Empirical Mode Decomposition of Geophysical Well log Data of Bombay Offshore Basin, Mumbai, India Gaurav S. Gairola and E. Chandrasekhar Department of Earth Sciences Indian Institute of Technology Bombay Powai, Mumbai – , INDIA. ABSTRACT No. 1835

Conventional signal analysis tools quite inadequate Conventional signal analysis tools quite inadequate Geophysical well log data: Geophysical well log data:  Chaotic, non-stationary and non-linear  reflect complex natural processes  always important and essential to understand these complex natural processes using effective signal analysis tools Besides wavelet analysis and multifractal analysis, Empirical Mode Decomposition Technique (EMDT) has also been found to be an efficient technique to unravel hidden information in well log data. Besides wavelet analysis and multifractal analysis, Empirical Mode Decomposition Technique (EMDT) has also been found to be an efficient technique to unravel hidden information in well log data. Rationale for Present Study

To decompose the well-log data into different frequency constituents (known as Intrinsic Mode Functions (IMFs)) using Empirical Mode Decomposition Technique (EMDT). To decompose the well-log data into different frequency constituents (known as Intrinsic Mode Functions (IMFs)) using Empirical Mode Decomposition Technique (EMDT). To use the estimated IMFs to perform Hilbert Spectral Analysis (HSA) and heterogeneity analysis. To use the estimated IMFs to perform Hilbert Spectral Analysis (HSA) and heterogeneity analysis. To interpret the heterogeneity indices by comparing them with the multifractal analysis results for reservoir characterization and gas-zone identification. To interpret the heterogeneity indices by comparing them with the multifractal analysis results for reservoir characterization and gas-zone identification. Objectives

Study Area Geographical location of study area (Chandrasekhar and Rao, 2012) Litho-stratigraphy of study area (after Bhandari and Jain,1984)

Well log data sets have been procured from three wells A, B and C from Oil and Natural Gas Corporation (ONGC) India. For the present study only Well B and Well C data used. Data Base Well AWell BWell C Logs Gamma ray, Sonic and Neutron Porosity Depth Range m Sampling Interval 0.15 m or 6 inches 0.1 m or 4 inches0.15 m or 6 inches Well topsL-I, L-II, S-I and L-III Data Details Inter-well distance: ~ 10 km

Depth Location of L-III identified by Wavelet Analysis (Chandrasekhar and Rao, 2012) and Multifractal Analysis (Subhakar and Chandrasekhar, 2016) WELL B WELL C L-III Data Base

Empirical Mode Decomposition Technique Introduction and Algorithm Fully data adaptive techniqueFully data adaptive technique Suitable to handle nonlinear and nonstationary signalsSuitable to handle nonlinear and nonstationary signals Decomposes data into its oscillatory signals of different wavelengths known as Intrinsic Mode Functions (IMFs)Decomposes data into its oscillatory signals of different wavelengths known as Intrinsic Mode Functions (IMFs) IMFs directly used in Hilbert Spectral Analysis (HSA) to determine instantaneous amplitudes (IA) and instantaneous frequencies (IF) of the signalIMFs directly used in Hilbert Spectral Analysis (HSA) to determine instantaneous amplitudes (IA) and instantaneous frequencies (IF) of the signal IA and IF –useful to do heterogeneity analysis of wells, albeit qualitativelyIA and IF –useful to do heterogeneity analysis of wells, albeit qualitatively

Make upper envelope (E max ) using cubic spline on maxima (X max ) Make lower envelope (E min ) using cubic spline on minima(X min ) Compute mean envelope E mean =(E max +E min )/2 Subtract E mean from X (proto_IMF=X-E mean ) NO YES IMF i = Proto_IMF Signal (X) EMDT Algorithm NO YES STOP X= X-IMF i SD k ≤ 0.1 Is X Monotonic i = i+1

Application of EMDT and HSA to Well-log Data The L-III is the thickest limestone pay zone (470 m) in the Bombay offshore basin.The L-III is the thickest limestone pay zone (470 m) in the Bombay offshore basin.  Contains about 80% of the total reserves in the basin. EMDT and HSA have been applied to Gamma-ray and Neutron porosity log data sets corresponding to the thickest reservoir zone (of about 60 m) within L-III. Heterogeneity analysis of the derived IMFs of both wells was done to quantify the degree of heterogeneity assessed by HSA.

