Gravity and Capillarity Effects on Imbibition in Porous Media
Authors: Du Prey E. Lefebvre 
Published: December 2007

Abstract
This paper tries to assess the laboratory experiments used to scale gravity and capillarity-two active forces in the recovery process from matrix blocks in fissured reservoirs. We performed imbibition tests that show a great discrepancy among the scaled recovery curves corresponding to different block sizes.
Several reasons tire considered to explain the failure of scaling rules:flow boundary conditions,local heterogeneities, andinstabilities in the water sweep.

Introduction
The numerical models used to forecast the behavior of fissured reservoirs now in service imply a knowledge of the particular recovery functions for matrix blocks. The aim is to provide the reservoir engineer with the simplest way w determine these recovery functions - by defining the conditions that must be respected so that laboratory tests on small samples may be used with scaling rules to simulate the behavior of a reservoir block.
To keep the proper relationship between capillarity and gravity, Kyte suggested that gravity be artificially increased by carrying out the test in a centrifugal machine. This study tests the validity of this method.
First we must examine from an analysis of the equations governing the problem, on which dimensionless groups (combinations of physical quantities) the recovery function of a block depends. Next, we must verify the theoretical conclusions of this analysis by experimenting on small-scale samples of a given shape and size, simulating the intensity of gravity by tests in a centrifugal machine. Then, we try to check the validity of scaling rules using cases in which experimental comparison can be achieved - imbibition experiments on samples geometrically similar, but of different sizes (diameters of 200, 70, and 40 mm).
Results showed that these scaling rules were not valid. We then tried to isolate the phenomena that lead to the inadequacy of the conventional mathematical formulation by direct observation and by local measurement of saturation on the blocks during imbibition.

THEORETICAL BASES
Consider oil recovery from a cylindrical block of homogeneous, porous medium, initially saturated with oil and interstitial water, and then suddenly plunged into water. In the sample, the two plunged into water. In the sample, the two mechanisms of oil displacement by water (capillarity and gravity) are associated closely to contribute to production from a block, but their relative importance production from a block, but their relative importance depends on the dimensions of the block. Gravity becomes more important when the block is bigger, compared with capillarity.
Theoretical study is based on the validity of the classical formulation of polyphasic flows in porous media on a macroscopic scale - that is, porous media on a macroscopic scale - that is, relative permeability and capillarity pressure. An analysis of the structure of the equations (Appendix) made it possible to reduce the parameters of the problem to a small number, such as problem to a small number, such as three dimensionless groups:(shape factor)(mobility ratio)(capillarity/gravity ratio)initial water saturationthe shape of the relative permeability curves and the reduced capillary pressure
SPEJ
P. 195