ISSN:
1573-1987
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Notes:
Summary The interface between two moving fluids in a porous medium will, in general, deform under the influence of gravity and drag forces. An example of some importance is the formation of so-called gravity tongues in oil reservoirs. This paper deals with the displacement of oil by water in a homogeneous non-horizontal oil stratum. The deformation of such an interface can be deduced by numerical procedures based upon exact methods. The use of these methods is limited, however, owing to the fact that in oil reservoirs the dip is usually smaller than 10 to 20 degrees. In such cases, where the interface is initially horizontal, the computation of the form of the interface as a function of time becomes so enormous, even when a fast electronic computer is used, that an approximative method is more useful. In this paper two approximate solutions are presented. The first one is obtained by using a simplified form of the dynamic interface condition, in which the flow velocity component perpendicular to the dip direction of the reservoir is neglected. This simplification has previously been used by Dietz, who gave a first-order approximation with respect to time. More complicated results are obtained by using the second approximation where, in accordance with the dynamic boundary condition, this velocity component is more or less taken into account. In both methods, the form of the interface as a function of time is expressed in a parametric representation. Moreover, the amount of water that has passed a given cross-section and the flow of water at this section are obtained as a function of time and the parameter used. Results of both methods are compared with each other and with those obtained by an exact method. Both approximations are found to be good in those cases where the dip of the reservoir is not too high, but this is precisely when exact methods are impracticable.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00382235
Permalink
