石油教材出版基金资助项目 石油高等院校特色教材 The Oil-gas Percolation In Porous Media 油气渗流力学 (英文版) 李陈军斌编著 石油工业出版社
前言 改草开放以来,石油出版界在岀版我国的石油科技学术专著、引进和翻译出 版西方石油科技文献方面成绩斐然,但是将我国学术著作和教材译成英文岀版的 并不多。作为一亼经济和石油大国,将我国石油科硏和教学成果以专著和教材形 式介绍给国际社会是一项十分必要的工作。这是让世界了解中国所必需的,也是 我们推进世界石油科研和教学发展所应当做的。 教高〔20071号文件《教育部财政部关于实施高等学校本科教学质量与教学 改草工程的意见》中提岀:鼓励和攴持校內及聘请国内外著名专家学者和高水平 专业人才承担教学任务和开设讲座,推动双语教学课栏建设,探索有效的教学方 法和模式,切实禔高大学生的专业英语水平和直接使用英语从事科硏的能力。但 是,日前我国高等院校实施双语教学的过桯中所遇到的主要问题是教材选择无所 适从,部分学生无法承受外文原版教材的价格。 为此,我们在《油气渗流力学》中文版的基础上编写本书。目的不外乎两方 面:一是为了提高¨渗流力学”双语课程的教学质量以及大学生的专业英语水平; 二是希望本书的英文版能向世界的渗流力学界展示我们的教学硏究成果,了解我 们的渗流力学的教学水玶,同时接受国际同行的裣验,期待他们的批评指正。 归于木书是由《油气渗流力学》中文版翻译而来,所以它对外国在华的留学生 学习渗流力学和大学科生学习专业外语均有所裨益 本书第、五、六章由陈军斌翻译,第二、三、四章由双立娜翻译,第七、八章和 附录由黄海翻译,全书由李璗审定。 我们虽然从事渗流力学教学研究多年,但理论水平及写作能力都还不够高,特別是英文水 平,离准确而漂亮的行文还差得远,敬请海內外冋行不吝指正 最后,我们诚挚感谢西安石油大学和石油工业岀版社的支持,使得本书能够与广大读者见 2011年8月
Contents Chapter 1 The basic principle of percolation mechanics in porous medium 1. Static conditions in reservoirs 1. 2 The driving forces and driving mechanism in reservoir The basic law of seepage flow Darcy's law 4 The limitations of Darcys law and non-Darcy seepage flow Chapter 2 Steady seepage flow of single-phase incompressible fluid 2. I Three basic seepage flow modes 2.2 The planar one-dimensional steady seepage flow of single-phase incompressible 18 2.3 The planar radial tluid flow of single-phase incompressible fluid 2. 4 The incomplete well 5 The systematic well testing( Step rate testing 2. 6 The diflerential equation of single-phase fluid seepage flow Exercises Chapter 3 The interference theory of oil well under rigid water driving 3. I The phenomenon of well interference 2 The superposition principle of potential 3.3 The image retlection method 4 The application of complex function theory to the planar seepage lield Exercises Chapter4 The unsteady seepage flow of slightly compressible fluid 4. I The physical process of elastic fluid seepages towards wells 4.2 The planar one-dimensional unsteady seepage flow in semi-infinite formation . .......95 4.3 The law of pressure transient of clastic fluid unsteady seepage flow toward a well 4.4 The approximate solution of pressure change of fluid seepage flowing towards well in finite closed elastic formation 4.5 The multi-well interference of elastic unsteady seepage flow 4. 6 The unsteady well testing analysis cercis II8 Chapter 5 The seepage law of natural ga 121 5. I The properties of natural gas and its basic differential equation of seepage flow . .,121 5. 2 The steady seepage flow of gas
132 135 Chapter 6 The foundation of water /oil displacement theory 6. I The Piston Like Water Displacing Oi 38 6. 2 The bottom water cone 144 6. 3 The theoretical foundation of non-piston like water displacing oil Exercises 175 Chapter 7 The seepage theory of oil-gas two phases( dissolved gas drive 177 7.1 The basic differential equation of oil-gas two-phases seepage flow 177 7.2 The oil-gas two-phase steady seepage flow 180 7.3 The unsteady seepage flow of gassy fluid Exercises 190 Chapter 8 Seepage flow in dual-media 8. I The seepage characteristics in dual-media 8. 2 The basic seepage cquation of single-phase slightly compressible fluid in 192 8.3 The pressure distribution in infinite dual-media 8. 4 The oil-water two-phase seepage flow in the dual-media 198 8. 5 The seepage of tluid in pure fracture formation 206 Chapter 9 The seepage of non-Newtonian liquid 9. I The mechanical behavior and ty pe of non-Newtonian liquid 9. 2 The seepage of non-Newtonian power law liquid Chapter 10 The theory of similarity 10. I The concept of similarity 10.2 The kinematical and dynamic similarity 10.3 The scaled physical model and law of similarity 10. 4 The dimension analysis examples for the known equation of physical asten 10. 5 The examples of analo 10. 6 The partial similarity in the scaling model 10. 7 The special aspects of standard fitting of porous medium model Appendix a The flow equation in cylindrical coordinate 236 Appendix b to obtain the solution of one-dimensional unsteady llow by the laplace transiormation
Appendix C The calculation procedure of error function erf(x) 240 Appendix d The calculation procedure of exponential integral function -Ei(-t) …244 Appendix e The calculation procedure of function r(x) 246 Appendix f The conversion relationship between the commonly used units in reservoir engineering Appendix g The factor and signs of commonly used prefixes in SI system and imperial system of unit 250 Reference
Chapter 1 The basic principle of percolation mechanics in porous medium T'he tlow of fluid( liquid, gas and their mixture )in porous medium is called seepage flow Solid body containing pores or solid collection is called porous medium. Large pores are called cavern and its diameter is from 2mm to lens of meters; the porous media with micron diameter called pores, as for the fractures that divide the solid into non-contact parts, its width has a wide range, while the throats connecting pores are rather narrow, No matter whether they are cavern fractures or pores, there is no strict detinition at home and abroad at present. Sandstone limestone are commonly seen as porous media; shale, igneous and metamorphic rocks with cracks that are scen as porous media too. The process of oil and gas development is the procedure that the i. gas and water flow from the reservoir to the well bottom and then from bottom to the surface Only the seepage