Petrophysical reservoir modeling and the ability to generate a spatially accurate description of properties such as porosity and permeability are crucial to the understanding of fluid distribution and flow properties within the reservoir and act as vital input to reservoir management decisions.
Yet petrophysical modeling today comes with a number of challenges. Fundamentally, there is the challenge of scale. Well logs and analogue outcrop studies indicate that heterogeneity in petrophysical properties occurs over a variety of scales. From fine-scale diagenetic processes that affect flow properties to larger scale compaction and deformation trends, the quality of reservoir rock is known to vary in ways impossible to detect before drilling.
Another challenge is the increasing complexity of reservoirs. This includes fluid flow characteristics that are difficult to predict, large variations in permeability, and complex geologies and geometries that lead to highly heterogeneous reservoir descriptions. Petrophysical models that simplify these complexities fail to deliver the vital information operators require and can ultimately lead to misplaced wells and lower recovery.
A third challenge is the growth in giant reservoirs and reservoir models—models that can sometimes contain millions of cells and thousands of wells. In such cases, there is a need to upscale the model for reservoir simulation without losing the original structure and petrophysical characteristics of the model. All geological data affecting fluid flow and rock properties such as porosity and absolute and relative permeability need to be upscaled accurately.
There also is the importance of incorporating seismic constraints into the petrophysical model. With seismic imaging and interpretation being the standard workflow for mapping and developing subsurface reservoirs, it’s essential that all features and anomalies in the seismic data are incorporated into the petrophysical model. The goal here is to translate features and anomalies in the seismic data into heterogeneities in reservoir rock properties.
Finally, there is the importance of a seamless workflow in petrophysical modeling with links to volumetric calculations, connectivity analysis, full well planning functionality and reservoir simulation.
In summary, petrophysical modeling today can only be truly effective if interpreters have the necessary tools to integrate all available data—especially well and seismic data—and from all reservoirs, including the largest and most complex. It is only then that multiple scenarios can be assessed and reservoir uncertainty better quantified.
Handling reservoir complexities
Petrophysical properties within the reservoir are strongly controlled by depositional facies and a variety of post-depositional diagenetic processes. It’s therefore essential that, to represent the reservoir’s complexities, as wide a variety of trends be incorporated into the petrophysical model as possible.
Emerson’s reservoir modeling software Roxar RMS, for example, comes with fast and memory-efficient kriging and simulation algorithms that integrate a number of trends in the petrophysical model. These include large-scale compactional/depositional processes, intrabody trends, upward fining or coarsening, proximal-to-distal and axis-to-margin lateral trends, facies-related trends, and cloud transforms. The kriging methods also include universal, Bayesian and colocated co-kriging with the kriging algorithms optimized to handle giant fields with thousands of wells.
Incorporating seismic data
The software also comes with a selection of methods that allow seismic data to be incorporated into petrophysical modeling. This includes a tool that allows interpreters to blend the seismic data and interpretations with stochastic modeling techniques to close the resolution gap between the two methods.
An object-based facies modeling tool has been developed where data extracted from seismic are combined with geostatistical tools such as guidelines and trends to generate well-constrained sedimentary bodies.
The ability to access both deterministic and statistical techniques gives the modeler access to the gray area between seismic resolution and data-constrained statistical modeling, resulting in realistic property models that are conditioned to well observations and come with accurate volume calculations.
Another property modeling technique is a multipoint statistics tool that uses a pixel-based (grid cell by grid cell) approach for building stochastic facies realizations. This allows the user to condition 3-D training images of the interpreted heterogeneities in the reservoir in addition to wells and seismic volumes. Furthermore, the ability to execute petrophysical modeling jobs on parallel CPUs enables users to incorporate large seismic data volumes into petrophysical modeling and reduce the computation time exponentially. The result is the incorporation of seismic into petrophysical modeling.
Upscaling—a Middle East example
As mentioned before, one of the biggest challenges in capturing petrophysical characteristics in the model and ensuring that they can be taken to simulation is the ability to handle giant reservoirs and to upscale models for simulation without losing their original petrophysical characteristics.
In one field example, RMS helped a leading Middle East operator upscale a geological model of 20 million cells into a simulation grid of only 2.5 to 3 million cells without losing the reservoir heterogeneities and petrophysical properties within the model.
The field in question was a complex carbonate reservoir in the Arabian Gulf that contained highly heterogeneous porous and dense layers including lithology limestone and dolomite with high-permeability streaks. Petrophysical properties that were modeled included the stochastic distribution of the rock type and porosity, the stochastic distribution of permeability, and the saturation conditioned to rock type.
The method applied to the model was a recursive algorithm that operates by merging two adjacent layers with minimal variation changes until a single layer model is generated. The algorithm uses model properties such as bulk volume, porosity, permeability and rock type as input for quantifying the model’s heterogeneity, and it was implemented as programming script within the software.
The workflow consisted of a layer coarsening script where quantitative parameters were generated to measure variation changes and determine where two cells could be merged while keeping maximum heterogeneity. Figure 1 illustrates how the heterogeneity is plotted vs. model layers, with the point of inflexion on the curve being the optimal point where the minimized model layers combine with the maximum retained heterogeneity.
At each stage, the layer coarsening script reports the total number of layers, the proportion of each layer and the combination sequence based on the original layer index.
The control lines, created through the programming script, also helped to define the columns and rows in the grid-building process. As can be seen in Figure 2, when evaluating lateral heterogeneity, the distribution of controls lines shows that the bigger cell sizes are on the flanks and the smaller cell sizes on the crest. Figure 3 shows a histogram that was undertaken from the upscaled simulation grid with very close correlations to rock type, permeability and porosity.
The result for the operator was a simulation grid of 2.8 million cells and a model that will enable reservoir engineers to conduct the fluid flow simulation process with an excellent approximation of the high-resolution calculations performed in the original model.
Furthermore, all of this takes places within an integrated workflow alongside other petrophysical modeling tools from 2-D interpolation to 3-D stochastic modeling conditioned to wells, facies and seismic data.
Rising to the challenge
Petrophysical modeling should always be based on combining all available data, especially well and seismic, with the geological interpretation of the reservoir.
It should also come with the necessary capabilities to handle all types of reservoirs and models, no matter how large or complex.
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