One of the goal of our research group is to develop new software and technologies. Consortium sponsors can use and industrialize software, royalty-free. In addition to internal use of software by sponsors, several commercial software products have been based on RING technologies.

### Gocad

The Gocad software was initiated by Prof. Jean-Laurent Mallet and his research group in 1989 (Mallet, 1992b). The main goal of this academic project was to develop a geomodeling software using triangulated surfaces, which have the capability to manage overturned and highly faulted geological surfaces. From its inception, Gocad made the choice to use graphics workstation and work in three dimensions and not only with depth maps. One of the key technologies introduced in Gocad was Discrete Smooth Interpolation, DSI in short (Mallet, 1989; Mallet, 1992a; Mallet, 1997). This original method uses least-squares minimization to smooth triangulated surfaces under constraints representing geological information. The systematic approach to represent subsurface data and geological objects consistently with points, lines, surfaces and volumetric grids has been a distinctive feature of Gocad as compared to other software aimed at solving just one class of problems. This led to interesting uses of Gocad in geophysics, reservoir modeling, archeology, ore geology and even medicine!

During the 90's, the Gocad software, orgininally developped in C, was translated into C++ with the help of several sponsor companies. A spin-off company (T-Surf) was created in 1998 to take care of the software evolution, maintenance and support. The source code of the Gocad software was then fully transferred to T-Surf (acquired by Paradigm in 2006). Since then, RING has mostly been using the Gocad software development kit to do its research.

### Skua

At the beginning of the 2000's, Jean-Laurent Mallet started developing the Geochron concept and the first software prototypes with the help of his graduate students. The main idea is described in his 2004 Mathematical Geosciences paper (Mallet, 2004) and on several conference papers at the same period (Mallet et al., 2004; Macé et al., 2004; Moyen et al., 2004; Caumon et al. 2005; Royer et al., 2006; Caumon & Mallet, 2006; Tertois & Mallet, 2006; Frank et al., 2007; Tertois & Mallet, 2007). It is to numerically compute a chronostratigraphic transform mapping any subsurface point into its image in a flattened depositional space. The first implementation of this model used implicit surfaces (also known as level sets) on a tetrahedral mesh (Moyen et al., 2004). Implicit surfaces are able to deal with a very large number of data and make modeling more automatic than classical surface-based modeling.

In 2008, what had started as a research project to make the application of geostatistics easier became a commercial product: Paradigm introduced SKUA, the first commercial implementation of the Geochron concept, which also provided new reservoir gridding algorithms (Jayr et al., 2008; Gringarten et al. 2008a,b).

More recently, the SKUA Structure Uncertainty product (Tertois et al., 2010) has also benefited from prior research by the Consortium on the stochastic perturbation of implicit structural models (Caumon & Mallet, 2006; Caumon et al., 2007; Tertois & Mallet, 2007).

Since Prof. Mallet retired from the university in 2006, he has been deeply involved in further developing the theoretical framework of Geochron, as attested by his two recent books (Mallet, 2008; Mallet, 2014).

### Petrel Volume Based Modeling

In 2013, Schlumberger introduced a new structural modeling approach called volumetric based modeling (Souche et al., 2013). This method also builds on the concepts of implicit surfaces in tetrahedral meshes introduced by the Consortium during the 2000's.

### PetroKarst

In 2019, following several work peformed at RING:

- Méthodes de discrétisation et de changement d' échelle pour les réservoirs fracturés 3D
- APPROCHE PSEUDO-GENETIQUE POUR LA SIMULATION STOCHASTIQUE DE LA GEOMETRIE 3D DE RESEAUX FRACTURES ET KARSTIQUES
- A Stochastic Methodology for 3D Cave Systems Modeling
- ODSIM: An Object-Distance Simulation method for Conditioning Complex Natural Structures
- An algorithm for 3D simulation of branchwork karst networks using Horton parameters and A-star. Application to a synthetic case.

Emerson industrialized a plugin named PetroKarst for Petrobras. industrialized

### What is next?

If your company is a member of the Consortium, you can readily use the software prototypes developed by RING to test, evaluate and steer the technology before it becomes available on the market...

#### References

*Geostatistics Banff 2004*(pp. 703-712). Springer, Netherlands.

*Int. Assoc. for Mathematical Geology–XIth International Congres. 4p*.

*Petroleum Geostatistics, EAGE*.

*Computers & Geosciences*,

*33*(7), 932-943.

*9th European Conference on the Mathematics of Oil Recovery*, EAGE.

*Computer-aided design*,

*24*(4), 178-191.

*Three-dimensional modeling with geoscientific information systems*(pp. 123-141). Springer Netherlands.

*Mathematical Geology*,

*36*(1), 1-32.

*66th EAGE Conference & Exhibition*.

*9th European Conference on the Mathematics of Oil Recovery, EAGE*.

*Proceedings of International Association of Mathematical Geology*, S14-22.

*75th EAGE Conference & Exhibition incorporating SPE EUROPEC 2013*.

*Proc. IAMG’2006*.

*Geological Society, London, Special Publications*,

*292*(1), 89-101.

*72nd EAGE Conference & Exhibition*.