Laboratory breakthrough curves obtained from field cores are used to characterize the dispersion of miscible displacement. The analysis presented is based upon a set of equations for miscible flow which have been recently proposed by the authors. A solution to these equations is applied to breakthrough curves. This allows one to determine the underlying functions of the proposed equations. The kinernatic behaviour of miscible floods and their rate of dispersion are examined; in particular it is shown that the theory proposed here implies that the standard dispersion coefficient must be scale dependent. Comparison with laboratory results indicates that this prediction is consistent with the observed discrepancies between the "old" convection-diffusion theory and laboratory experiments.
Predictions of the evolution and performance of miscible floods are performed by using computer simulations. The two basic elements of any successful simulation are a dynamical theory of miscible displacement and a corresponding knowledge of field characteristics. To obtain an accurate prediction we need a good dynamical theory as well as accurate field data. Such data typically consists of values for porosity, grain size, dispersion coefficients, permeability, etc. A typical procedure to obtain this data is to extract a core sample from the field and use it to measure the required data; in particular, the core can be used in a miscible displacement experiment to obtain a breakthrough curve. The interpretation of a breakthrough curve depends upon the theory which will be used to simulate the miscible flood; there are, broadly speaking, two types of theory used to model miscible displacement. By comparing and contrasting these two theories, we will show how to improve our analysis of breakthrough curves. Hopefully, this improvement will lead to more accurate predictions of miscible flood performance.
The first type of theory for miscible displacement is the standard theory found in textbooks on fluid flow (e.g. Bear, 1972). This theory describes the dynamics of the fluid by introducing a dispersion tensor in analogy to Fick's law for diffusion. When this description is combined with the equation of continuity (conservation of mass) the dynamics is embodied in the well known convection-diffusion equation. In this case, the analysis of breakthrough curves is directed towards determining the dispersion tensor. There is however, a long standing puzzle using this approach. The value of the dispersion needed by a simulation to match actual field scale miscible displacements is usually much larger than the dispersion value obtained from the breakthrough curves (Pickens and Grisak,1981); therefore the dispersion is apparently scale dependent. The usual explanation for this discrepancy is that the dispersion is being affected in some unknown way by field scale heterogeneities. We have found a simple explanation for this scale dependence. We will present this explanation below and show it is operative even in homogeneous media.
The other type of theory describes the flow using a set of equations for immiscible two phase flow Traditionally, the equations used are those of the Buckley-Leverelt solution to Muskat's equations (Koval,1963; Todd and Langstaff, 1972).