Integration of Time-Lapse Seismic and Production Data: Analysis of Spatial Resolution
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Integration of Time‑Lapse Seismic and Production Data: Analysis of Spatial Resolution Gill Hetz1 · Akhil Datta‑Gupta1 Received: 5 February 2019 / Accepted: 4 August 2020 © Springer Nature B.V. 2020
Abstract An analysis of spatial resolution is incorporated into an efficient model calibration approach with multi-scale data integration to examine the reliability of the estimated solution. The resolution is a measure of the degree of averaging of the local-scale (grid block) permeabilities during parameter estimation via inverse modeling. For a given set of data, it indicates the regions where our estimate is well constrained. By examining the spatial resolution in time-lapse seismic data integration, we can quantitatively evaluate the relative contribution of pressure and saturation changes on the calibrated permeability field. We illustrate this concept using synthetic and field applications. The synthetic example is a 5 spot pattern, where the time-lapse seismic data are incorporated as inferred pressure and saturation changes. The field example involves waterflooding of a North Sea reservoir with multiple seismic surveys. The results demonstrate that the analysis of spatial resolution provides quantitative information on our ability to estimate the subsurface heterogeneity. It is found that integration of seismic data based on inferred pressure changes better determine the barriers to the flow (e.g., low permeability areas), while calibrating the model based on saturation changes provides complementary information to identify the channels (e.g., high permeability regions). Keywords Reservoir characterization · 4D seismic · Resolution and uncertainty List of Symbols 𝜏 Time of flight along streamlines 𝜓 Streamline trajectory s Slowness 𝜈⃗ Interstitial velocity 𝜆 Mobility k Permeability 𝜙 Porosity Sw Water saturation Fw Fractional flow of water * Gill Hetz [email protected] 1
Petroleum Engineering Department, TAMU 3116, Texas A&M University, College Station, TX 77843, USA
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P Hydrostatic pressure Peff Effective pressure Pext Lithostatic pressure ΔP Pressure drop along streamlines 𝛿m Model parameter change kHM Bulk modulus of the Hertz–Mindlin formula Kma Bulk modulus of the matrix Kfr Bulk modulus of the porous rock frame Kf Bulk modulus of the pore-filling fluids Ksat Bulk modulus of the fluid saturated rock 𝜌sat Density of the fluid saturated rock Gfr Shear modulus of the porous rock frame Vp Compressional (p-wave) velocity Zp Acoustic (p-wave) impedance R Resolution model COVm Model covariance COVd Data covariance
1 Introduction It is well recognized that integration of 4-D seismic acquisitions, along with production data, improves reservoir characterization and reduces the uncertainty associated with the estimated model. Such information has great potential in inferring reservoir properties, such as permeability and porosity through the reservoir model calibration process. Different algorithms of dynamic data integration have bee
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