Reservoirs are conventionally considered a chain of various types of heterogeneities at different scales. It is obvious that the degree of understanding concerning each type of heterogeneity, and the way they are processed, is different from one end of the scale chain to the other.
Recent efforts have been made towards limiting the erasement of heterogeneity during up-scaling procedures applied to physical properties when moving from fine-gridded stochastic models to coarse-gridded flow simulation models. The scale change between these two models is of the order of 102 since the transition is made from a fine-grid of about 25 x 102 cu meters (50 meters by 50 meters by 1 meter) to a coarse-grid of about 4 x 105 cu meters (200 meters by 200 meters by 10 meters).
This magnitude of 102 seems very moderate in comparison with the magnitude of the scale change applied between the scale of property measurements and that of the stochastic model grids. Actually, when moving from a plug (10-5 cu meters) to a fine-grid model, the magnitude of the scale change is about 108 whereas it is about 106 between a full-size core (25 x 10-4 cu meters) and the fine grid.
The main challenge in up-scaling actually resides in assigning physical properties deduced from core measurements to grid blocks in the fine-grid model. Obviously, when up-scaling from a plug to a grid block in a stochastic model, a whole series of nested heterogeneities of different scale must be described, from those found within laminae (the basic component) to those found within the organization of genetic units in the sedimentary bodies.
Until now, a sustained effort has been made to study both the organization of laminated and cross-bedded sandstones and the mechanisms of capillary trapping in such deposits. However, most of this work focuses very rarely on rock volumes larger than 1-5 cu meters, which is very far from the volumes that must be quantified for cells in fine-gridded reservoir models. Several explanations can be given concerning the lack of awareness of the missing scale:
- There is difficulty in characterizing the reservoir at a scale that is larger or smaller than that of the main tools and techniques used. Prime quality outcrop surveys are necessary to study and quantify sedimentary structures.
- There is no industrial method for 3D modeling of structures as complex as sedimentary structures.
- Above all, there is underestimation of the effects on flows of heterogeneity at this scale.
Flow behavior
Very often, small-scale heterogeneity is considered as an accessory property, or of secondary importance with respect to larger-scale heterogeneity. The latter is usually considered as key heterogeneity, having the greatest impact on fluid flow.
When small-scale heterogeneity is neglected, stochastically modeled sedimentary bodies (objects, SIS, etc.) are filled with properties which are usually isotropic, at least in the horizontal direction. It is actually extremely rare to introduce different permeability values along the x and y axes in fine grid blocks. However, up-scaling from plug to grid blocks of stochastic models should generate permeability anisotropy, which is a consequence of extremely complex and sedimentary structures.
Results were compared from flow simulations run on fine-grid models, whose grid blocks were filled either with isotropic horizontal permeability or with anisotropic horizontal permeability supposedly representing the heterogeneity of small-scale sedimentary bodies. Synthetic models were built with anisotropic sand bodies for channels, and run using a waterflooding recovery mechanism.
Simulation results
The simulations conducted on a significant number of models using variable geological and dynamic parameters have demonstrated the significance of horizontal permeability anisotropy on the results of flow simulations. It has been demonstrated that the relative recovery factor can vary 40-100%, depending on whether or not the permeability anisotropy generated by small-scale heterogeneity is taken into account.
The degree to which sand bodies are connected at large scale also plays a significant role: the fewer the connections between the sand bodies, the greater the effect of phenomena induced by such permeability anisotropy. In the same way, it has been shown that in channels the mobility ratio plays a role comparable to that of the degree of connectivity between sand bodies: the more the mobility ratio is in favor of water, the greater the influence of the permeability anisotropy on recovery.
The missing scale
Geological descriptions of sedimentary bodies for reservoir models are generally based on sedimentary facies (lithology, grain-size, and structures) and petrophysical properties (porosity, permeability, bulk density). At reservoir scale, natural heterogeneity is often displayed in two ways:
- Large-scale heterogeneity acting as screens between different sedimentary bodies (faults, lithological contact, tight layers)
- Very fine-scale heterogeneity (lamina scale) as evidenced by recent works.
Fine-scale heterogeneity (within sedimentary bodies) is scarcely described. Accurate relationships between sedimentary bodies and fine-scale heterogeneity must be defined to estimate permeability anisotropy within a studied reservoir. The reservoir geologist is waiting for a practical tool to be able to anticipate the type of heterogeneity within a given sedimentary body, and the effects on permeability tensors.
One solution to that need is to construct a catalog that defines the relations between sedimentary bodies and fine scale heterogeneity, displaying their geometric patterns. This catalog was constructed for all sedimentary environments. Heterogeneity was labeled and given an acronym and a symbol. Small-scale heterogeneity is classified in three types: surfaces, sedimentary structures, and other structures.
Each structure is described in terms of geometrical patterns, well log responses and sedimentological origin, and is illustrated by cores or outcrop photos. The relationships between the sedimentary structures and the best permeability vectors to be considered are a function of the paleo-current direction deduced from the understanding of the structures themselves.
An illustration of this catalog is shown for channel sand bodies. A channel is a very common sedimentary body in a fluvial sedimentary system, regardless of whether the depositional environment is braided, low sinuosity, meandering, or anastomosed. Channels can also be found in slope and basin systems in the turbiditic complexes.
Heterogeneity modeling
Building 3D models of heterogeneity appears to be a truly difficult task. The problem is to fill the domain in a non-deterministic manner, while reproducing repetitive structures arranged randomly in space. With respect to heterogeneity conventionally modeled at a larger scale (sedimentary bodies) and whose contours can be less well defined, the geometry at smaller scales is precise and an interaction (deformation or erosion) exists between an object being modeled and an underlying (previously modeled) object.
A pseudo-genetic methodology was developed for modeling internal channel sedimentary heterogeneity. The principal of the modeling is to position sections representing the channel profile along a line that represents the channel path. Channel sections are positioned orthogonally to the channel path to accurately reproduce the meandering river's shape. According to observations, a meander tends to increase its amplitude while undergoing other possible composite movements such as rotations or translations.
To simplify modeling, the lateral meander shift built by introducing an increase in the meander radius that is roughly orthogonal to the riverbed. The facies distribution inside the meander loop deposits are reproduced as realistically as possible by respecting the fining upward trend of the facies as well as the distinctive features between different stages of deposition.
Conclusions
This demonstrates the following:
- The necessity of managing a scale of heterogeneity intermediate between that of laminae and of the sedimentary bodies - the missing scale
- The ability for sedimentologists to propose models of facies and sedimentary structure organization within reservoir bodies
- The difficulties in modeling this scale of intermediate heterogeneities.
Extension of the modeling technique that was proposed for channels appear to be indispensable to finally take into account this scale of heterogeneity. In most cases, modeling missing scale is still a challenge.
