r=C( grade)(0.5≤m≤1 With the increase of seepage velocity, the value of n changes from I to 0. 5 continuously Igh the formula is simple, n and C are not constants in the process age flow. they also change with the seepage velocity. If n is assumed as a constant, this seepage law is very convenient to use even though its physical meaning is vague, it is still in use. What should be pointed out is both the binomial law and exponent seepage law are nonlinea The pores of low permeability reservoir are very all. the thickness of tluid adsorbed laver on the wall of ores is as big as the size of pore, and the flow resistance of adsorbed laver is much bigger, so fluid is hard to flow low permeability reservoir does not obey the Darcy's law when pressure gradient is very small. Only if the pressur Figure 1-9 The relational diagram of the is obeyed( Figure 1-9), that 人 Exercises is diameter is D=6c I', porosity is d=0. 2 oil flow through the rock sample along its axial direction, and the viscosity of oil is 4mPa. s, its density is 800kg/m, the pressure of the inlet end is p.=0.3MPa the pressure of the exit end is P,=0. 2MPa. Please solve the following problems:( 1) The flow quantity of every minute. (2)The Reynolds number. (3)The Reynolds number of fluid with the Aw=162mPa., density is 1000kg/m when passing though rock sample( the rest conditions are unchanged 2 Assuming a kind of liquid passes through a sand pipe with the D=lOcm, L=30cm and d=0.2,n=0.65mPa·s,斗p=0.7MPa,S。=0.3,K,=0.2um· Please solve the problems the production @, the seepage velocity and the average true seepage velocity e, 1-3 Assuming that the length of sand layer is L=500m, width B=100m, thickness h K=O 3um, porosity =0. 32, un =3. 2mPa. S,Q=15m/d, Sw=0. 17. Please solve the ollowing problems:(1)The pressure difference Ap, the seepage velocity c and the average truc seepage velocity r.(2)If (=30m/d, what is Ap, v and 4i ?(3 )The needed time T, and when oil passing through the oil sand of both condition 1-4 Please derive the relational expression of total coefticient of compressibility C, with ocfticicnt of compressibility of oil, gas and water and its saturation
Chapter 2 Steady seepage flow of single phase incompressible fluid 2. 1 Three basic seepage fle It is called single-phase seepage flow when there is only one kind of fluid flows in formation While it is called two-phase flow or multiple phase fluid flow when there are two or more than two kinds of fluid flow simultaneously in formalion. In the cause of seepage flow, if the main parameters of movement the pressure, flow velocity for example only change with the location, and have nothing with time, then the movement is called steady flow on the contrary, if one of the main paramcters is in connectio with time, the movement is called unsteady state llow through porous medium. The seepage flow in actual reservoir is all unsteady seepage flow, and the real stcady seepage flo w does not exist However. somctimes the seepage flow can be treated as stcady seepage flow in short period In the oil field with suflicient edge water or artif icial water flooding. oil is forced to the bottom hole of production well mainly relying the energy of edge water or injected water. There is only the oil tlow around the production well in a given period. Because the formation pressure is unchanged. and the elastic action of fluid and rock can be omitted the fluid and rock can be treated as rigid medium, that is the fluid and rock are incompressible. As to the reservoir with sulficient producing energy, the formation pressure is unchanged during quite a long time, and such kind of seepage flow problem can be illustrated through a mode with a unchanged pressure p in the supply boundary. Hence, if the bottom hole pressure production does not change with time. While if the production maintains as a constant, the bottom hole pressure will certainly not change with time, an such kind of seepage flow belongs to stcady The shape of actual reservoir is varied, and the well spacing is also manifold. As for the horizontal reservoir with sealed fault as the boundary from three sides as shown in Figure 2-l beyond the area that is half of the well spacing, the streamlines are basically parallel. And this area is like a big core, the unique features of rectangular reservoir are reflected intensively. The flow velocity and the flow rate is the same on the every section, and the pressure is only in connection with one coordinate, Such kind of flow is called planar one-dimensional seepage flow Most reservoirs are rarely real rectangular, but only the shape is analogous, The conclusion here is effective As for the similar round horizontal reservoir as shown in Figure 2-2, beyond the area that is half of the well spacing, the streamlines to the well array along the direction of radius of well array
