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Flow Simulation Models of Fractured Carbonate Reservoirs: Challenges, Current Practices and Future Prospects

Olivier Gosselin¹,², Luc Pauget¹, and Ahmad Abushaikha²
¹TOTAL S.A, E&P, Pau Cedex, France
²Imperial College London, Department of Earth Science and Engineering, London, UK

Carbonate reservoirs in general, and fractured carbonate reservoirs in particular, exhibit a complex type of heterogeneity, with local high contrasts in feature scales, geometry, storativity and dynamic properties, which make reservoir modelling and flow simulation of NFR non standard and very challenging.

Despite years of experience, consolidation of methods, and development of software tools, each new field under study is a new story, which requires specific approaches, and often custom designed models, and software developments. Any efficient approach needs to combine pragmatism and use of advanced research and development techniques.

The well-known difficulty is the coexistence of several scales of geological features, several of them having a possible dynamic impact on the hydrocarbon recovery mechanisms. These various scales (ranging from micro to hectometre, or more) are rarely reducible to only one fundamental heterogeneity, and not always to only two. Obviously most efforts have been focused on two-scale dynamics, where the reservoir behaviour can be explained by a flowing domain (fracture network, interconnected vugs), and a stagnant domain (matrix blocks surrounded by fractures). This so-called ‘dual-medium’ dynamic behaviour, with two-velocity flows, and highly contrasted HC stores, has been, and still is, a major challenge for efficient flow simulation models, using not straightforward effective properties. Another very common situation occurs when a reservoir is dominated by diffuse fractures (bed-confined) and their exchange with the matrix domain, while presenting also flows along fracture corridors or conductive faults: the modelling and simulation techniques cannot be identical for both features.

Before choosing or tailoring any simulation models, a proper static and dynamic conceptual model must be determined. This is a compulsory preliminary step of any field study, not only a static conceptual fracture model (SCM as in Nelson 2011), but a true dynamic synthesis is needed. For instance a dual-medium behaviour must be diagnosed by cross analysis of static and dynamic data, and this is not synonym of dual-porosity (or dual-permeability) flow simulation model (as available in commercial simulators).

Any of these solution techniques, classic or novel, are based on effective, scale-dependant properties: the definition of these parameters are simulation-model-dependant, and their computations are based on appropriate geomodels, including fracture network models. Contrary to matrix reservoir modelling, the necessary change of scales does not remain in the same continuous domain, but involves going from discrete networks at small scale to continuous medium at larger scale. An additional issue comes from the high number of degrees of freedom, and the necessary management of stochastic realisations, where very few calibration data are available.

Geological modelling and flow simulation techniques, leading to reliable reservoir management, must accurately represent the recovery mechanisms involved in the field. They are mostly driven by the exchanges between the flow/storage domains, where the understanding of competition between forces relies on a good matrix properties knowledge (e.g. wettability), and where the determination of flow anisotropy is crucial, and relies on a fair estimation of the connected fracture network (geometry and dynamics).

In our current practices, according to a static and dynamic conceptual model (we won’t give any details on this stage in our presentation), we have to choose amongst these types of simulation model:

  1. single-medium type: with homogeneous matrix+fracture properties, in case on single-phase flow (depletion);
  2. single-medium type: if we need to represent large scale features, like fracture corridors or conductive faults, with various possible local solutions, none of them being optimal;
  3. dual-medium type: in case of multi-phase flow, when both domains contribute, and when the time-scale of fracture-matrix exchange governs the recovery mechanisms;
  4. single-medium type: when the matrix is mostly tight.

The cases (3) supposes that the two domain have been identified, possibly after lumping different scales together (three to five) to define pseudo-fracture and pseudo-matrix.

The case (3) and (4) requires a suitable modelling of the effective fracture network permeability tensor (Cf. Cottereau et al., 2010), generally based on an analytical solution, overestimating the permeability, or on a flow-based method, using numerical simulation of single-phase flow across a connected fracture network, but requiring some simplification assumptions to be affordable in terms of computing cost. These techniques also need a appropriate management of uncertainties, dealing with multiple realisations, and properly conditioned to dynamic data.

