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Integration of Time-Lapse Seismic and Production Data: Analysis of Spatial Resolution

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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).

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Abbreviations

\(\tau\) :

Time of flight along streamlines

\(\psi\) :

Streamline trajectory

s :

Slowness

\(\vec{\nu }\) :

Interstitial velocity

\(\lambda\) :

Mobility

\(k\) :

Permeability

\(\phi\) :

Porosity

\(S_{\text{w}}\) :

Water saturation

\(F_{\text{w}}\) :

Fractional flow of water

\(P\) :

Hydrostatic pressure

\(P_{\text{eff}}\) :

Effective pressure

\(P_{\text{ext}}\) :

Lithostatic pressure

\(\Delta P\) :

Pressure drop along streamlines

\(\delta m\) :

Model parameter change

\(k_{\text{HM}}\) :

Bulk modulus of the Hertz–Mindlin formula

\(K_{\text{ma}}\) :

Bulk modulus of the matrix

\(K_{\text{fr}}\) :

Bulk modulus of the porous rock frame

\(K_{\text{f}}\) :

Bulk modulus of the pore-filling fluids

\(K_{\text{sat}}\) :

Bulk modulus of the fluid saturated rock

\(\rho_{\text{sat}}\) :

Density of the fluid saturated rock

\(G_{\text{fr}}\) :

Shear modulus of the porous rock frame

\(V_{\text{p}}\) :

Compressional (p-wave) velocity

\(Z_{\text{p}}\) :

Acoustic (p-wave) impedance

\(R\) :

Resolution model

\({\text{COV}}_{\text{m}}\) :

Model covariance

\({\text{COV}}_{\text{d}}\) :

Data covariance

References

  • Aki, K., Richards, P.G.: Quantitative Seismology. Freeman San Francisco, San Francisco (1980)

    Google Scholar 

  • Aster, R.C., Borchers, B., Thurber, C.H.: Parameter Estimation and Inverse Problems, 2nd edn. Academic Press, St. Louis (2011)

    Google Scholar 

  • Backus, G.E., Gilbert, T.I.: Numerical applications of a formalism for geophysical inverse problems. Geophys. J. R. Astron. Soc. 13, 247–276 (1967)

    Article  Google Scholar 

  • Backus, G.E., Gilbert, T.I.: The resolving power of gross earth data. Geophys. J. R. Astron. Soc. 16, 169–205 (1968)

    Article  Google Scholar 

  • Backus, G., Gilbert, F., Crisp, B. E.: Uniqueness in the inversion of inaccurate gross Earth data philosophical transactions of the Royal Society of London. Series A, Math. Phys. Sci. 266, 123–192 (1970). https://doi.org/10.1098/rsta.1970.0005

    Article  Google Scholar 

  • Cheng, H., Wen, X.-H., Milliken, W.J., Datta-Gupta, A.: Field experiences with assisted and automatic history matching using streamline models. Soc. Pet. Eng. (2004). https://doi.org/10.2118/89857-MS

    Article  Google Scholar 

  • Dadashpour, M., Landrø, M., Kleppe, J.: Nonlinear inversion for estimating reservoir parameters from time-lapse seismic data. J. Geophys. Eng. 5, 54–66 (2008)

    Article  Google Scholar 

  • Dadashpour, M., Echeverría-Ciaurri, D., Kleppe, J., Landrø, M.: Porosity and permeability estimation by integration of production and time-lapse near and far offset seismic data. J. Geophys. Eng. 6, 325–344 (2009)

    Article  Google Scholar 

  • Dadashpour, M., Ciaurri, D.E., Mukerji, T., Kleppe, J., Landrø, M.: A derivative-free approach for the estimation of porosity and permeability using time-lapse seismic and production data. J. Geophys. Eng. 7, 351–368 (2010)

    Article  Google Scholar 

  • Datta-Gupta, A., King, M.J.: Streamline Simulation: Theory and Practice, vol. 11. Society of Petroleum Engineers, London (2007)

    Google Scholar 

  • Datta-Gupta, A., Yoon, S.: Inverse modeling of partitioning interwell tracer tests: a streamline approach. Water Resour. Res. 38, 6 (2002)

    Article  Google Scholar 

  • Datta-Gupta, A., Vasco, D.W., Long, J.C.S.: On the sensitivity and spatial resolution of transient pressure and tracer data for heterogeneity characterization. SPE Form. Eval. 12(02), 137–144 (1997)