EMD of Gamma-ray log Intrinsic Mode Functions (IMFs) obtained after Empirical Mode Decomposition (EMD) of Gamma-ray logs of Wells B and C

Hilbert Spectral Analysis (HSA) HSA was applied to the derived IMFs to determine instantaneous amplitude and instantaneous frequency. They help in qualitative assessment of heterogeneity in the wells The Hilbert transform of a signal is given by The instantaneous amplitude, a(s) and the instantaneous frequency, ω(s) are estimated by computing the analytic signal, A(s), given by P : Cauchy Principle Value f (x) represents each IMF

Instantaneous amplitude Instantaneous phase Instantaneous frequency Analytical signal Hilbert Spectral Analysis (HSA)

Smaller instantaneous amplitudes (Blue) at low IMFs (indicative of high frequencies): suggest less heterogeneity in Well B (Gamma-ray log)

Hilbert Spectral Analysis (HSA) Larger instantaneous amplitudes (Red) at low IMFs (indicative of high frequencies): suggest more heterogeneity in Well C (Gamma-ray log)

Heterogeneity Analysis To quantify the qualitative assessment of heterogeneity observed in L-III zone, heterogeneity analysis was done using each IMF. By establishing a nonlinear relationship between the IMF number ( m ) and its mean wavelength ( I m ), a heterogeneity index, ( ρ ) associated with subsurface layers can be determined by (Gaci and Zaourar, 2014) where, k is constant. bears an inverse relation with the degree of the heterogeneity of the subsurface. where, k is constant. ρ bears an inverse relation with the degree of the heterogeneity of the subsurface.

Well C reservoir zone (within L-III) is more heterogeneous than that of Well B. Heterogeneity Analysis

Well C reservoir zone (within L-III) is more heterogeneous than that of Well B. Heterogeneity Analysis (Subhakar and Chandrasekhar, 2016) (Comparison with Multifractal Analysis)

Heterogeneity Analysis (Validation) Higher shale volume in well C than in well B confirms well C to be more heterogeneous than well B.

EMD of Gas zone: Comparison with Multifractal Analysis The density-porosity crossover marks a presence of gas in a reservoir. The sensitivity of EMD technique is tested towards the presence of gas in the reservoir in a 20 m thick column in L-III. Subhakar and Chandrasekhar (2016) Matrix density = 2.71 g/cc Fluid density= 1.0 g/cc Well C

EMD of Gas zone: Comparison with Multifractal Analysis Presence of gas in the subsurface as reflected in the original neutron log makes the reservoir zone less hetero- geneous (high ρ value). Absence of gas in the synthetic neutron log makes the reservoir zone more heterogeneous (low ρ value). Well C

EMD of Gas zone: Comparison with Multifractal Analysis Subhakar and Chandrasekhar (2016) Well C Subhakar and Chandrasekhar (2016)

The fully data adaptive and nonlinear EMDT proves its worthiness over the conventional signal analysis techniques in unravelling the hidden information in signals. The fully data adaptive and nonlinear EMDT proves its worthiness over the conventional signal analysis techniques in unravelling the hidden information in signals. The combined EMD and HSA techniques, together with the heterogeneity analysis has been important and essential to quantify the heterogeneity of the reservoir zones within the L-III zone of the Bombay High region. The combined EMD and HSA techniques, together with the heterogeneity analysis has been important and essential to quantify the heterogeneity of the reservoir zones within the L-III zone of the Bombay High region. L-III zone of Well C is more heterogeneous than that of Well B due to higher shale content in it. L-III zone of Well C is more heterogeneous than that of Well B due to higher shale content in it. Results of neutron log agree with those of multifractal analysis and confirm that the presence of gas in the subsurface reservoir zone makes it homogeneous than the non-gaseous zone. Results of neutron log agree with those of multifractal analysis and confirm that the presence of gas in the subsurface reservoir zone makes it homogeneous than the non-gaseous zone. Conclusions

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