The Use of Capillary Tube Networks in Reservoir Performance Studies: II. Effect of Heterogeneity and Mobility on Miscible Displacement Efficiency

Part II of this series extends the network technique to all miscible displacement mobility ratios and introduces a heterogeneity factor called H. As a result, the network model can be used to study the general miscible displacement case, i.e., miscible displacements with all mobility ratios in linear or areal flow systems having a range of heterogeneities. Engineering charts are presented which show the relationship between recovery, mobility ratio, heterogeneity and pore volumes injected. Introduction Part I of this series dealt with equal viscosity, and equal-density miscible displacements. Part II extends the network technique to miscible displacements with all mobility ratios. Part II also introduces a heterogeneity factor, H, used in designing network models. The equal-density limitation is retained. Plug flow is assumed in the capillary tubes. The Plug flow is assumed in the capillary tubes. The original fluid and injected fluid are considered ideal so there are no heat or volumetric effects from mixing. Viscosity of the mixtures is discussed in the section on Calculations. Part II is divided into three main sections. The first discusses the calculation methods. The second shows comparisons of data calculated by the network technique and data measured for real porous media. These comparisons demonstrate that porous media. These comparisons demonstrate that network models can indeed be used to predict the performance of displacements in real porous media. performance of displacements in real porous media. The third section illustrates the application of network methods to reservoir engineering problems. The illustration is accomplished with a series of charts that relate oil recovery to heterogeneity, mobility ratio, and pore volumes injected for the special cases of a linear system (length/width = 3/1) and five-spots. CALCULATIONS Two primary steps are required to calculate the effect of heterogeneity and mobility on miscible displacement efficiency. The first is to design a network with the desired heterogeneity. The second is to calculate the displacement phenomena that occur as the injection fluid advances through the network. A network is designed by specifying the following:Type linear or areal flow models.Tube configuration diamond, hexagonal, etc. In this paper all networks are the diamond configurations shown in Fig. 1.Size number of tubes in the network.Heterogeneity by using the heterogeneity factor (see Fig 2a).Tube radius distribution function all tube radius distribution functions are the single modal type shown in Fig. 2a.Tube location distribution all location distributions are random. SPEJ P. 345