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Determining anisotropic diffusivity in a volume affected by microseismic activity using real volumes rather than laboratory tests as laboratory results do not scale up correctly
Determining anisotropic diffusivity in a volume affected by microseismic activity using real volumes rather than laboratory tests as laboratory results do not scale up correctly
A number of data sets are determined, each set representing a wavefront and including coordinates of the point of appearance and a time of first appearance at the point. A matrix is calculated by second derivation by space of a function representing the minimum appearance time of the microseismic waves as a function of the data sets. The matrix is inverted and the diffusivity tensor deduced : A front of a first appearance of microseismic waves propagating in the volume is provoked by a pressure increase in the volume caused by a source and causing the object of the measurements bearing on its location and time of appearance. The relation between the second derivation matrix and the diffusivity is D=H(- 1)/2pi , where D is the diffusivity tensor, H is the matrix obtained by second derivation of the function representing the minimum time of appearance and H(-1) represents the inverted matrix H. The volume is modelled by a mesh of cells and each set of data corresponds to a cell and includes the point of appearance corresponding to the minimum appearance time from among the measured microseismic waves which are found in the cell. The matrix is regular or non- structured (tetrahedric or stratigraphic). A function representing the minimum appearance time is calculated on the mesh by interpolating the appearance time values in the data sets and the second derivation matrix is obtained by second order spatial derivation of this function. An independent claim is made for a method of determining permeability in a volume affected by microseismic activity, giving a front of first appearance of the microseismic wave propagating in the volume, caused by an increase in pressure in the volume from a source. The diffusivity is calculated using the method above and the anisotropic permeability tensor is calculated from the anisotropic diffusivity tensor thus obtained.
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