21224October 1990,The Hague ,Netherlands :SPE ,1990:2192231.
[5]PEACEMAN D W.Interpretation of well 2block pressures
in numerical rervoir simulation with nonsquare grid blocks and anisotropic permeability [J ].SPE Journal ,1983,23(3):5312543.
[6]J OSHI S D.Horizontal well Technology[M ].Tulsa :Joshi
Technologies International ,1991.
(修改回稿日期 2008204218 编辑 韩晓渝)
・
08・开发及开采 天 然 气 工 业 2008年7月
GU O Yong2cun(professor),born in1965,is now engaged in studies of fluid mechanics in porous media.
Add:School of Mechanical Engineering,Anhui University of Science and Technology,No.168,Middle Shun2geng Rd.,Hua2 inan City,Anhui Province232001,P.R.China
永不为奴T el:+86255426668045 E2m ail:pbg1@
PR OD UCTIVIT Y CALCU LATION OF H ORIZONTAL WE LLS IN LOW2PERMEABI L IT Y G AS RESER2 V OIRS CONSIDERING STARTING PRESSURE GRADIENT
GAO Hai2hong1,C H EN G Lin2song2,FEN G Ru2yong3(1SINO PEC International Pet roleum Exploration and Production Corporation;2China U niversity of Pet roleum・Beijing;3CNOOC Rearch Center).N A2 T U R.GA S I N D.VOL UM E28,ISSU E7,pp.75277,7/25/2008.(ISSN100020976;In Chine) ABSTRACT:The development of low2permeability gas rervoir plays an important role in petroleum industry.Owing to its pe2 culiar stimulation advantage,horizontal wells have been widely ud in the development of low2permeability gas rervoirs.Due to the comparatively high cost input of horizontal wells,it is necessary to forecast their productivity accurately so as to provide a scientific basis for designing the drilling and production engineering projects of horizontal wells.The productivity prediction of a horizontal well in low2permeability gas rervoirs mostly neglected starting pressure gradient effect,which leads to the great difference between the predicted and the actual productivity.Bad on the Joshi percolation theory of horizontal wells and tak2 ing the low2permeability gas rervoirs with enclod top and bottle boundaries as an example,the formula for productivity cal2 culation of horizontal wells in low2permeability gas rervoirs considering starting pressure gradient was deduced and the dimen2 sionless parameter s
was introduced to reprent the degree of production loss caud by starting pressure gradient.The field data have verified the productivity formula’s accuracy and analyzed the influence trend of starting pressure gradient to gas wells ’deliverability.Results showed that with the increasing of starting pressure gradient,the loss of gas amount would increa lin2 early,which provides a theoretical support for the development of horizontal wells in low2permeability gas rervoirs.
SUB JECT HEADING S:low2permeability rervoir,horizontal wells,production capacity,starting pressure,non2Darcy flow G AO H ai2hong(nior engineer),born in1975,halds a Ph.D degree,and is currently engaged in rearch works on oil and gas rervoir engineering and percolation theory.
Add:Room506,Shining Tower,BUAA Science Park,No.263,Middle Rd.,North4th Ring Rd.,Haidian District,Beijing 100083,P.R.China
Mobile:+86213466567615 E2m ail:
PR OD UCTIVIT Y OF H ORIZONTAL G AS WE LLS CONSIDERING RESERV OIR DAMAGE EFFECTS
WU Xiao2dong1,AN Y ong2sheng1,L I Fan2hua2(1MO E Key Laboratory for Pet roleum Engineering,
Chi2 na University of Petroleum・Beijing;2CN PC Rearch Instit ute of Pet roleum Exploration and Develop2 ment).N A T U R.GA S I N D.VOL UM E28,ISSU E7,pp.78280,7/25/2008.(ISSN100020976;In Chi2 ne)
ABSTRACT:With the start of"West to East Gas Transmission"project,more and more horizontal wells are applied in the de2 velopment of gas rervoirs.However,due to the low permeability of gas rervoirs,the rervoir damage caud in drilling process is much more rious than that of conventional rervoirs.Bad on the coordinate transformation method,the aniso2 tropic space of rervoir can be converted into isotropic space.Then after the coordinate transformation,by using similarities of percolation characteristics between rervoir damage regions of horizontal wells and near bore zones of vertical f racturing wells, a new calculation model for skin factor is derived,which is employed in the productivity formula for horizontal gas wells.The result of the analysis and computation showed that the impact on horizontal gas wells caud by the degree of permeability loss in rervoir damage region is far more rious than that of rervoir damage depth.This method,f ully considering the influence of anisotropy and with advantages of easy and efficient calculation,can be widely ud in early evaluation for the development of horizontal wells in gas rervoir and productivity predication of horizontal gas wells.
