Buckley leverett simulation example NTNU Auther : Professor Jon KleppeProfessor Jon Kleppe Assistant producers: Farrokh Shoaei Khayyam Farzullayev

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio Characterization of model  This is a demonstration of 1D Buckley-Leverett problem.  Oil is being displaced by water in a horizontal, linear system under diffuse flow conditions.  The pressure is maintained during the displacement process.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio Animation of Oil Saturation for Case 1, Geometry: 10 x 1 x 10 Effect of grid numbers  The water can travel through a course gridded model more quickly than a fine gridded model. Consequently the water front becomes smeared causing a prematurely water break through in the coarse gridded model. This effect is called numerical dispersion.  In practice there are other factors contributing to numerical dispersion such as the averaging of relative permeabilities and of saturations.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio  The greater the number of gridblocks the more closely the model approaches continuum in space in which Buckley Leverett shock-front displacement is honored. Animation of Oil Saturation for Case 2, Geometry: 50 x 1 x 25

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio Case 3, the capillary pressure is included,the geometry is 50 x 1 x 25. Capillary pressure effect  When capillary pressure is included in simulation, the fluid front has relatively round shape.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio Case 4, oil viscosity is 10 times higher, geometry: 50 x 1 x 25. Effect of mobility ratio  With the increase of mobility ratio, M, the shock-front decreases.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio SWSW FWFW  o = 1.0 cp  o = 10.0 cp  This graph shows that with the increase in viscosity, curve moves to the left.  From the mobility ratio equation, the increase in oil viscosity brings an increases to the mobility ratio, M.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio  o=1.0 cp and M=2.0  o=10.0 cp and M=20.0 This slide illustrates two runs of simulation with different mobility ratios, M.  In first case when M is less or equal to 1 cp, the displacement is piston-like.  In case 2, the mobility ratio is much greater than 1 cp, there is some degree of shock-front displacement that is less than piston like.  As oil has high viscosity, the water is relatively more mobile and it moves bypassing the oil.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio References  Kleppe J.: Reservoir recovery course, buckley leverett analysis note Kleppe J.  Snyder R. W. and Ramey H. J.: ”Application of Buckley-Leverett Displacement Theory to Noncommunicating Layered System”. SPE paper 1645 Snyder R. W. and Ramey H. J.

Buckley leverett simulation example Characterization of model Effect of grid numbers Capillary pressure effect Effect of mobility ratio  Title: BUCKLEY LEVERTT SIMULATION EXAMPLE  Author:  Name: Prof. Jon Kleppe  Address: NTNU S.P. Andersensvei 15A 7491 Trondheim  Website Website   Size: 300 Kb About this module