Multi-rate mass-transfer dual-porosity modelling using the exact analytical solution for spontaneous imbibition

Christine Maier, Karen Sophie Schmid, Mohamed Ahmed Elfeel, Sebastian Geiger

Research output: Chapter in Book/Report/Conference proceedingConference contribution

21 Citations (Scopus)


Multi-phase flow in carbonate reservoirs, which hold about half of the world's remaining oil reserves, is strongly influenced by fractures present in the geological formations. Fractures are often the main flow conduits, leaving most of the oil behind in the low permeability rock matrix, and cause early water breakthrough. An accurate characterization of fracture flow and fluid exchange between fracture and matrix is needed to forecast oil recovery and optimise production in fracture-dominated and fracture-assisted reservoirs.

Dual-porosity simulations are traditionally used to model naturally fractured reservoirs. However, the classical dual porosity models miss some key physics of fracture - matrix fluid exchange: (1) They tend to simplify mass transfer due
to spontaneous imbibition since they typically cannot include arbitrary petro-physical properties due to e.g. wettabilities, viscosity ratios, initial water content, etc. (2) They cannot account for the fact that matrix blocks within a single simulation grid cell have various sizes and permeabilities, giving rise to different transfer rates, which should be captured by a distribution of transfer functions in each grid cell.

In this paper we present a novel multi-rate dual-porosity model. It is based on an unstructured finite element - finite volume technique, which solves the governing equations for two-phase flow fully implicitly. This allows us to represent complex large-scale geological structures (e.g., non-orthogonal faults and fracture corridors) accurately while small-scale diffuse fractures are modeled with an improved dual-porosity approach. Until recently, calculating the mass transfer between fractures and matrix blocks due to spontaneous imbibition for arbitrary petro-physical and fluid properties exactly was not possible because a general and exact transfer rate for arbitrary petro-physical and fluid properties was not known. In our new dual-porosity model we compute fracture-matrix transfer using the only known analytical and general solution of the Darcy equation including capillarity. This provides us with a generalised transfer function for arbitrary wettability, viscosity ratios, rock types, initial water content and boundary conditions. Each reservoir simulation grid block can contain multiple of these generalised transfer functions to model different matrix permeabilities and/or matrix block sizes present at the sub-grid scale.

Using a series of proof-of-concept simulations, we show that the difference in oil recovery using a standard single-rate dual-porosity model and our new multi-rate dual-porosity model cannot be neglected. This demonstrates that our proposed model with the generalised transfer function predicts oil recovery more accurately compared to a classical dual-porosity model.
Original languageEnglish
Title of host publication75th European Association of Geoscientists and Engineers Conference and Exhibition 2013
Subtitle of host publicationChanging Frontiers: Incorporating SPE EUROPEC 2013
Place of PublicationHouten
PublisherEAGE Publishing BV
Number of pages14
ISBN (Electronic)9781613992548
ISBN (Print)9781629937915
Publication statusPublished - 2013
Event75th EAGE Conference and Exhibition 2013 - London, United Kingdom
Duration: 10 Jun 201313 Jun 2013


Conference75th EAGE Conference and Exhibition 2013
Abbreviated titleSPE EUROPEC 2013
Country/TerritoryUnited Kingdom


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