・140・ /e/abstracts.asp
SUB JECT HEADING S:gas wells,production capacity,anisotropy,skin factor,formation damage
WU Xiao2dong(professor),born in1959,holds a Ph.D degree and is a tutor for doctoral students.He has long been engaged in teaching and rearch works on exploration and development of oil/gas fields and coalbed methane in China.
公司授权委托书范文
Add:Oil and Gas Engineering Institute,China University of Petroleum,Changping District,Beijing102249,P.R.China
T el:+86210289734626 E2m ail:
PR OD UCTIVIT Y PREDICTION OF ACID FRACTURING WE LLS CONSIDERING THE EFFECT OF WORM H OL E IN FRACTURE SURFACE
CH EN Ji2mei,XU Le(Pet roleum Engineering Instit ute of Sout hwest Pet roleum U niversity).N A T U R. GA S I N D.VOL UM E28,ISSU E7,pp.81284,7/25/2008.(ISSN100020976;In Chine)
ABSTRACT:In the process of acid f racturing operation,the wormhole zone will be formed due to the
acidizing fluid flowing and filtrating along the f racture surface.Conquently,the productivity of a well will be affected by the wormhole zone after acid f racturing.Therefore,the study on the productivity prediction of acid f racturing wells considering the effect of wormhole in f racture surface is of important significance for improving acid f racturing effect.On the basis of analyzing the impact of worm2 hole formation on productivity,the wormhole zone is considered as a dual2porosity system and a new model considering the in2 fluence of wormhole zone on the productivity has been propod.The model divides the overall flowing in formation into four stages including the linear flow in f ractures,improved bilinear flow,linear flow in formation and p udo radial flow,and a cor2 responding percolation mathematical model has been established;bad on the theory for wells with finite2conductivity vertical acid fracturing f racture,by using Laplace transform and combining wormhole zone dual2porosity percolation mathematical mod2 el with flowing model in f racture,linear flow model in formation and pudo radial flow model in formation,solutions of the bottomhole pressure equations have been obtained in four flowing periods;analysis results showed that the wormhole zones have obvious impact on the productivity of acid f racturing wells in low2permeability rervoir.By using the established binomial model for productivity prediction of acid f racturing wells,the impacts of f racture half2length,f racture conductivity and forma2 tion pressure on productivity have been analyzed,and results of the productivity prediction in the Tarim oilfield are clo to well test data.
SUB JECT HEADING S:gas wells,acid f racturing,f ractured(rock),production capacity,prediction
CHEN Ji2mei(associate professor),born in1953,is currently engaged in rearch and teaching works on exploitation of rer2 voir and stimulation of oil and gas wells and has published over20academic papers at home and abroad.
Add:Southwest Petroleum University,Xindu District,Chengdu,Sichuan Province610500,P.R.China
T el:+86228283033252 E2m ail:
REASONAB L E PR OD UCTION PRESSURE DIFFERENCE AN D PR OD UCTION DETERMINATION OF G AS WE LLS IN ED GE WATER D RIVE G AS RESERV OIRS
L I Xiao2ping1,WAN G Hui2qiang2(1State Key Laboratory for Oil and Gas Rervoir Geology and Exploita2 tion,Sout hwest Pet roleum University;2Rearch Instit ute of Exploration and Develop ment of Pet roChina Sout hwest Oil&Gasfield Company).N A T U R.GA S I N D.VOL UM E28,ISSU E7,pp.85286,7/25/ 2008.(ISSN100020976;In Chine)
晚饭的英语ABSTRACT:In the process of water2drive gas rervoir development,the stable movement and uniform advance of gas/water interface have a relatively significant influence on the stable and norm
al production of gas wells and the recovery improvement of gas rervoirs.The paper analyzed the homogeneous isotropic edge water drive gas rervoir with certain inclined angle.On the assumption that the initial gas/water interface is horizontal,by using the basic law of Darcy epage,we derived out condition of gas epage velocity of stable movement for gas/water interface theoretically,obtained the expression of reasonable produc2 tion pressure difference and productivity and analyzed a gas well in edge water drive gas rervoirs.Results showed that the cal2
土壤压实