    Article  Google Scholar 

  • Dong, Y., Oliver, D.: Quantitative use of 4D seismic data for reservoir description. SPE J 10, 91–99 (2005)

    Article  Google Scholar 

  • Fahimuddin, A., Aanonsen, S., Skjervheim, J.-A.: 4D seismic history matching of a real field case with EnKF: use of local analysis for model updating. Paper SPE 134894 Presented at the SPE Annual Technical Conference and Exhibition. Florence, Italy (2010)

  • Falcone, G., Gosselin, O., Maire, F., Marrauld, J., Zhakupov, M.: Petroelastic modelling as key element of 4D history matching: a field example. Paper SPE 90466 Presented at the SPE Annual Technical Conference and Exhibition. Houston, Texas, USA (2004)

  • Feng, T., Mannseth, T.: Impact of time-lapse seismic data for permeability estimation. Comput. Geosci. 14(4), 705–719 (2010)

    Article  Google Scholar 

  • Gassmann, F.: Elastic waves through a packing of spheres. Geophysics 16(4), 673–685 (1951)

    Article  Google Scholar 

  • Golub, G.H., Reinsch, C.: Singular value decomposition and least-squares solution. Numer. Math. 14, 403–420 (1970)

    Article  Google Scholar 

  • Gosselin, O., van den Berg, S., Cominelli, A.: Integrated history-matching of production and 4D seismic data. Paper SPE 71599 presented at the SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, USA: 30 Sept–3 Oct (2001)

  • Hansen, P.C.: Rank-Deficient and Discrete Ill-Posed Problems, Numerical Aspects of Linear Inversion. Society of Industrial and Applied Mathematics, Philadelphia (1998)

    Book  Google Scholar 

  • He, Z., Yoon, S., Datta-Gupta, A.: Streamline-based production data integration with gravity and changing field conditions. SPE J. 7(4), 423–436 (2002)

    Article  Google Scholar 

  • Hetz, G., Kim, H., Datta-Gupta, A., King, M.J., Przybysz-Jarnut, J.K., Lopez, J.L., Vasco, D.: History matching of frequent seismic surveys using seismic onset times at the peace river Field, Canada. Soc. Petroleum Eng. (2017). https://doi.org/10.2118/187310-MS

    Article  Google Scholar 

  • Huang, X., Meister, L., Workman, R.: Reservoir characterization by integration of time-lapse seismic and production data. Paper SPE 38695 presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA (1997)

  • Kennett, B.: Seismic Wave Propagation in Stratified Media. Cambridge University Press, Cambridge (1983)

    Google Scholar 

  • Lanczos, C.: Linear Differential Operators. D. van Nostrand Co, Princeton (1961)

    Google Scholar 

  • Landro, M., Digranes, P., Strønen, L.: Mapping reservoir pressure and saturation changes using seismic methods: possibilities and limitations. First Break 19, 671–677 (2001)

    Article  Google Scholar 

  • Mavko, G., Mukerji, T., Dvorkin, J.: The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  • Memke, W.: Geophysical Data Analysis—Discrete Inversion Theory. Academic Press Inc., New York (1984)

    Google Scholar 

  • Menke, W.: Geophysical Data Analysis: Discrete Inverse Theory. 1st Edition, Academic Press, San Diego, p. 289 (1989)

  • Menke, W.: Geophysical Data Analysis: Discrete Inverse Theory, 3rd edn. MATLAB Edition, Saint Louis (2012)

    Google Scholar 

  • Menke, W.: Resolution and Covariance in Generalized Least Squares Inversion. Lamont-Doherty Earth Observatory of Columbia University, Palisades (2014)

    Google Scholar 

  • Mindlin, R.D.: Compliance of elastic bodies in contact. J. Appl. Mech. 16, 259–268 (1949)

    Google Scholar 

  • Paige, C.C., Saunders, M.A.: LSQR: An algorithm for sparse linear equations and sparse least squares. ACM Trans. Math. Softw. (TOMS) 8(1), 43–71 (1982)

    Article  Google Scholar 

  • Parker, R.L.: Geophysical Inverse Theory. Princeton University Press, Princeton (1994)

    Book  Google Scholar 

  • Reuss, A.: Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle. ZAMM J. Appl. Math. Mech. 9(1), 49–58 (1929)

