西安石油大学：《油藏物理（油层物理学）Petro-physics》精品课程教学资源（英文课件）Flow 3.2 Capillary pressure curve 油藏岩石的毛管压力曲线

Capillary pressure curve Xuanqi zhang Petroleum engineering college

Capillary pressure curve Xuanqi zhang Petroleum engineering college

油藏物理学一油藏岩石的毛管压力曲线 The phenomena of liquid rising along capillary Pw OB B 油 自由水而 OA 水 P.prgh= 2oc0sθ r (1)

油藏物理学——油藏岩石的毛管压力曲线 The phenomena of liquid rising along capillary r Pc w gh    2 cos   （1）

油藏物理学一油藏岩石的毛管压力曲线 If there are oil and water in the reservoir Poa =Pua If the section area is so large Poa Pob +Pogh (2) Poa Pub +Pwgh (3) (2)-(3): Pb-Pb=(pn-P。)gh Pob-Pb=P

油藏物理学——油藏岩石的毛管压力曲线 If there are oil and water in the reservoir Poa  Pwa If the section area is so large Poa  Pob  o gh Poa  Pwb   w gh （3） (2)－(3)： o b wb c o b wb w o P P P P P gh     (   ) （2）

油藏物理学一油藏岩石的毛管压力曲线 P。 20 coseo (3) The height of water h= 20o coseo (4) r(P。-Pm)g For the system of oil and gas,the height of oil 20og CoS0o (5) r(P。-Pg)g 1

油藏物理学——油藏岩石的毛管压力曲线 The height of water r P wo wo c 2 cos  （3） r g h o w wo wo ( ) 2 cos       （4） For the system of oil and gas, the height of oil r g h o g og og o ( ) 2 cos       （5）

油藏物理学一油藏岩石的毛管压力曲线 the additional pressure in random surface By Laplace'low 水 油 o:interfacial tension R R2:maximum radius of curvature of the curved surface

油藏物理学——油藏岩石的毛管压力曲线 the additional pressure in random surface By Laplace’ low ) 1 1 ( 2 R1 R Pc    σ: interfacial tension R1、R2 : maximum radius of curvature of the curved surface

油藏物理学一油藏岩石的毛管压力曲线 The curved surface of capillary maybe part of sphericity,cylinder or random shape. 1.If the curved surface is sphericity R=R2=R 20 P R r R 三 cos? 2ocose P

油藏物理学——油藏岩石的毛管压力曲线 The curved surface of capillary maybe part of sphericity, cylinder or random shape. 1. If the curved surface is sphericity r P r R R P R R R c c     2 cos cos 2 1 2     

油藏物理学一油藏岩石的毛管压力曲线 2.If the curved surface is cylinder R1=0,R2=r P=G 3.the capillary pressure of random surface horizontal:R2 vertical:R

油藏物理学——油藏岩石的毛管压力曲线 2. If the curved surface is cylinder r P R R r c   1  , 2  3. the capillary pressure of random surface horizontal: R2 vertical: R1

油藏物理学一油藏岩石的毛管压力曲线 R1↑，R2↓with Sw↑， P=攻+之=侵 R -average pore radius R-→R、R2→distrubutionofoilandwaterinporousmedia-→Sw So P。=f(Sm) The capillary pressure is associated with water saturation in random surface

油藏物理学——油藏岩石的毛管压力曲线 R1 ↑ ，R2 ↓ with Sw ↑ , ) 1 ) ( 1 1 ( 1 2 R f R R Pc     —average pore radius R R R  R1 、R2 distrubutionofoilandwaterinporousmedia  Sw ( ) c Sw So P  f The capillary pressure is associated with water saturation in random surface

油藏物理学—一油藏岩石的毛管压力曲线 various resistance effects 1.If oil or gas is at rest Cylinder surface:P.'= point to the center of tube) r Spherical surface 20 cose point to the wall of tube) r 20 cose O P,=P。"-P'= B-20(e0s6-0.5) This is first resistance effect

油藏物理学——油藏岩石的毛管压力曲线 various resistance effects 1. If oil or gas is at rest Cylinder surface： r Pc  '  （point to the center of tube) Spherical surface r Pc 2 cos ''  (cos 0.5) 2 2 cos '' '            r P r r P P P I I c c （point to the wall of tube) This is first resistance effect

油藏物理学一油藏岩石的毛管压力曲线 2.When oil intend flow,spherical surface occur transmutation B-2ag A-20(c0s0-c0s0) this is second resistance effect. From this,when oil get over first and second of resistance,the oil can flow

油藏物理学——油藏岩石的毛管压力曲线 2. When oil intend flow, spherical surface occur transmutation (cos '' cos ') 2 ) ' 1 '' 1 2 (         r P R R P Ⅱ Ⅱ this is second resistance effect. From this, when oil get over first and second of resistance, the oil can flow