principles of oil, gas, water and their mixture are mastered can more and more oil and gas be produced from reservoir. Percolation mechanics in porous medium seepage and gas is the science that studies movement principles of oil, gas, water and their mixture in Most of pores in sandstone reservoir are intergranular and they are more evenly distributed compared with the fractures. Shale, igneous and metamorphic rocks are fractured reservoir and the distribution of fractures is of great random. Sandstone is known as the porous medium: while shale with cracks, igncous and metamorphic rocks are known as fractured medium. Limestone dolomite and some sandstone with both pores and fractures are known as double medium. Th rocks talked above are the main reservoir of oil and gas of industrial valuc in china According to the current teaching program of relevant speciality, fluid statics in and character of fluid and porous mediu is introduced in the course of oil and gas reservoir physics. In order suit the needs of petroleum engincering and without loss of generality, the static distribution of oil, gas and water in reservoir is introduced first in this chapter, and several oil displacement forces are introduced focusing on teaching the concepts. On this basis, the basic principle of seepage-Darcy's law is introduced and then is used to analy ze a variety of practical 1.1 Static conditions in reservoirs 1. 1 The distribution of oil and gas in reservoirs Most of oil and gas reservoirs remain a state of relative equilibrium before development. the distribution of oil, gas and water in reservoir is associated with the properties of rocks and fluid in it. If the reservoir contains oil, gas and water at the sae time. as the lightest component, gas
will occupy the top of the structure, so it is known as gas cap; oil will gather in the lower wings ind water with greater density will gather under oil. as In reservoir the oil-water contact surface is called ller interface. and it shall be the oil bearing boundary when projected onto the horizontal plane. Strictly speaking, oil-bearing boundary should be classif ied as inner boundary and outer boundary. In lact, average of the two oil boundaries is generally taken as the oil-bearing boundary. The intersecting line of oil-gas interface and reservoir top is called gas boundary. If the outer-ring of reservoir connects to source that supply for reservoir, then the reservoir is called open-reservoir, the projecton ovei protile is called supply boundary( Figure 1-1), If the outer-ring of reservoir is closed and its altitude is the same as oil-water interface. then the reservoir is called closed reservoir. and its overall protile is called closed boundary According to the distribution of oil. gas and water. w outside the oil-bearing boundary is called edge water; if the reservoir is of large thickness or relatively flat structure that makes the water under the oil then the water is called bottom water In actual oil tield. it is rare to scc reservoir with only a single oil laver, most of reservoirs are The litho not always the same from layer to layer. Therefore. the distribution and features of oil, gas and water should be understood first before oil tields development Figure 1-1 Reservoir with recharge area Figure]-2 Oil and gas boundar 1.1.2 Concept of various pressures Reservoir pressure is the character of formation energy, if the pressure field of reservoir is lavers. In the oil field development process, the concept of different pressures are oflen encountered, some will introduced as follows Initial formation pressure p T'he reservoir pressure is the fluid pressure within the pores in the middle of oil formation reservoirs remain a state of relative equilibrium before development generally, and at th int the fluid pressure is called initial formation pressure. When th latively big. the mid-lepth ol each usually not the same, wells lie on the top of structure have a shallower mid-depth while the lie in the wings have a deeper mid-depth, The total
of tigure. o0' is base level. and initial oil-water intertace is aly the height Irom the base level; p is the density acceleration of gravity Figure 1-3 Reduced pressure figure the first exploration well di and gas llow, and pressure should be lesled in the beginning of each exploration well, the lesled pressure of mid-depth of reservoir is the initial formation pressure of each wel Strictly speaking, the initial equilibrium is destroyed and the initial formation pressure cannot be obtained any more as long as only once well produces. If the pressure manometer cannot be put in the mid-depth of reservoir. the initial formation pressure can be calculated from tested pressure gradient.Clearly, in order to improve the measurement accuracy. the pressure manometer should be put in the mid-depth of reservoir as far as possible 2. Current formation pressure p In the process of oil gas reservoir development, if a well is ofl production and others are sti producing stably, the bottom-hole pressure of the shut-down well will gradually increased. After a long time, the pressure will no longer increase and stabilize. The measured pressure of mid-depth of reservoir of this well is called current formation pressure, and it is also known as static prcssurc 3. Supply pressure pe When there is a fluid supply zone, the pressure of supply boundary is called supply pressure with pe stands for it 4. Bottom hole pressure p The pressure measured in the mid-depth of well bottom in the process of production is called well bottom pressure, also known as flow pressure, with p. stands fo 5. Reduced pressure pr As is known from fluid mechanics, except pressure energy, the fluid in the reservoir also has if it is in kinematical state, it is also has kinetic cnergy. As a point M in reservoir shown in figure 1-3. the total cnergy of unit mass lluid is Where: -The movement velocity of point M. Of course. as for the original state v,=o Because flow rate is very small in reservoir and the order is 10 m/s, and its square haller than hydrostatic head which should be omitted. So the total energy can be written as.'s H1=Z+