    Article  Google Scholar 

  • Rey, A., Bhark, E., Gao, K., Datta-Gupta, A., Gibson, R.: Streamline-based integration of time-lapse seismic and production data into petroleum reservoir models. Geophysics 77(6), M73–M87 (2012)

    Article  Google Scholar 

  • Rwechungura, R., Bhark, E., Miljeteig, O., Suman, A., Kourounis, D., Foss, B., Hoier, L., Kleppe, J.: Results of the first Norne field case on history matching and recovery optimization using production and 4D seismic data. Paper SPE 157112 Presented at the SPE Annual Technical Conference and Exhibition. San Antonio, Texas (2012)

  • Skjervheim, J.-A., Evensen, G., Aanonsen, S., Ruud, B.O., Johansen, T.-A.: Incorporating 4D seismic data in reservoir simulation models using ensemble Kalman filter. SPE J. 12(3), 282–292 (2007)

    Article  Google Scholar 

  • Tanaka, S., Kam, D., Datta-Gupta, A., King, M.J.: Streamline-based history matching of arrival times and bottomhole pressure data for multicomponent compositional systems. Soc. Pet. Eng. (2015). https://doi.org/10.2118/174750-MS

    Article  Google Scholar 

  • Tarantola, A.: Inverse Problem Theory. Elsevier Science B.V, Amsterdam (1987)

    Google Scholar 

  • Tura, A., Lumley, D.: Estimating pressure and saturation changes from time-lapse AVO data. Paper OTC 12130 Presented at Offshore Technology Conference, Houston, Texas, USA (2000)

  • Vasco, D.W., Datta-Gupta, A., Long, J.C.S.: Resolution and uncertainty in hydrologic characterization. Water Resour. Res. 33(3), 379–397 (1997)

    Article  Google Scholar 

  • Vasco, D.W., Datta-Gupta, A., Behrens, R., Condon, P., Rickett, J.: Seismic imaging of reservoir flow properties: time-lapse amplitude changes. Geophysics 69, 1425–1442 (2004)

    Article  Google Scholar 

  • Vasco, D.W., Daley, T.M., Bakulin, A.: Utilizing the onset of timelapse changes: a robust basis for reservoir monitoring and characterization. Geophys. J. Int. 197, 542–556 (2014)

    Article  Google Scholar 

  • Veeken, P.C., Priezzhev, I.I., Shmaryan, L.E., Shteyn, Y.I., Barkov, A.Y., Ampilov, Y.P.: Nonlinear multitrace genetic inversion applied on seismic data across the Shtokman field, offshore northern Russia. Geophysics 74(6), WCD49–WCD59 (2009)

    Article  Google Scholar 

  • Watanabe, S., Han, J., Hetz, G., Datta-Gupta, A., King, M.J., Vasco, D.W.: Streamline-based time-lapse-seismic-data integration incorporating pressure and saturation effects. SPEJ Soc. Pet. Eng. (2017). https://doi.org/10.2118/166395-PA

    Article  Google Scholar 

  • Wen, X.-H., Durlofsky, L.J., Chen, Y.: Efficient 3D implementation of local-global upscaling for reservoir simulation. Soc. Petroleum Eng. (2006). https://doi.org/10.2118/92965-PA

    Article  Google Scholar 

  • Wiggins, R.A.: The general linear inverse problem: Implication of surfacewaves and free oscillations for earth structure. Rev. Geophy. 10(1), 251–285 (1972)

    Article  Google Scholar 

  • Williams, M., Keating, J., Barghouty, M.: The stratigraphic method: a structured approach to history matching complex simulation models. SPE Reserv. Eval. Eng. 1(2), 169–176 (1998)

    Article  Google Scholar 

  • Xia, J., Xu, Y., Miller, R.D., et al.: A trade-off solution between model resolution and covariance in surface-wave inversion. Pure Appl. Geophys. 167, 1537 (2010)

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge the sponsors of Model Calibration and Efficient Reservoir Imaging (MCERI) at Texas A&M University.

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  1. Petroleum Engineering Department, TAMU 3116, Texas A&M University, College Station, TX, 77843, USA

    Gill Hetz & Akhil Datta-Gupta

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Correspondence to Gill Hetz.

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Hetz, G., Datta-Gupta, A. Integration of Time-Lapse Seismic and Production Data: Analysis of Spatial Resolution. Transp Porous Med 134, 679–705 (2020). https://doi.org/10.1007/s11242-020-01463-4

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