circumference. Such kind of seepage flow along the direction of radius is called planar radial fluid llow, Of cause, it is kind of simplification of similar round reservoir. Many problems can be illustrated using this simplified mode, and it is also of high accuracy. No matter how complicated the well network is. il can always be Ireated as radial lluid flow around a well oooo Figure 2-1 The model of planar Figure 2-2 The model of planar one-dimensional seepage fl adial fluid flow When a part of oil layer of a given well is drilled or the perforation completion, the similar globe radial fluid flow will happen around the bottom hole within a small area In all the planar one-dimensional seepage flow, planar radial seepage flow and the globe radial fluid flow are the basic seepage flow modes, and the planar radial fluid flow is the main 2.2 The planar one-dimensional steady seepage flow of single-phase incompressible fluid Assuming that there is a horizontal strip oil layer, and its length is L, width is B, height is 1 the reservoir is rigid water drive, and the fluid and rock are incompressible. And the formation is homogeneous, and isotropic. The pressure of the supply boundary is P, and the delivery end is a drainage pit whose pressure is P. And the flow of the fluid in the oil layer is planar one-dimensional steady seepage tlow A coordin 3. the flow velocity of a arbitrary point r in formation can be shown with diflerential form of the s law k dp Choosing two random scctions of tho and assume the volume flow rate of the two scctions Figure 2-3 The model of plana one-dimensional seepage flow is selectively q, and q>. Because the formation and
the fluid is incompressible. the volume of fluid in the laver between the two sections can not increase or decrease. Then the equation (,=Q. can be oblained. That is the volume flow rate passing through a random section in formation is a constant, marked as (, from the formula(2-1), the lollowing can be obtained K1业 In the formula above A is cross-section area, Separating the variables of the formula(2-2) and integrating, the integrating interval of x is 0>, and the integraling interval ol pressure P is P→”s, then the following equation can be got: Then we can obtain the formula(2-4)as shown below K1( T'he formula(2-4) is the lla of pl tlow. if the integrating interval(, L) of formula (2-3) is changed to(0, r) or (R, L). the following expression can be obtained Substituting the formula(2-4) into formula(2-5), the following expression can be obtained Formula(2-5) and formula(2-6) are the pressure distribution formula of planar one dimensional steady seepage flow. When the botto hole pressure p and the production stays unchanged, the pressure p and x has a linear relationship. On the other hand. the pressure p of a arbitrary point in formation is only in connection with coordinate x; when the valuc of xr is cqual the value of pressure is equal. The line( surface connected by the points with equal pressure is called isobar (surface ) and the lines that are vertical with the isobar( surface is called stream The vertical grids constituted by constant pressure lines and streamlines is called stream field which also called stream net, As to the planar one-dimensional seepage flow, numerous constant pressure lines can be obtained. In order to see the pressure distribution in formation clearly, like drawing the electric field diagram, the rule is regulated when drawing seepage lield diagram: the pressure diffcrence between two arbitrary adjacent isobar must be equal at the same time, the flow rate between two arbitrary streamlines also must be equal. The seepage lield diagra illustratively reflect the behavior of seepage flow, the pressure changes steeply in the place where
the isobars are condensed, while the pressure changes slowly in the place where the isobar are rare According to the spacing of the streamlines, the flow velocity can also be decided Differentiating the both sides of the formula(2-6) with respect to x, the following expression can be got Under the condition that p, P, or the production is a constant, the pressure gradient of a arbitrary point is a constant that is the pressure change on unit length is equal. So the isobars of planar one-dimensional steady seepage flow of incompressible fluid is a tuft of equal-spaced parallel lines Substituting the formula(2-7) into formula (2-1), then the llow velocity of a arbitrary point in formation Is arbitrary point Is a constant. so the streamlines are also a tutt of equ parallel lines. The Fi igure 2-4 is the seepage field diagram of planar one-dimensional stead seepage flow of incompressible fluid mass point moving in the porous mediaL,is And from formula (2-8), the following Figure 2-4 The seepage tield diagram of planar equation can be obtained one-dimensional steady seepage flow K( Obviously,1 dt dul Assuming that the location of a arbitrary fluid mass point is x= N, when time is 1=0, after time (, the location of the mass point is x, then integrate the formula(2-9), the following expression can be obtained (2-10a) According to the production formula(2-4). the following expression can be obtained Substituting the expression above into formula(2-1Oa), the following expression can be obtained