A new reservoir characterization methodology promises to be more than "yet another channel simulator."

The modeling of geologically realistic channel reservoirs has always been a concern. Channels have usually been created using object-based facies modeling techniques that, simply put, use trial and error to match subsurface data constraints. Therein lies the most challenging obstacle in using them. There will very often be discrepancies between the modeled objects and the actual reservoir data, especially for large amounts of data. The discrepancies can be minimized, but usually at the expense of considerable central processing unit (CPU) cycles. The new method we propose uses much less computer time to generate (possibly highly meandering) channels that will match all observed well data.
Let's look at what drives the geoscientist to strive for a better understanding of the channel network. A reservoir model needs to accurately position channel sands in order to understand the reservoir behavior (past and future) and appropriately plan field development; this is especially true in lower net-to-gross reservoirs where clear channel shapes are present.
Connectivity of the channels and their tortuosity determine fluid flow and ultimately production. To construct an accurate reservoir model, it is therefore necessary to properly capture the inter-connectivity of the channel system and the possible meandering of individual channels, i.e., generating geologically realistic features.
Modeling of fluvial-deltaic reservoirs generally requires algorithms that can represent realistic geological objects typically found in these environments: these include channels, associated levees and crevasses, and deltaic or turbiditic lobes. These types of reservoirs have the unique characteristic of a clear contrast between very high porosity and permeability rocks in the channel sands and very low porosity and permeability rocks in the flood plain. These contrasts determine where the hydrocarbons are and how fluid will flow through the reservoir. Reproducing accurately these contrasts, their continuity and tortuosity stimulated the research behind "yet another channel simulator" (YACS) that will be described below.
The YACS approach
To improve on existing methods, any new algorithm must have the following criteria:
• Well data must be perfectly honored;
• Simulated objects must be continuous throughout the modeling area;
• Simulated objects must be "geological-looking" and allow for highly meandering channels and branching of individual channels and, if a fairway is specified, then simulated channels must stay within it and follow its curvature; and
• The algorithm must be faster than existing modeling techniques.
The core of the new method lies in the modeling of a fairway or riverbed in which the channels are simulated. A potential field is defined within the fairway. Thickness and realistic channel geometries are obtained by simulating a residual component added to the potential and by using a transfer. The degree of deformation can be controlled and allows the creation of channels with high sinuosity, including oxbows.
Conditioning to well data is obtained by applying the inverse transfer function at the data location to derive the residuals. The algorithm uses sequential Gaussian simulations (SGS; Deutsch and Journel, 1994) to simulate the residuals that guarantee convergence and speed as there is no iteration or optimization loop. YACS allows simulating channels that honor both well data and channel proportions, following arbitrary shapes guided by fairways. YACS can also simulate levees and lobes, channels can have multiple branches, and conditioning a single channel branch to pass through multiple pre-defined well observations is also possible.
Overview of the method
As in most petroleum-related applications of stochastic property modeling, simulations are performed in the deposition space before being mapped back onto today's reservoir depth. Simulation of a single channel consists of first selecting a particular deposition time (i.e., a given depth in the deposition space). As channels are an erosive entity, they will be placed underneath the selected depositional surface. On this surface, a channel belt is defined that corresponds to the part of the valley in which channels form. This can simply be rectilinear in a given principal direction of deposition or explicitly specified if interpreted on seismic data.
A potential property is then computed in between the two boundaries of the channel belt, using an interpolation such as the Discrete Smooth Interpolation method (DSI; Mallet 2002) in the case of curvilinear channel belts. Assuming, say, +a and -a potential values respectively, on the left and right bank of the fairway, the absolute value of this potential corresponds to the valley at the bottom of which the channel lies (Figure 1).
A perturbation is then applied to the channel belt to add the necessary channel sinuosity. A correlated noise is simulated and added to the potential property (Figure 2). The 0 isopotential curve is considered to be the channel center line, and the potential values are mapped into channel, levees or lobe thicknesses through the use of a transfer function. The resulting thickness is painted underneath the depositional surface (Figure 3).
This procedure is repeated for every channel simulated in the reservoir model as necessary to honor both the observed well data and proportion constraints.
Simulation parameters
The input parameters are the geological characteristics necessary to describe the geometry of a channel: thickness, width, undulation wavelengths and amplitudes, and sinuosity (tortuosity) of the channels. Sinuosity is defined as the ratio of the stream length over the length of the valley (Figure 3). Sinuosity, amplitude and wavelength are actually dependent parameters as compared to existing object-based techniques, and they are mapped through empirical relationships to the variogram and probability distributions required by the SGS.
All geological parameters can be specified as (spatially varying) stochastic variables to accommodate for variability of channel dimensions, realistic positioning by incorporating trend modeling, and uncertainty about the exact dimensions and position of the channels and associated geological entities.
Conditioning to well data
Since the principal stochastic engine of the method is SGS, it is easy to constrain the simulated channels to pass through channel observations at wells and similarly to avoid locations where it is known that no channel exists.
In order for a channel to pass through given data points, the simulated random field must be such that the resulting property made up of the noise and the original potential (which maps back into channel thickness) is close to the zero value (i.e. towards the bottom of the channel). On the other hand, to avoid known non-channel locations, it must be made large. In other words, well observations are first transformed into channel thicknesses, which in turn are mapped into potential values leading to their residual values. These values are used to condition the SGS, meaning that the method is fast and that it can accommodate any number of well data.
Additional features
YACS allows for simulating not only channels but their associated levees. Areas can be defined where channels branch off and further areas defined where these branches turn into lobes. This enables modeling of deltaic and turbiditic environments. All simulated facies are perfectly conditional to their well observations. The algorithm also enables the user to specify if two or more data points belong to the same channel or branch. Furthermore, each channel object is treated as a specific entity in which exact positions and local anisotropy angles are known, enabling petrophysical property modeling (e.g. porosity, permeability) using algorithms that account for varying azimuth and trends.
Conclusion
The algorithm presented in this paper is not just "yet another channel simulator," as the satirical acronym used to refer to the method would lead to suggest - it addresses important gaps in features of current algorithms and methodologies used to stochastically model fluvial reservoirs. YACS improves existing channel modeling techniques by allowing simulated channels to have realistic features such as meanders, oxbows and branches and to stay within observed fairways. It also guarantees continuity of the channel objects throughout the modeling area. Above all, it is fast, 100% conditional to well observations and complements the existing toolbox of modeling applications. YACS is commercially available as part of the Gocad Suite of modeling workflows.

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