4D Gravity Inversion Hyoungrea Bernard Rim Korea Institute of Geoscience and Mineral Resources (KIGAM) Gravity Workshop in KRISS December 1, 2016

Outline Background Formulation 4D gravity inversion Numerical examples Application to fluid fronts Two different model objective functions Numerical examples compare single-time versus 4D inversion compare single-component versus vector gravity Summary

Time-Lapse Gravity Monitoring Mimic Prudhoe Bay, GCWI Δρ = 0.12 g/cm3 Year 2 Year 5 Year 10 Year 15 Year 20 Brady et al, 2002 (Krahenbuhl et al. 2013)

Research question: How should the multiple sets of time-lapse data be interpreted coherently?

Separate single-time inversions Layer-density distribution (e.g., Hare et al, 2008) Binary inversion (e.g., Krahenbuhl & Li, 2012) FCM inversion (Maag, 2014) 4D inversion for density change with time 4D inversion for reservoir properties Capriotti (2013) 4D inversion for fluid front

Vector gravity: synthetic examples Expanding plumes Simulate vector gravity due to expanding plumes

Expanding plumes Injection vertical borehole 500 m expanding plumes discrete representation with cubes

Expanding plumes vertical borehole Injection 500 m expanding plumes

Statement of problem Data: borehole gravity at multiple times Model: fluid fronts at corresponding times Known top and bottom of the reservoir Known density contrast due to fluid substitution

Model representation Distance from a reference point Function of azimuth angle

Inversion Regularized approach Data misfit Two different model objective functions

Model objective function-1 Generic regularization over azimuth and time

Model objective function-2 Regularization over arc length and time

synthetic example

Single-hole Single-time inversions

Single-hole 4D inversion

Data comparison Time-1 Time-2 Time-3 Time-4 observed single-time inv 4D inv

Vertical- components gravity 3-component gravity

Data comparison (3-component data) Time-1 Time-2 Time-3 Time-4 gx gy gz

Comparison of model objective functions Time-3 Time-4 Model obj. function-1 Model obj. function-2: Better accommodates rapid changes

Data comparison - 3 wells - vertical component Time-1 Time-2 Time-3 observed

Time-lapse vector gravity Prudhoe Bay

Time-lapse gravity inversion vertical gravity only vector gravity 3 monitoring wells 4 monitoring wells

Summary 4D gravity inversion for fluid front Better performance than single-time inversions Arc length-based model objective function better suited for detecting rapid change in the fluid front Vector gravity

Work ahead Efficient modeling for reservoir with variable thickness and depth Consistent data misfit as a function of time Choice of time-dependent weighting coefficients Refine algorithm with field data

Thank You!