Mass transfer between fractures and matrix blocks is crucial to oil recovery by waterflooding in fractured reservoirs Mattax and Kyre (1962) proposed a scaling equation for rate of oil recovery by spontaneous imbibitions. Results were presented as oil recover vs dimensionless time. Many conditions apply to this scaling equation, including identical core sample shares and fluid viscosity ratios. Recent investigation of these two factors has resulted in a more generalized scaling equation for strongly water-wet systems with a general definition of characteristic length and a viscosity ratio term included in the definition of the dimensionless time.

In this paper, published data on oil recovery by imbibitions have been analyzed and correlated through application of the new definition of dimensionless time. These data sets were for different porous media, core dimensions. Boundary conditions, and oil and water viscosities. All of the systems were strongly water-wet. The generalized correlation was fitted closed by an empirical mass transfer function with the new definition of dimensionless time as the only parameter.


Spontaneous imbibitions is an important phenomenon in reservoir engineering, especially with respect to oil recovery from fractured reservoirs. The problem of scaling imbibition and tow-phase flow phenomena in general is of widespread interest. 1–6

Mattas and Kyre 4 published a widely applied paper on sealing of oil recovery by imbibitions form fracture reservoirs. A scaling group was proposed for systems with different rock and fluid properties. Many condition were set for the derivation of the scaling equation. Including identical core shaped, viscosity rations, and initial water saturations. Two sets of imbibitions data were used to test the scaling equation (see Table 1 and 2) One set was for two cylindrical sandstone core samples with all faces (AFO) to imbibitions (fig 1a) the oil/water viscosity ration was 176. The other set was for four alumdum cylindrical cores of different lengths with only one end open (OEO) to imbibitions (Fig. 1b: the old water viscosity ratio was about 9. In all cases except for one. The water viscosity was 0.9 cP. The two sets of data therefore provided examples of boundary condition, oil/water viscosity rations, and porous media that all different. Independent correlations were presented for each set of data.

The effect of core length and boundary conditions on Imbibition rate was studied later by Hamon and Vidal6 The cores were made of aluminum silicate with lengths ranging from about 10 to 85 cm and boundary conditions (as shown in Fig I) of all-faces-open (AFO) two-ends-open (TEO), and one-end-open (OEO). The same water and oil phases were used for all of these experiments (Table3).

In Older to develop improved scaling of spontaneous imbibition all extensive experimental study was performed by Zhang et al. 7 Twenty Berea cores were prepared with core lengths ranging from 1.17 to 10.24 cm and boundary conditions of AFO. TEO. OEO. and two-ends-closed (TEC) In these experiments, oil viscosity ranged from about I to 156 cP.

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