Physical model for the downhole orbital vibrator (DOV) - II. Rotary correlation wavelets and time-lapse seismics

Abstract

SUMMARY The downhole orbital vibrator (DOV) acts as a rotating acoustic point force coupled to the borehole fluid. Operated as a Vibroseis source modulated over rotational frequencies 50- 350 Hz, the DOV can generate crosswell seismic signals at well separations up to 800 m in oilfield sediments. Source-wavelet stability and crosswell seismic traveltime resolution are estimated from an ensemble of 13 000 wavelets recorded at a crosswell seismic facility with 300 m source-sensor separation. DOV auto-correlation source wavelets Si cross-correlated against the ensemble mean wavelet Smn give correlation coefficients γ i = SiS mn having mean γ mn ≈ 99.97 per cent and standard deviation γ rms ≈ 0.03 per cent. S wavelets give observed traveltimes τ i with normalized standard deviation �τ rms/τ mn ≈ 0.03 per cent. This level of seismic monitoring source stability and crosswell traveltime resolution offers considerable promise for accurate, cost-effective time-lapse seismic imaging of active geofluid reservoirs. Application of stable DOV waveform production to time-lapse seismic imaging is, how- ever, affected by the dual-wavelet nature of rotary motion cross-correlations. In general, DOV cross-correlation signals mix time-symmetric (even) wavelets χ cc(t) ∼ cos(ω(t)t) � cos(ω(t)t) ∼ χ cc(−t) and time-antisymmetric (odd) wavelets χ cs(t) ∼ cos(ω(t)t) � sin(ω(t)t) ∼ − χ cs(−t), wheredenotes correlation, ω(t) describes the modulation of rotational frequency, and time-reversal t ↔− t equates to interchanging clockwise/counter-clockwise (cw/ccw )D OV rotations. Cross-correlating sensor motion along source-sensor axis x with source motion along axis g mixes wavelet symmetries as χ g(t) ∼ cosφχ cc(t) + sinφχ cs(t) where cos φ = g · x and angle φ orients the DOV relative to the source-sensor axis. DOV orientation uncertainty �φ affects the sensor wavelet apparent traveltime as �τ ≈ 1.3(�φ/2π )T min, T min the period of peak modulation frequency. Since source orientation un- certainty can generate apparent traveltime uncertainty as large as 1-2 ms, time-lapse seismics cannot effectively ignore DOV orientation. Traveltime resolution can be improved to order 0.1 ms without knowing DOV orientation if traveltimes are computed using even/odd wavelets composed by summing/differencing cw/ccw wavelets. Prospects for time-lapse resolution im- prove if observers can orient the DOV. A DOV equipped with a collar of rotation-phase point detectors surrounding the rotating mass permits observer selection of the monitor sensor, hence controlling effective source orientation. DOV orientation can be guided by an on-board biaxial tiltmeter (for borehole tilt δ along an axis making angle φ with DOV sensor orientation, biaxial tilts T 1 and T 2 fix φ as T 1 =− cos φtan δ and T 2 = sin φtan δ). Numerical simulation of full-sensitivity time-lapse reservoir monitoring suggests it is feasible to resolve migrating oil/water substitution volumes of characteristic dimension 20 m with crosswell transmission data over ≈600-800 m offsets, or in backscatter data at offsets ≈100-200 m using a DOV and sensor array operating in a single well.