Voxel model

The voxel model is comparable with a three-dimensional bitmap. The name is an artificial word for volume element or volumetric pixel. The geometric object is represented by a number of cubes of the same size. The cubes are located on an equidistant three-dimensional matrix (Fig. 1). The actual structure for representation of this model is an array of Boolean values, indexed by integers for x-, y-, and z-position. If 0 is considered no material and 1 as material, the... 

The voxel model is very easy to implement but has the disadvantage of a memory amount of order n. To describe a cube of edge length of 200 mm with an accuracy of 0.1 mm, a bit array of size 8 X 10 is necessary, which is 1 Gb of memory. To reduce the amormt, special data structures have been introduced. One of these is the octree model which varies the size of the cubes. 

Geometric Modeling of Machining, Fig. 2 Voxel model of a cuboid... 

Fill U, Zankl M, Petoussi-Henss N etal. (2004) Adult female voxel models of different stature and photon conversion coefficients for radiation protection. Health Phys... 

It is shown in the following subsections that combining the voxel model approach, introduced hereafter, together with three-dimensional seismic facies results fulfil all of the above specifications. 

A voxel model then defines a voxelized voxel grid, i.e., a voxel grid associated with numeric values representing some measurable properties or independent variables of the real phenomenon or object residing in the unit volume represented by the voxels [20]. These properties or variables can be of different types sampled data, computed data, simulation results etc. 

Fig. 8. Workflows. Left the classical workflow. Right the voxel model workflow. The abscissa summarizes the main steps in a chronological order. The ordinate gives an estimate of the time that each step roughly requires. For each step, black means the time usually needed and grey the time required in some particular cases.

When overlaid on the voxel grid, these surfaces are intersecting the voxels as it can be seen in Figure 12 (top). One approach to solve this problem would be to establish a set of rules defining which voxels faces make the best representation of the fault surface. This approach may although produce a stair-cased representation of the fault surface in the voxel model. In this respect, the CP geometry offers a better representation of faults. 

To some extent, the voxel model offers some advantages when compared to standard CP geometry models, where each fault necessitates accurate structural modelling and individual closure of the volume compartments. This structural modelling tends to be cumbersome when complex structures, such... 

For the voxel model in general, faults modelling needs more thorough investigations especially when complex fault geometries are involved, but this is a research topic on its own and is beyond the scope of this chapter, cf. [13, 14, 23, 44]. 

Finally, the voxel model is flexible and can be tuned to provide the best representation of the heterogeneity of the reservoir. As mentioned in the automated geometry extraction step, this is achieved by comparing the size of the voxel with the size of 3D seismic facies. Yet when more than one type of... 

Advantages and Limitations of the Voxel Model. In the Crane case study, well data indicated a regional OWC (oil water contact) with equal pressure in all wells as initial conditions. Prom these observations it is inferred that there seems to be no or only few barriers and no compartmentalization of the reservoir sand lobe. 

Due to the observations and because of the small voxel size chosen, the inclusion of faults in the reservoir model does not appear as a priority for this case study. As mentioned earher and as seen in Figure 12, the detailed heterogeneities of the reservoir captured with the tree-dimensional seismic facies are brought forward to the reservoir voxel model thereby implicitly modelling the discontinuities. 

The effect of three-dimensional seismic facies on the voxel model were evaluated by using two case studies. On the one hand, a voxel model based on acoustic impedance only, and on the other hand a voxel model based on both acoustic impedance and three-dimensional seismic facies were built. 

Figure 18 shows porosity at the top of the reservoir obtained for the two voxel models. The second voxel model (Figure 18 (b)) does not only show a less scattered representation of the porosity but also that high porosity values reproduce better the sand lobes. 

Figure 19 compares the horizon map of the top reservoir with the porosity obtained for the second voxel model, at the same location. Here, a fairly good correspondence between the position of the sand lobes and the high porosity zones is observed. 

Fig. 18. [Reproduced in colour in Plate 27 on page 441.] Comparison of porosity at the top of the reservoir for the two voxel models, (a) Voxel model based on acoustic impedance only, (b) Voxel model based on acoustic impedance and three-dimensional seismic facies results.

The computer used for simulation is a Sunblade 1000 with two CPUs at 750 MHz and 4 gigabytes memory. About 30 CPU hours were needed to run a three phases streamline simulation for 4800 production days. Figure 20 (a) shows a three-dimensional view of the porosity distribution obtained for the voxel model based on acoustic impedance and three-dimensional seismic facies results. Figure 20 (b) shows the initial oil saturation together with the location of the seven wells used for the simulation. 

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