If oil volume Iactor B, is lead in. and another formula of compressibility of oil Co can be educed from formula(1-2)as dB dp p>P, his is because when the formation pressure is lower than the saturation pressure, volume factor is the increasing function of pressure, so there is no negative sign in front of formula, The negative sign is needed when the formation pressure is higher than the saturation pressure Similar rock particles stand compression of formation pressure, when the formation pressure comparing with that of liquid and gas, so it can be omitted. The formation lies deep underground it stands overburden force F. and this force is balanced by the sum of the product of rock frame stress Um multiplied by the contact area of cap formation and reservoir bed Am plus of the product of formation pressure hydrostatic pressure of lluid in reservoir pores )p multiplied by the cross- section arca of pores A. the formula is shown below F=U +BA the process of oil rccovery, the formation pressure will drop; especially arround the bottom hole, the pressure drop even more. Because the overburden acting force Fis a constant, the stress that the rock stands will increase which causes its deformation and the decreasing pore tion of porosity and permeability. Figure 1-5 is the deformation ligure of rock (a Before deformation (b)After deformation If the water injection pressure is increased, the stress that the rock frame stands will decro and rock frame will recover which makes the pore volume increase. In fact. this process is irreversible, the increase of rock Frame stress will cause plastic deformation, such as the destruction of cementation texture, and it will not recover after the build up of TO Ien the reservoir is not deep, the process can be considered as reversible, i, e, elast and the crror is not great. When the depth of reservoir is more than 4000m or it is abnormal pressure reservoir, the change of porosity and permeability with pressure cannot be ignored. The experience of low permeability oil and gas field development has shown that the change of
permeability with pressure of low permeability oil and gas field is noticeable, and this problem can not be ignored From the analysis above we know: when the formation pressure decreases, the pore volume decreases: while the formation pressure increases, the pore volume increases. So the compression coelficient of formation pores( formation compressibility for short)C is defined cN四间m数mmm compressibility Bu is defined by rock bulk volume V as denominator as shown If the porosity of formation is d, and the equation V, =dV can be oblained, then 卢.=C From Russian and West literatures, this difference should be noticed. The formula(1-5) is used as the definition of coefficient of compressibility of formation pores In actual oil fields. the situation that oil-water two-phase exists or oil-gas-water three-phase introduced now. It shows the total fluid driven from unit pore volume depends on the expansion ot oil, gas and water and the reduction of pore volume when the formation pressure drops one unit When the saturation of oil, gas and water is respectively S,, S, and S., the In the formula above Co, C, and Cu is respectively the coelficient of compressibility of oil The oil and gas flow from reservoir to hole bottom depending on elasticity of formation only called clastic driving. Generally speaking, as a driving force, elastic drive accounts for less than 10%c of whole drive but it exists in the entire developing process, especially when the work system 1.2.3 The elastic energy of dissolved gas There is a large number ol natural gas dissolved in crude oil, ar when formation essure on pressure, the previously dissolved gas will escape Irom oil and change to be r kind of driving mode relying on only dissolved gas without any other energy is called dissolved gas drive. The driving energy of dissolved gas drive and elastic drive is uniformly distributed in the oil reservoirs, and it is different from the energy of water drive irom outer boundar 2. 4 The elastic energy of gas cap As for the saturated oil and gas reservoir with gas cap, when wells are put into production the decrease of formation pressure will inevitably cause the pressure decline of gas cap which leads
the natural gas in gas cap to expend and drive the oil to the bottom hole. Apparently, the gas ca drive must be along with dissolved gas drive. 1.2.5 Action of gravity Oil will naturally flow from the structural high place to the lower place, Irom the top of oil layer to the bottom; the gravity of oil is also a driving force when there is no other driving energy The driving forces listed above are the driving energy that is met often. As for a particular servoir. several driving cner y can exist simultaneously, but in different stages of pro in secondary status, To depend on which energy to drive oil in the production process is called the driving mode ol reservoir, The according to the dilferent driving energy above, the driving mode can be divided into water drive elastic drive, dissolved gas drive, gas cap drive and gravity drive. However, the driving mode is not unchangeable; it can be converted from one driving mode and there is big recharge area around the reservoir, but, because the production of reservoir is too much making the energy supplement of edge water cannot catch up with the consumption of reservoir,then the pressure will decrease and below saturation pressure in part area of reservoir and now in this parts of area the water drive with high efficiency change to the dissolved gas drive with low cfficicncy. Conversely, if there is no supply of natural