Numerical simulation of first-order backscattered P and S waves for time-lapse seismic imaging in heterogeneous reservoirs

Abstract

Summary First‐order elastic wave scattering theory, validated in general features by deep‐borehole seismic coda wave observations, is used to numerically simulate time‐lapse borehole seismic data aimed at monitoring oil–water substitution in heterogeneous hydrocarbon reservoirs. A first‐order perturbation solution of the vector wave equation leads to P–P and S–S backscattered displacement vector motion expressed as the angular summation of the second radial derivative of P‐ and S‐wave velocity and density fluctuations α′/α, β′/β, ρ′/ρ over expanding spherical wave fronts of radii ξ = αt/2 and ξ = βt/2. P‐ and S‐wave velocity and density spatial heterogeneity is modelled as long‐range correlated random fluctuations consistent with the power‐law‐scaling character of crustal rock physical properties measured by borehole logs. The spectra of model scattering displacement seismograms for a power‐law‐scaling volumetric noise distribution duplicate the frequency enrichment observed in the spectra of broadband earthquake coda waves recorded in a deep well. Modelling of time‐lapse scattering in power‐law‐scaling permeability structures suggests that a stable borehole seismic source can locate oil–water substitution in reservoir volumes tens of metres on a side at distances of up to a few hundred metres from an observation well using currently available borehole seismic technology. Time‐lapse tracking of oil–water substitution and the monitoring of reservoir stress conditions can lead to spatially well‐constrained reservoir models, despite large‐scale, large‐amplitude correlated random heterogeneity.

Power-law scaling of spatially correlated porosity and log(permeability) sequences from north-central North Sea Brae oilfield well core

“…The technology of seasonal gas storage in reservoirs suggests the potential for gas injection into aquifers as a means of providing target volumes for suitably low-cost, highresolution time-lapse seismic imaging (Leary 2002;Yuh & Gibson 2001). However, the cost of well infrastructure similar to that deployable at candidate waste disposal sites could be better justified if the power-law-scaling complexity of geofluid reservoirs were more widely and comprehensively understood.…”

“…In analogy with neutron and optical scattering data for ferromagnetic and opalescent fluid fixtures, Leary (2002) showed that the temporal spectra of seismic coda waves recorded deep in crustal rock (Leary & Abercrombie 1994a,b) are explained by seismic scattering in 1/k-scaling spatial fluctuations of elastic parameters recorded in a deep crustal well in crustal granites (Leary 1991). The concept of infinite correlation length for crustal rock percolation systems yields the power-law-scaling correlation function x(r)3r x2 and its frequency-domain dual the Fourier power spectrum S(k)31/k appropriate for crustal rock.…”

Time-lapse traveltime change of singly scattered acoustic waves

“…Leary (2002) used first‐order elastic wave scattering theory to numerically simulate time‐lapse borehole seismic data aimed at monitoring oil–water substitution in heterogeneous hydrocarbon reservoirs. In his work, P ‐wave backscatter ‘snapshots’ of a heterogeneous rock can be acquired with a borehole seismic source and sensor located at the centre of the volume.…”

Time-lapse seismic reservoir monitoring with a local waveform inversion technique

“…Leary, 2002;Sarkar et al, 2003). The characterization of the depletion process in a producing hydrocarbon reservoir is of importance for both fluid injection strategies (e.g.…”