In history matching and sensitivity analysis, flexibility in the structural modelling is of great importance. The ability to easily generate multiple realizations of the model will have impact both on the updating workflow in history matching and uncertainty studies based on Monte Carlo simulations. The main contribution to fault modelling by the work presented in this paper is a new algorithm for calculating a 3D displacement field applicable to a wide range of faults due to a flexible representation. This gives the possibility to apply this field to change the displacement and thereby moving horizons and fault lines. The fault is modelled by a parametric format where the fault has a reference plane defined by a centre point, dip and strike angles. The fault itself is represented as a surface defined by a function z = f (x, y), where x, y and z are coordinates local to the reference plane, with the z-axis being normal to the plane. The displacement associated with the fault outside the fault surface is described by a 3D vector field. The displacement on the fault surface can be found by identifying the intersection lines between horizons and the fault surface (fault lines), and using kriging techniques to fill in values at all points on the surface. Away from the fault surface the displacement field is defined by a monotonic decreasing function which ensures zero displacement at a specified distance from the fault. An algorithm is developed where the displacement can be increased or decreased according to user-defined parameters. This means that the whole displacement field is changed and points on horizons around the fault can be moved accordingly by applying the modified displacement field on them. The interaction between several faults influencing the same points is taken care of by truncation rules and the ordering of the faults. The method is demonstrated on a realistic synthetic case based on a real reservoir.
Fault models are often based on interpretations of seismic data that are constrained by observations of faults and associated strata in wells. Because of uncertainties in depth migration, seismic interpretations and well data, there often is significant uncertainty in the geometry and position of the faults. Fault uncertainty impacts determinations of reservoir volume, flow properties and well planning. Stochastic simulation of the faults is important for quantifying the uncertainties and minimizing the impacts. In this paper, a framework for representing and modeling uncertainty in fault location and geometry is presented. This framework can be used for prediction and stochastic simulation of fault surfaces, visualization of fault location uncertainty, and assessments of the sensitivity of fault location on reservoir performance. The uncertainty in fault location is represented by a fault uncertainty envelope and a marginal probability distribution. To be able to use standard geostatistical methods, quantile mapping is employed to construct a transformation from the fault surface domain to a transformed domain. Well conditioning is undertaken in the transformed domain using kriging or conditional simulations. The final fault surface is obtained by transforming back to the fault surface domain. Fault location uncertainty can be visualized by transforming the surfaces associated with a given quantile back to the fault surface domain.
Fault geometry is modelled on basis of seismic data, but restricted by fault observations in wells. Due to uncertainties in depth migration, seismic interpretation and well data, there is a significant uncertainty in the geometry and position of the faults. Fault uncertainty impact reservoir volume, flow properties and well planning, and can be studied by stochastic simulation of faults. We have developed a method for stochastic simulation of fault surfaces and fault networks using standard geostatistical methods. This is made possible by the fault parameterization used, where the faults are modelled as tilted surfaces. This new method is more flexible and efficient compared to already existing algorithms due to a simpler parameterization. Conditioning to fault observations in wells is also made simpler. The fault is defined as a two-dimensional surface on a tilted reference plane. The uncertainty for a fault surface is bounded by a volume enclosing the fault surface. The smoothness of the simulated fault surfaces is controlled by variograms. The simulation is done by adding a simulated Gaussian residual. Well conditioning is done by kriging. Using the described method we can simulate a set of fault realizations where the simulated faults look realistic, are within the defined uncertainty volumes, and honour well observations. Technical contributions compared to previous work include efficient simulation of fault geometry, a flexible uncertainty model and well conditioning with no performance impact.
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