3D Restoration and mechanical properties

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Who is working on this?
Joachim Müller, Chris Guzofski,
John Shaw

In colaboration with:
Chevron, Unocal,
Nancy School of Geology, gOcad

put online:
december 2005

Abstract

Sequential, three-dimensional restorations and strain analyses of geologic structures provide important information of their kinematic evolution, helping to validate structural interpretations and define the temporal evolution of prospective hydrocarbon traps. Most current methods of restoring three-dimensional structural models, however, are based on two-dimensional (horizon or cross section based) approaches that impose restoration kinematics and do not consider mechanical rock properties, limiting their applicability and effectiveness. In contrast, we apply a new volumetric restoration technique (Muron & Medwedeff, 2005) based on finite-element methods that uses mechanical properties to guide volume conservation and strain minimization constraints.

The method is implemented as a plug-in in GoCAD (© Earth Decision Sciences). We use this tool to restore structures from the Niger Delta and Caspian Sea, including detachment and shear fault-bend folds that are defined by 3D seismic reflection data. Our results demonstrate that 3-D restorations with fault compliance based on this technique provide reasonable results in terms of derived structural kinematics and strain fields. This offers the potential to use these techniques as a means of better validating structural interpretations, particularly in cases where major strength contrasts (i.e. salt, over-pressured shales) influence structural styles, and for predicting reservoir-scale deformation.

Method

The 3D restoration plug-in developed for GoCAD by Pierre Muron (e.g., Muron & Medwedeff 2005) is based on the principals of the FE method and is mainly governed by volume conservation and strain minimization. The flattening of a reference horizon to a specific depth (external force) is balanced by the internal resistance (internal force) of the SolidModel depending on the rheology or mechanical properties of the rocks.

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Getting started - with a SolidModel from the FrameModel plug-in

Starting with the interpreted stratigraphic horizons and faults from seismic data or other sources, (a) triangulated surfaces are created in GoCAD (© Earth Decision Sciences) forming a geologically consistent surface model . (b) A volumetric SolidModel consisting of some hundred thousand tetrahedrons is built from these surfaces and their defined interactions with the FrameModel plug-in (Lepage 2003). (c) This SolidModel consist of different regions, separated by the stratigraphic horizons and faults of the surface model.

Fig. 1: Work-flow to build a volumetric SolidModel with the FrameModel
          plug-in from Lepage (2003).

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Mechanical properties, boundary conditions and constitutive laws

The rheologic behavior - like strength and compressibility - of different regions of the model is described by:

      1st Lame constant l [ GPa]
      (= bulk modulus k - (2/3)m)
      2nd Lame constant m [GPa]
      (= shear modulus)

These parameters can be set to the whole model or to the different layers (3D regions).

Fig. 2: Example of mechanical properties attributed to the different layers
         (3D regions).

Pin points, pin lines, pin walls and pin regions may be set as boundary condition to fix the model during restoration (Fig. 3). A reference horizon has to be defined - what is usually the top horizon - and a level of horizontal flattening of the reference horizon has to be set - what is usually the lowermost level of the top horizon.

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In terms of faults it is important to define hanging-wall and foot-wall as well as the intersection of the faults with the reference horizon.

Once the rheology, reference horizon and reference level are defined, and the pins are set, the restoration can be calculated according to the principles of FE method. Thereby, the restoration path of each node is calculated, equilibrating the flattening of the reference horizon (Fig. 4).

Fig. 3: Pin points, pin lines (not shown here), pin walls, and pin regions (not
          shown here) may be set as boundary conditions.

For the calculation of the restoration vectors, the Hookean or the Neo-Hokean constitutive laws may be applied, assuming either linear or non-linear elastic behavior. The calculated restoration field defines fold and fault kinematics (Fig. 4), and provides analysis of the strain during deformation, which can be used to evaluate reservoir scale deformation.

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Fig. 4: Restoration vectors at each node are calculated according to the flattening of the colored reference horizon. Pins are fixing the model during restoration in the undeformed foreland. Please, notice long restoration vectors in the core of the anticline and small restoration vectors at the edges.

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