The case (3) requires a reliable representation of exchanges between the two domains, through a so-called transfer function (TF). The formulation of this analytical function is usually based on a steady state approximation. The Kazemi formulation might represent expansion adequately, but not capillary and gravity phenomena, which require a modified transfer function like the one proposed by Quandalle and Sabathier (Cf. Abushaikha and Gosselin, 2008). Although not the most important component, the geometric factors (so called shape-factors) are the main adjustable parameters.

These available transfer functions are unfortunately based on single-block calculation, and are not taking into account the multi-rate component of the exchanges between matrix blocks and fracture network. The effective geometrical properties are very poorly predictive, the multi-phase effective properties are a delicate to determine, and the treatment of EOR mechanisms is still unsatisfactory.

The needs for improvement are obviously significant:

  • the fracture models (fracture sets, orientation, distribution, conductivity, etc.) must integrate geo-mechanics constraints in addition to other drivers and well data conditioning;
  • the physics of exchanges and the recovery mechanisms must be deeply investigated under various constraints and production conditions, and at various scales;
  • more advanced and reliable numerical flow simulation tools must be developed, also at various scales, for various production mechanisms, in particular at small scale (below matrix block size), but also at full-field scale;
  • workflows of effective properties calculation for a chosen running scale, with a practical update procedure (new data acquisition, history-matching).

The small scale simulations with an explicit representation of discrete fracture network and matrix blocks are a very valuable numerical experimental laboratory, as understanding and analysis tool, and also as an element of an “upscaling” factory (Cf. ISF publications).

The type of flow simulation models (too roughly speaking summarised as single- versus dual-medium models) is at the core of a not completed kind of controversy. The dual-porosity simulation model (the most commonly used phrase, with the dual-permeability variant) is in a paradoxical situation, as it is a more than 50-year old idea (starting with Barrenbatt, Warren & Root, Kazemi), which took some time to be accepted. Even in the 90’ it was often considered as too a complicated, and not robust enough numerical model. Progress were made, in particular at the level of the transfer function, but even 5 or 10 years ago, only the Kazemi TF and its (in)famous shape factor s were popular and used, despite very bad performances. In the industry the dual-porosity models are now more routinely used, especially when a single-porosity approach would lead to completely wrong and non predictive models. Recent works suggested further improvements focused on the TF, not reduced anymore to the geometrical factors, but on an analytical formulation taking into account the recovery mechanisms (Cf. Lu and Blunt, 2007, and Abushaikha and Gosselin, 2009).

In the meantime, new academic works started on the basis that the dual-porosity models are far too limited, and cannot represent the key mechanisms. The proof of dual-porosity failure is easy to demonstrate, while the engineers don’t have yet any mature and industrial alternative. These new researches are all proposing very detailed explicit and realistic representation of the fracture network geometry and of the dual matrix domain, with irregular sizes and shapes. The numerical toolbox (mixed finite elements, or control volume finite elements) is obviously sophisticated, with use of irregular and unstructured meshes.

There are several objections to this kind of approach, which is its limitation when dealing with a realistic full field scale, larger than a limited sector, and not only for a phenomenological purpose, the computing cost – which is not a solid argument on the long run – but also the difficulty to deal with stochastic multiple realisations. The question remains on the level and the location where simplifications are relevant: full physics in a deterministic framework, or simplified fracture/matrix models in a stochastic configuration?

Actually the intrinsic difficulty of modelling sharp contrast and discontinuity, and flows in this context, are not at all eliminated by the new fractured reservoirs simulators (small scale and limited domain, or larger scale but fewer events): the treatment of exchanges between fracture and matrix domain is still a big issue, and requires non trivial solutions (Cf. Matthäi and Nick, 2011).

