Fault displacement modelling using 3D vector fields

Abstract

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.

A parametric fault displacement model to introduce kinematic control into modeling faults from sparse data

“…Our three-dimensional fault operator extends the work of Laurent et al (2013) and Georgsen et al (2012). It deforms a first approximated continuous horizon geometry along faultparallel lines in the dip directionusing a 3D discontinuous displacement field.…”

“…They represent not only the fault geometry but also the displacement, which is integrated through the fault operator. Such operators have been proposed for modeling reservoirs with subseismic faults (Munthe et al, 1994;Hollund et al, 2002), for easily modifying reservoir models in stochastic modeling (Holden et al, 2003;Georgsen et al, 2012), and for taking geological history into account during model construction (Laurent et al, 2013). Georgsen et al (2012) and Laurent et al (2013) implement fault operators where fault geometry and slip are modeled according to the description of Barnett et al (1987).…”

“…Several authors have also integrated fault kinematics, i.e., the distribution of the slip on and close to the fault surface, directly into the modeling process. In these approaches, the slip distribution is expressed by a numerical fault operator (Munthe et al, 1994;Hollund et al, 2002;Holden et al, 2003;Georgsen et al, 2012;Laurent et al, 2013).…”

“…Such kinematic fault operators have demonstrated their applicability to the modeling of synthetic (Munthe et al, 1994;Georgsen et al, 2012;Laurent et al, 2013) and real (Hollund et al, 2002;Holden et al, 2003) faulted structures. Our three-dimensional fault operator extends the work of Laurent et al (2013) and Georgsen et al (2012).…”

“…In the direction orthogonal to the fault surface, flanking structures (due for instance to fault drag or fault-related folding) have been observed (Chapman and Meneilly, 1990;Grasemann et al, 2005;Coelho et al, 2005;Mulchrone, 2007;Spahić et al, 2013;Mukherjee, 2014). These orthogonal structures coupled with the observations close to the fault surface have been used to propose threedimensional parameterizations of the fault-related displacement (Georgsen et al, 2012;Laurent et al, 2013).…”