Geophysical Journal | 2014 volume 36 5

Dispersion effects modeling while forecasting physical-geological parameters of heterogeneous media

© A.I. Kobrunov, 2014

A problem of forecasting the parameters of physical-chemical model for heterogeneous media based on available standard data selection considered as a field of corresponding parameters dispersion is being considered. Dispersion of parameters is considered as an observed component of medium heterogeneity effects manifestation, which is simulated by a function of concentration based on diffusion equations. Diffusion operator is being designed based on fundamental solutions of diffusion equations, which made possible to obtain prognostic field of dispersion for sought for parameter. A problem of reconstruction of heterogeneities density concentration in distribution of expected parameter as a solution of integral equation of the first kind is formulated. On the basis of Mamdani rule of logical conclusion chain rules of calculation for resultant dispersion field for prediction of heterogeneities of final parameters have been designed. An example of modeling the dispersion field for presence of oil by one of conditional oil deposits is presented, which demonstrates validity of new notions introduced.

Key words: prediction of parameters, heterogeneity of medium, dispersion of parameters, field of dispersion, diffusion equations, fundamental solution, operator of diffusion, Mamdani rule, function of concentration, inverse problem, chain rules of forecast, α-sections, localization curve.

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