Megascopic dispersivity

Megascopic Dispersivity. The megascopic scale is the full-aquifer dispersivity whose value determines the volumetric sweep in numerical simulation blocks. Figure 3 shows the behavior of (expressed as inverse Peclet number) as a function of time for miscible displacements in a two-dimensional stochastic permeability field. The parameter V is the Dykstra-Parsons coefficient, a dimensionless measure of the spread of the permeability distribution to which the flow field was conditioned. = 0 corresponds to a... 

Figure 9. Schematic representation of the growth of megascopic dispersivity with distance traveled. All displacement pass through three regimes (noii-Fickian, transition and Fickian) which may be large or small depending oii the correlation length and D. Even displacement which are strongly Fickian do not lose the evidence of their non-Fickian beginning. (Reproduced from Ref. 1.)...

Whatever the geologic causes, there are several purely statistical inferences to be drawn from Figure 16 which bear directly on the issue of reservoir simulation. The size of grid four may be a natural choice for the grid block size in a deterministic simulation model. Such a selection would minimize the variation between blocks and may, in fact, make stochastic assignments of secondary importance (thus, reducing the differences between realizations). The variation of the fifth scale would be incorporated as pseudo functions or megascopic dispersivity into individual blocks. 

Figure 11. Comparison of calculated macroscopic dispersivities (solid curve) to experimentally measured megascopic (laboratory scale) dispersivities. d is the grain diameter for the packing in the experimentSl measurements and the correlation length for the calculated curve. Better agreement could be obtained by letting d be about live times the correlation length in the calculated curve. (Reproduced from Ref. 4.)...

Figure 12. Comparison of megascopic (upper curve) and macroscopic (lower curve) dispersivities from simulations with large correlation length and no diffusion. In all cases, the macroscopic dispersivity is smaller and grows slower. (Reproduced from Ref. 5 )...

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