Object Based Modeling

• Methodology

• Object Based Fluvial Modeling

• Object Based Deep Water Systems

• Lecture 9 Quiz Introduction

As in the previous lecture, there may or may not be a need to model the lithofacies. Two motivations for modeling lithofacies is to improve the accuracy of the reservoir model by injecting as much deterministic information as possible and for crisp geometric representations of geologic objects.

Object based modeling injects more information than cell based modeling. The cost of having improved accuracy comes by way of time and effort. Object based models require much more effort because there are many more parameters to consider. Object based models are constructed in a hierarchical fashion; that is, the large scale features are modeled first, the large scale features are then disassembled and then small scale features are modeled within each of the large scale components, the small scale features are then populated with the desired petrophysical properties, the model is completed by reassembling the small scale components within the large and then large scale reassembly. This lecture will discuss some current aspects of cell based modeling.

Methodology

Object-based stochastic 3-D modeling of well defined geometric objects pseudo genetically simulates depositional history of a reservoir. Two common objects that are simulated are fluvial channel complexes and fluvial channel and deep water lobes. Statistical control is obtained from cores, logs, seismic and outcrops Specifically, object-based modeling techniques require information on the size, shape, and relationship between the different objects for statistical control. For braided fluvial reservoirs, some of the needed information includes:

• fraction of channel sand (could vary areally and vertically)

• width and thickness of channel sands (could vary vertically and follow a distribution of possible sizes)

• measures of channel sinuosity (depend on size of channel and vertical position)

• geometry of channel "families" or multi-story channels.

For example, the channel size could change with depth. Figure 9.1a illustrates the size of three different channels with respect to depth. This trend must be included in the model.

Figure 9.1a Shows the change in size of three different channels with respect to depth (stratigraphic position). (Deutsch, 1999)

The vertical axis on this plot represents restored stratigraphic position and the horizontal axis is channel thickness. The Q1, Q2, and Q3 lines represent the quartiles (25%, 50% and 75%) values of the distribution. Note how the channels are smaller at the top of the zone.Simulate the deposition of the reservoir by stochastically positioning geometric shapes

The methodology is hierarchical: start from the bottom and alternately lay down floodplain sediments and channel fill. Specify the distribution of channel sizes, spacing, and so on. The methodology presented here is simplistic, it is easy to imagine model crevasse deposits and point bar sands. Deep water systems are modeled in the same hierarchical fashion: start from the bottom and alternately lay down sediment lobes at the end of channels. As with all simulation algorithms honoring data is the goal. The need to honor the conditioning data can also be a problem when there is too much data as there will not be enough degrees of freedom for the algorithm.

Object Based Fluvial Modeling

Object based Fluvial modeling is performed in a hierarchical manner. Figure 9.1 illustrates the hierarchy that will be adopted in this lecture. Each of the steps has a label. Each of the steps will be discussed below.

Figure 9.1b Illustration of the hierarchical object modeling method. (Deutsch, 1999)

The modeling approach in figure 9.1b continually adapts the coordinate system to the appropriate principle directions of continuity. This approach, while appearing quite complex, is quite simple to follow. In general the goal is to separate each of the components in the model, convert them to a regular volume, populate the model, and reassemble the model into its original format.

STEP A

After modeling the geologic surfaces separate them for independent modeling. Recall that the picture of the depositional environment will never be complete for petroleum reservoir, thus the goal of geologic modeling is to characterize the reservoir. Since geologic parameters tend to be more uniform within the lithofacies the reservoir is broken into time zones that can be modeled independently (chronostratigraphic layers)

STEP B

There are several transforms in step b. The first is to transform the stratigraphic layer into a regular grid. This is achieved by using a z coordinate transform:

(9.1)

where z2 is the transformed coordinate, z1 is the surface coordinate zrt is the restored top and zrb is the restored base. Note that, as in figure 9.2 the restored top and base need not conform to any specific surface, they only need house the layer of stratigraphic continuity. The transform may be reversed by:

(9.2)

Note that it is assumed that faults must be removed before the transform is performed.

Figure 9.2 The z transform which transforms the stratigraphic surface into a regular volume.

Areal Translation and Rotation

The reservoir coordinate system is based on some pre-existing or arbitrary coordinate system not aligned with the direction of maximal continuity. For ease of understanding, it is wise to translate and rotate the coordinate system to a coordinate system aligned with the maximal and minimal directions of continuity. Recall coordinate transforms:

(9.3) and the reverse transform:

(9.4)

Figure 9.3 The coordinate system is often translated to align with the reservoir. The translation and rotation are performed using equation 9.3, and reversed using equation 9.4. (Deutsch, 1999)

STEP C

At this step the channel complexes are modeled and separated from the stratigraphic layer. A channel complex can be defined as a large scale geologic structure.

STEP D

Fluvial channels often cluster together in channel complexes and at times the channel may not be aligned with the direction of maximal continuity. Another rotation and translation is used to bring the in line with the center line of the structure:

Figure 9.4 (Deutsch, 1999)

The transform uses the same matrices that we are familiar with for coordinate translation and rotation, however, there is no y translation:

(9.5) and the translation rotation can be reversed with:

(9.6)

The channel is likely to be sinuous and of non-uniform width. To prepare the channel for modeling the sinuousity must be removed, transforming the channel into a uniform width. Before the channel is straightened one other issue must be dealt with: the width of the channel is measured perpendicular to the y3 axis and this measure of width is incorrect; the true measure of width is perpendicular to the tangent, at an angle to the y3 axis as shown in figure 9.5. The following correction is used to increase the apparent width based on the effective width:

(9.7)

where β(y) is the angle between the y3 axis and the local tangent to the channel center line.

Figure 9.5 The addition of apparent width to repair the effect of sinuousity.

The channel still undulates; it must be straightened. The function x4 = x3 - f ^cc(y3) (9.8) measures the of the complex from the y3 axis, and translates the center line to the y3 axis as in Figure 9.6, and is reversed by x3 = x4 + f ^cc(y3) (9.9).

Figure 9.6 Transforming the sinuous complex structure into a straight structure using equation 9.8.

(Deutsch, 1999)

The last transform required to make the complex a regular volume is a straightening function:

(9.10)

Note that x4 is about one half as wide as W^cc. The result is shown in figure 9.7.

Figure 9.7 (Deutsch, 1999)

STEP E

The channels are created within the channel complexes. These are the small scale geologic features.

STEP F

As with the the channel complex, the channel must be transformed into a regular volume. The process is the same as the transform in STEP D except there is no need to rotate the channel; it is already oriented in the same direction as the complex (α=0). We need only translate the channel to have the y3

axis aligned with the center line of the channel using:

(9.11) which can be reversed using:

(9.12)

and using the same straightening transform to make the limits of the channel parallel with y3 axis:

(9.13)

STEP F

STEPS H TO M

The remaining steps are simply the reverse of the disassembly steps a through f. This will restore the reservoir to its original configuration