Combining Well Logs and Well Test Data in Permeability Modelling Using Fast Fourier Transform

Well test data and traditional log measurements give information about the effective permeability in the reservoir on very different scales. <br>The variable representing the well test permeability can be regarded as a spatial weighted average of the ordinary permeability variable. The kriging procedure thus involves covariances that are averaged over the well test volume. This gives an inverse block kriging problem.<br>Solving the expressions for the averaged covariances by straightforward computations on large grids in 3D, involves computations of big triple sums. Transforming the spatial averaging to the Fourier domain, and using the convolution theorem, means that the heavy summation is replaced by simple cell by cell multiplications. This combined with the Fast Fourier Transform algorithm gives a highly efficient method for solving the inverse block kriging problem.<br>