Determining isotropic diffusivity in a volume affected by microseismic activity using real volumes rather than laboratory tests as laboratory results do not scale up correctly

摘要

Data sets are determined, each representing a wavefront and including coordinates of the point of appearance and a time of first appearance at the point. The diffusivity is calculated by resolving for each point an equation giving the evolution of the wavefront along a line representing the trajectory of the front and using the diffusivity as a variable in a function of time and line position : 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. Slowing vectors are calculated by spatial derivation of a function representing the wavefront appearance time. An assembly of lines representing the trajectory of the wavefront are determined using these vectors., each line connecting the source and a point of appearance of the various data sets. The equation is of the form ar (ds/D(s, t)) = (4pi ( 0t(dt/D(r, tau ))))0>.5>, where r represents the distance travelled by the pressure front between the source of injection shown by a coordinate a and a point of appearance at which the diffusivity is determined along the line and D(s, t) represents the diffusivity at the point of the line represented by a coordinate s at time t. During calculation of diffusivity before microseismic waves, the equation can be simplified to D(r, 0) = 4pi t/( ar(ds/D(s,0)))2). The volume is modelled using 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 of the microseismic waves measured 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 slowing vectors are obtained by spatial derivation of this function. The minimum appearance time is filtered before calculating the slowing vectors. The diffusivity calculation is made successively on each of the points classed by increasing appearance time, and is done by approximation using a finite sum. 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 permeability is calculated from the diffusivity thus obtained.