Modelling reservoirs using a 3D grid is a common tool for both the geologist and the reservoir engineer. As models increase in structural and stratigraphic complexity the process of creating these grids has become cumbersome. In many cases the results are not satisfactory to either the geologist or the engineer.

### Present simple methodology

Using current techniques, there are two steps in the formation of a 3D grid; delineation of the top and base of the reservoir and the main stratigraphic horizons; followed by connecting these horizons with ‘pillars' of cells spread evenly on a 2D grid. Faults are defined using simple pillars and intersecting faults need to have one common pillar.

This approach works well in simple geometries where the faults are vertical or where the stratigraphy is not too complex. Unfortunately, geology is usually not that simple. Most rocks undergo several stages of structural deformation, creating complex fault geometries. In addition, internal stratigraphic changes and thin layers in the reservoir all need to be included in the model.

The main limitation to this method of building a 3D grid, however, is the construction of the fault pillars. This is a tedious and cumbersome process which is hard to automate. Constraints imposed by the requirement to use pillars will severely restrict the ability to model complex structures. Reverse faults, folds and crossing faults are all impossible to model using geocellular methods. In fact, when using this technique, there are occasions where faults need to be removed from the geological model or deformed substantially to allow construction of the reservoir model.

### Distortion in ‘pillars' method

To perform reservoir simulation or characterization, the 3D grids must be populated with properties such as net-to-gross, porosity and permeability. These values are usually known at the well location, so to populate the grids we estimate values away from the wells using a ‘paleospace' in which folding and faulting has been removed, and which simulate, as closely as possible, the conditions under which the sediments were deposited. Each plane of that space may be considered a paleosurface.

One method of estimation is based on geostatistics. Most geostatistical algorithms have a performance optimization which requires that the distance between two grid nodes is the same anywhere in the volume of the paleospace (to do it any other way would require too much computational time). Distortion can be introduced if the original distance between two samples is not preserved from the top to the bottom of the reservoir, or the restored space distances do not match the original depositional distance. These distortions can lead to poor spatial correlation of well samples and incorrect parameter estimation, which may then introduce errors in volumetrics.

### The structural transform

To solve these problems, we need to start looking at the grid in a different way. We can easily accept different ways of looking at a geographic space on the Earth - for instance, we happily understand that a street map, a ‘Google earth' image and a curvilinear Underground map are all ways of looking at London. In the same way, we need to fundamentally change the way we look at the area represented by a model.

This is done through the introduction of a new full 3D transformation from the XYZ space to the paleospace, which Paradigm calls the "UVT Transform". A given horizon is assigned a unique parameter T, which is broadly representative of geochronological time. In the normal XYZ space the surface defined by that T will be faulted and folded, but in the UVT space, the surface will be a plane at constant T. The U and V axes represent the two other dimensions of the paleospace and define the paleogeography of each T plane. Given a collection of (X,Y,Z) points where (U,V,T) are known, this transformation is interpolated for all other locations within the volume. Faults are discontinuities in XYZ space but not in UVT space. Intermediate horizons are then computed within the UVT space and are not a required input. In fact, all the horizons may be interpolated at the same time which greatly reduces errors due to collisions between horizons. This is a fundamental change in thinking.

From the transform and the intermediate horizons we can construct a grid in UVT space and its corresponding equivalent in XYZ space. The XYZ ‘geologic' grid will not have columns of cells parallel to faults, but instead cells will be split by faults and be offset both vertically and horizontally by the fault throw. The constant cell dimensions and their regular shape across the entire domain will be preserved during the structural interpolation.

### A revolution in modelling

This transform approach represents a revolution in modelling; in fact, it is the first new method of representing the subsurface since geocellular modelling was developed in the mid-eighties.

There are no horizon surfaces to create and no pillars to build between a top and bottom horizon. The user constructs a faulted volume with all horizons. The 3D grid is constructed at the same time as the paleogeochronological transform. Working with a paleogeographically correct mesh means that geobodies, reservoir properties and other attributes can be correctly modelled in their depositional state.

Models built using this technique contain all interpreted faults. Traditional models have to make approximations to fit the constraints of geocellular modelling so fewer faults can be modelled and many of those will be simplified or forced to be vertical.

Importantly, models can be constructed using this technique in hours, not weeks or months. This allows different structural scenarios to be considered. Currently the evaluation of uncertainty is restricted to uncertainty in the deposition and uncertainty in the water saturation model. It is far too time-consuming to build different structural models of the reservoir using geocellular techniques.

The ability to build more accurate geological models that honour structural and stratigraphic complexities will transform workflows between geophysicists, geologists and engineers. This will lead to better understanding of reservoir behaviour, an improved quantification of risk and a richer set of information for the reservoir management team, hopefully resulting in more accurate production forecasts. This allows better decisions to be made throughout the life of the field, especially in the period between discovery and the first production.

Understanding structural uncertainty is a very significant step in the reduction of exploration and development risk.