The total energy can be also expressed in the form of pressure Pr p+pg In the formula above: P is the reduced pressure at point M, it stands for the total energy of fluid point M, and p stands for the magnitude of pressure energy Betore oil and gas reservoir development. the pressure that is reduced to the initial oil-water interface of each well should be equal. Then the fluid llows from the place with high reduced pressure to the place with lower reduced pressure after oil and gas reservoir development. Because the reservoir uplift is always much lower than its lateral extension, therefore for the sake of convenience for lly simplitied to the planar seepage flow, hence the cepl of reduced pressure must be used days to come when studying the seepage flow of whole reservoir, all the pressures are reduced pressures if there is no added illustrations Example I-I The mid -depth of formation at a given well is -940m above sea-level, its oil water interface altitude is -1200m. the formation crude oil density is 800kg/m. The reservoir middle pressure actually mcasured is 12. 5MPa, and then what is the reduced pressure on the oil Solution the elevation of middle reservoir of this well is Z=1200-940=260(m) Pr=p+pg 12.5+800×9.8l×260×10 4.54(NPa) In the course of well performance analysis, the formation pressure of cach well need to be compared, and at this moment only use reduced pressure can we get right conclusions 1. 2 The driving fo driving mechanism in reservoir hen the bottom hole pressure of a well in reservior decreases, the oil or gas will flow to the bottom of well. What is the energy driving the oil in reservoir? Some kind of cncrgy is summarized as follows 1.2. 1 Hydrostatic pressure hen there is th area which is connected with oil and gas reservoir the hydrostatic pressure of water supply area is the driving force. The fluid will flow as long as the bottom hole pressure is lower than the pressure of supply area, When the water supply is ample. the pressure on the oil-water interface can be considered unchanged. If the depth of oil-water ressure on oil-water intertace interface is H( Figure 1-4). then the hydrostatic
pressure on the oil-water interface is: Pull Where: Pg-The density of water, kg/m H--The depth of oil-water interface, m p-The pressure on the oil-water interface, MPa This kind of driving force that relies on hydrostatic pressure of supply area to displace oil is led water drive. For most reservoirs, water supply is always less than the oil production. Apart from a few small oil and gas reservoirs, in the whole development stage, it is rare to see the reservoirs with natural water drive, and water injection is the main development scheme. The majority of oil and gas reservoirs in China are developed by water Flooding 2. 2 The elastic energy of formation and the fluid in it The crude oil in formation is long-tcrm under the original formation pressure, after the well is put into production, because of the drop of reservoir pressure, the tluid in the reservoir will expand, and then part of oil is driven to the bottom of wel The physical quantity that characterizes the magnitude of clastic energy of fluid is compacti factor of it is the reciprocal of bulk modulus of elasticity, and it shows the relative change of fluid vo when unit pressure changes. It is expressed as the following formula C i aL (1-1 In the formula above V is volume ol fluid, because tluid volume v is a decreasing function of pressure p, so its derivative is negative. In order to make C positive, a negative sign need to be added in front of the formula. Also, because tluid volume is function of temperature T, marked as V(p, T). so there appears a partial derivative in the formula, and CL is isothermal compressibility Normally, during development there is little change in temperature of reservoir, so the impact of temperature on the liquid volume is not considered generally. The coefficient of compressibilit of water is considered as a constant within the reservoir pressure variation range. Its magnitude is about(3. 7-5)x 10- MPa". the coefficient of compressibility is relevant to the natural gas content dissolved in it, and it has a big range, its magnitude usually is(7140)x10"MPa- While the coefficient of compressibility of gas is rather bigger than that of oil and water, an it cannot be considered as constant with pressure, When the temperature of reservoir is a constant formula(1-1)can be simplified as I<I1 (1-2) When the coeflicient of compressibility of fluid changes little, and it can be approximately considered as a constant, the formula above can be also be expressed as ⊥I (1-3)