Another approach, we would like to suggest here, is an extension, or re-visiting of this brilliant idea of dual-medium, in a more general and flexible framework. This has been already proposed, during the ISF-Phase II consortium, with an hybrid dual-medium approach, where the geometry of the fracture network is kept, in interaction with a continuous matrix domain (Cf. Evren et al., 2010). With another scope, an original approach of coupling fluid flow and solid deformation, also developed a new kind of dual-permeability technique (Cf. Lamb et al., 2010). Between explicit representation of the two domains, and a special treatment of discontinuity, and a dual-medium representation with new TF between the two domains, not sharing anymore the same mesh, the distance is close. The target could be a flexible and robust approach covering the various situations. First results will be shown following the previous works of A. Abushaikha (Cf. Abushaikha et al, 2012).

After raising more questions than bringing definitive solutions, our contribution would like to express another need to improve and make more efficient the collaboration between academic research centres and engineers in the O&G industry. How can we shorten the cycle of research-development-implementation? How can we improve the interaction between researchers and engineers, having in mind to motivate the first with real industry problems and field cases, and to provide to the second not only long-run consortium end products, but also more short-term and practical spin-offs?

We are expecting some answers during and after this workshop.

H. Lu, and M. J. Blunt (2007), “General Fracture/Matrix Transfer Functions for Mixed-Wet Systems”, SPE 107007, proceedings of the SPE Europec & EAGE conferences, London, UK, June 2007.
A. S. Abushaikha, and O. R. Gosselin (2008), « Matrix-Fracture Transfer Function in Dual-Medium Flow Simulation: Review, Comparison, and Validation », SPE 121244, proceedings of the SPE Europec & EAGE conferences, Rome (IT), June 2008.
A. S. Abushaikha, and O. R. Gosselin (2009), « Subface Matrix-Fracture Transfer Function: Improved Model of Gravity Drainage/ Imbibition », SPE 121244, proceedings of the SPE Europec & EAGE conferences, Amsterdam (NL), June 2009.
N. Cottereau, M. H. Garcia, O. Gosselin, L. Vigier (2010), “Effective Fracture Network Permeability: Comparative Study of Calculation Methods”, SPE 131126, proceedings of the SPE Europec & EAGE conferences, Barcelona (ES), June 2010.
A. R. Lamb, G. J. Gorman, O. Gosselin, and A. Onaisi (2010), « Coupled deformation and fluid flow in fractured porous media using dual permeability and explicitly defined fracture geometry », SPE 131725, proceedings of the SPE Europec & EAGE conferences, Barcelona (ES), June 2010.
E. Unsal, S. K. Matthäi and M. J. Blunt (2010), “Simulation of multiphase flow in fractured reservoirs using a fracture-only model with transfer functions”, Computational Geosciences, Volume 14, Number 4.
R. Nelson (2011), “Key Elements to a Quality Fracture Model for Simulation: The Need for Multi-Scale Fracture Measurements to Constrain the Model”, proceedings NFH02 of the EAGE Workshop on Naturally & Hydraulically Induced Fractured Reservoirs – From NanoDarcies to Darcies, 10-13 April 2011, Nafplio, Greece.
S. K. Matthai, and H. M. Nick (2011), “Comparison of three FE-FV numerical schemes for single- and two-phase flow simulation of fractured porous media.”, TIPM 90, 421-444 (2011).
A. S. Abushaikha, M. J. Blunt, T. C. LaForce, and O. R. Gosselin, (2012), « Improved Mobility Calculation for Finite Element Simulation », SPE 154480-PP, accepted for SPE Europec, Copenhagen, June 2012.
“Improved Simulation of Faulted and Fractured Reservoirs” Consortium (itf-ISF), phase III - Imperial College London (London), Montan University (Leoben), and Heriot-Watt University (Edinburgh):


AAPG Search and Discovery Article #120034©2012 AAPG Hedberg Conference Fundamental Controls on Flow in Carbonates, Saint-Cyr Sur Mer, Provence, France, July 8-13, 2012