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April #4 /
New Challenges in Geomodeling. Prompt Search for Next Generation Solution in 3D Analysis

**№ 4** (April
2008)

**So far, in the oil and gas industry, 3D grids have been used by two populations of geoscientists: the reservoir geologist and the reservoir engineers**

By Jean-Claude Dulac

Today when asking a reservoir geologist or reservoir engineer their most pressing difficulty in term of geomodeling, the most frequent answer is to fill the gap that exists between the geological structural model, typically modeled as a set of horizons and faults and the reservoir model, modeled as a 3D corner point grid.

In the industry, all grid modeling methods consist in modeling a 3D grid as a collection of cubic cells deformed to fit horizons and aligned in pillars along faults. We can imagine very easily the difficulty encountered when trying to fit these cubes inside certain geological configurations such as Y-faults. As models increase in structural and stratigraphic complexity the process of creating these grids has become cumbersome. The outcome is that in many cases the grids modeled do not honor requirements from either the reservoir geologist or the reservoir engineer. Based on these considerations, this article will show how gridding the subsurface should be addressed anew.*Current Methods*

In the upstream oil and gas industry field of 3D modeling and construction of 3D grids for reservoir simulation and reservoir characterization, the state-of-the-art among competing applications is roughly equal.

These 3D grids follow the sub-surface geometry (folding and faulting) to honor the current geological layers geometry. The current state of the art method for constructing these 3D grids is a three steps approach:

Construction of the top of the reservoir;

Construction of the base of the reservoir;

Connect the top and base of the reservoir with pillars spread evenly on a 2D grid. One additional requirement is that these pillars must be aligned on faults. Faults are themselves composed of pillars and intersecting faults should have one identical pillar.

The construction of a 3D grid model is therefore decomposed into a series of 2D and 1D operations through the creation of the two 2D surfaces, and the construction of 1D pillars in the 3D space. This approach works well in simple, vertically faulted, layer cake geometries, or when the stratigraphy is not too complex (Fig. 1).

Unfortunately, geology is not that simple and many different structural deformation regimes will create more complex fault geometries as shown below (Fig. 2). Equally difficult will be the definitions of internal stratigraphy in between the top and bottom surface, when the internal stratigraphic surfaces geometry will differ strongly from the geometry of the top and bottom surfaces, or where thin layers need to be modeled.

The main default and limitation of this technique is the construction of the fault pillars. This process is a manual or semi-automatic process, tedious, cumbersome and possesses serious limitations in the complexity of models that it can handle. The one-by-one construction of pillars does not automatically ensure the consistency of the 3D model. In fact, by using this technique, there are many geological settings where faults need to be removed from the geological model or deformed substantially to allow the construction of a reservoir model.

In environments containing Y-faults or oblique faults, the grid constructed using pillars aligned to faults introduces deformations of the cells geometry that are unacceptable as discussed below.*Artifact of the “Pillars” Method*

To perform reservoir simulation or reservoir characterization, the 3D grids must be populated with properties such as net-to-gross, porosity, permeability, etc. These properties are typically known at the well location and to populate these grids it is essential to perform extrapolation of log values away from the wells in a “geologic way”. More explicitly when extrapolating, we need to work in a space where folding and faulting is removed, and which “mimic” as close as possible the condition under which the sediment where deposited. We call that space the “Paleo space” as each plane of that space represents a paleo-surface.

One method of extrapolation is based on geostatistics. Geostatistics main requirement is that distance between two grid nodes is the same in the current space or in the Paleo space anywhere in the volume. In the two cases shown below (Fig. 3), where we constructed a 2D grid with pillars parallel to some faults (and truncated by other in the case of the Y- fault example) it is clear that original distance between two samples is not preserved from the top to the bottom of the reservoir or that the restored space distances do not match the original depositional distance.

These artifacts lead to volume deformation, wrong spatial correlation of well samples, wrong geobodies computation, and wrong volumetrics.*Introducing the Paleo-geochronological Transformation*

The pillar approach based on being able to construct column of cells from a top horizon to a base horizon while honoring faults introduces large deformation of the transformation of the XYZ space to the Paleo-space which leads to erroneous volumes.

To correct these problems we are introducing a new full 3D transformation from the XYZ space to the Paleo-space called the “UVT-Transform”. The construction of this transformation is simple. We assign to a given horizon (seismic interpretation scattered points and/or well markers) a unique geochronological time (T). In the XYZ space the surface defined by that T will be faulted and folded, but in the UVT space, the surface will be a plane (by definition). The UV represents the two other dimension of the Paleo-space and defines the paleo-geography of each T plane. Given a collection of (X, Y, Z) points where (U, V, T) is known this transformation is interpolated using D.S.I. in the volume where faults are discontinuities.

The key to the “UVT Transform” or paleo-geochronological transform is that this transformation is defined everywhere in the 3D space. Horizons surfaces are result of this transformation and not an input. This is the fundamental step change.*Introducing the Geologic Grid*

Using the paleo-geochronological transform we can construct a grid inside the XYZ space. This grid will not have cells column parallel to faults, i.e. cells will be split by faults and offsetted by the fault throw. An image of such a geologic grid is shown below (Fig. 4). The constant cell dimensions and their regular shape across the entire domain is ensured through the use of specific D.S.I constraints when interpolating the paleo-geochronological transform.*A Step Change in Modeling*

The new unified modeling approach is a step change in modeling. There are no horizon surfaces to create, no pillars to create between a top and a bottom horizon, no pillars to align when faults are in contacts, four time-consuming steps. The user constructs a faulted volume and all horizons and 3D grids are constructed simultaneously as the paleo-geochronological transform is computed.

Working with a paleo-geographically ‘correct’ mesh, geobodies, reservoir properties and other attributes can be correctly modeled in their depositional state.

The volumic approach is a step change compared to previous modelers. All the models constructed with the new unified modeling approach can be constructed in hours versus weeks or months. Below is a table comparing pillar-based modeling time and SKUA modeling time (Table 5). The models built in the new unified modeling approach contain all interpreted faults while traditional models have fewer and deformed faults to follow the pillar model constraints.*Better Reservoir Models*

The construction of geological models that honor structural and stratigraphic complexities lead to the construction of better reservoir models, which enable better history matching, and enable better production forecasts.

Requirements for flow simulators and geological modeling grids are different and the new unified modeling approach differentiates between a geological grid and a flow simulation grid which is not the case for most modeling applications. Flow simulation grids created in the new unified modeling approach are corner point grids which can have faults represented as pillars or as stair steps across mostly vertical pillars (Fig. 6). The choice is left to the reservoir engineer which technique will be used. Correct upscaling from the geologic grid to the reservoir grid is insured because of the information contained in the unified volumic model.*Conclusion*

Today modeling technology suffers from the assumption that geological grids and reservoir flow simulation grids should be modeled similarly. In fact, none are modeled optimally. Using the paleo-geochronological transform the new unified modeling approach revolutionizes the world of geological modeling producing in record time paleo-geographically “correct” mesh and a future paper will show how the new unified modeling approach also revolutionizes the world of reservoir flow simulation grids.

Removing the modeling barrier makes it possible to provide better reservoir models that will allow better history matching, which will produce better production forecast. In parallel, it will enable studying of more geological scenarios, thus reducing overall exploration and production risk.

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