recharge area, and we adopt the method of artiticial water flooding. then the dissolved gas drive and elastie drive can be change to water drive with high efficieney the driving mode is different, then the seepage flow mechanism is ditferent and also the seepage flow process, even the seepage fluid. In order to develop reservoir rapidly and efficiently the seepage law under different driving modes must be studied lo direct reservoir development There is no doubt that oil must overcome the resistance when flowing in formation The flow resistance is mainly viscosity resistance because of the complex pore structure, uneven distributed and narrow porous channel and extremely rough channel surtace. However, because of the existence of local loss caused by inertia, the Jamin action will cause extra resistance when there is multiphase flow 1.3 The basic law of seepage flow-Darcy's law 1.3.1 Continuous medium all objects are composed of molecule. Even though its appearance is static, the molecule is constantly in motion, Strictly speaking, all the objects are not continuous, although molecular movement laws can be predicted when we know the initial state theoretically. In fact, it is full of trouble when study ing the movement of more than three molecules, so it is impossible to study the moving law of tluid at molecular level
What we care about is the assembly of many molecules and the study of the movement of this assembly, All the properties that characterize the movement of fluid( velocity for example )is th average value of each molecule in the assembly. If the assembly is taken as the basic unit, then tluid can be considered to be continuous, and the basic unit is called mass point, while it is not a mathematical point. The mass point must be as small as possible to fully reflect the flow property Also,the mass point must include sufficient molecules to guarantee the sleady of the average value. The so called densily of one point p express with formula is Where: AV--The volume around given point,m According to the continuum theory, Av-0 is to approach one material point, while the ere are plenty of molecules in the mass point and it is not the infinitesimal in mathematics, To study the tluid movement is not starting from the molecular level but Irom the mass point of continuous medium, it is called microscopic level Seepage flow is the movement of fluid in porous media. Porous media include not only solid but also pores. So one mass point of porous media must include enough solid and pores. It can be imaged that the mass point of porous media is bigger than that of fluid or solid mass point. The so lled property of one point in porous media( pressure and velocity for example) is the average value in this point. Because of the extreme complexity of the porous media constructure, in most cases the macroscopic field is studied in percolation mechanics in porous medium, which is the average value of mass point parameter and the microscopic mcchanism is less related 1.3. 2 The Darcy's law Assuming that the porous medium is composed of isodiametric ball type particles. whose radius is the average value derived from grain size analysis. According to the result of ball ty pe particles packing study, the porosity of porous media has nothing to do with the size of particles but the mode of arrangement of particles. The porosity is the smallest when the four centre of sphere arrange as rhombus and the value is 0. 259, and the stable filling mode with the biggest porosity is not found until today, while the biggest porosity found already with stable arrangement is 0.875 The actual shape of rock particles is not globular, there is cementing matter except particles It's hard to explain the real issues with globular particle model, The smallest reservoir porosity around the world is less than 0. 259. So far the effective way to simplify the porous media has not All the complex mechanical phenomena and movement in macro-world comply with the Newton’ s law withe different, it also has general character. And this general character is the basic law of seepage seepage flow-the special seepage law adapts to a given specific case
The nature of seepage flow is the actual fluid flow through the porous media. Deducing fron the property that the diameter of pores is very small and the contact surface is very big when fluid tlow through porous medium. the conclusion can be obtained that the viscous loss is the main loss. Therefore, if a kind of liquid with viscosity u passes through a formation with the cross- section area A and length L with flow rate and causes the diflerential pressure of formation is △p, it is easy to know If the formula above is written in the form of equation =K14 This is the Darcys law: In 1856 a French engineer Darcy proved this law by laboratory experiments, Darcy made a straight metal cy linder about Im tall with loose sand in it, and sealed the top and bolom of lube with screen, then fixed piezometer tube on both top and bottom water flows from top to bottom( Figure 1-6). He found that no matter how the rate of f changed, the seepage velocity t is directly proportional to hydraulic slope where: v-The seepage velocity, it is the quotient of flow rate dividing by cross section arca of er column in L-The length of sand column m K。— The seepage coefficient,m Figure 1-6 The flow diagram of Darcy s ex If only the seepage coelficient Ks is changed and the sand type remains unchanged, the relationship between hydraulic slope and velocity is unchangeable. Darcy only cared about water at that time, so he used hydraulic slope instcad of pressure gradient. While as for each kind of sand