Calibration – The Basis for Successful Modeling

J. L. Gevirtz and K. E. Williams
Halliburton, Houston, TX, USA

By its very nature, geology is an observational science. The appearance of any geological phenomenon represents the results of a complex experiment performed by nature. Unfortunately, the processes and some of the materials that are components of this experiment are lost because they are ephemeral and do not remain in the system. Often, the job of the geologist is to estimate the experimental conditions and materials responsible for the observed phenomenon because testing by direct observation is not possible.

Numerical modeling provides an avenue to investigate the possible set of conditions that results in a given geological observation. Therefore, the current practice for many areas of geological study involves some aspect of numerical modeling. Many software packages that implement these methods have become commercially available over the last 25 years. These software systems provide sophisticated techniques for developing predictive models of geological phenomena. These models can be constructed from concepts alone. They do not specifically require actual measured data. However, it is implicitly assumed that, if the model has been carefully calibrated to mimic measured data, it can then be used to create meaningful predictions about some aspect of the modeled situation. The calibration of geological models therefore involves comparing the computed geological variables with measured values at the same locations. If the model is found to be different from the measured data, then the model elements are altered until a close match between observed and modeled data is obtained. The calibrated model can then be used to predict geological variables, such as structure, seismic velocity, oil generation and migration, and downhole pore pressure and porosity.

Geological models, by their very nature, are incomplete representations of the real world. These models are constructed to satisfy a perceived need. For example, the purpose of the petroleum systems model is to predict the volumes of in-place hydrocarbons necessary for economic decisions regarding an exploration and accompanying drilling program. The primary purpose of pore pressure modeling is to provide pressure predictions that can confidently be applied to wellbore design and wellbore stability. Therefore, the models applied to each of these problems contain approximations necessary to accomplish the primary goal and are by definition limited with respect to spatial and/or temporal aspects.

There are two types of error inherent in any modeling process: measurement error and modeling error. Measurement errors, familiar to most students, result from sampling and measurement processes. These errors have well-defined statistical properties and therefore can be controlled.

A model of any particular geological phenomenon involves the simplification of the earth materials and processes necessary to allow them to be expressed as a set of partial differential equations. Model errors arise as a result of these simplifications and can result in loss of spatial or temporal resolution. The loss of resolution implied by these simplifications must be evaluated before the predictions obtained from a model can be applied with confidence. If the assumption can be made that these errors contribute variation at a lower level than the desired result, they can be ignored.

The variables used for model calibration are obtained by direct laboratory measurement of the particular rock component or property in rock samples collected from outcrops or drilling sites. They can also be obtained from indirect estimates of rock properties and/or components obtained from petrophysical well logs and seismic data. Each of these variables suffers from several errors that arise from measurement and sampling processes. Laboratory measurements can be quality controlled by submitting blind samples and standards as part of the laboratory analysis. Petrophysical and seismic data are far more difficult to quality control.

Beyond several comparisons of vitrinite reflectance and other thermal indices over the past 20 years, little public attention has been paid to the effects of variance in calibration data on the final modeling results. Therefore, the quality (such as precision and reproducibility) is usually not known. However, it is advantageous to attempt to assess the effect of measurement error on the resultant model calibration so that the limits of predictions can be recognized.

For the reasons described briefly above, it is good practice when applying a modeling tool to a particular problem to take a “research design” approach to the project. Such an approach involves the consideration of several important a priori issues. These issues are defined by how the end result of the model will be applied and include the level of required resolution, data required to adequately describe geological framework on which the model will be based, and the quality of the data to be used to calibrate the model. A workflow that covers all aspects of the modeling process should also be constructed.

After a design for the project and an accompanying workflow have been developed, the first steps that include the development of the geological framework can begin. After the geological framework is developed, the model is calibrated with observed data.

Commonly, model calibration is accomplished by a tedious trial and error procedure that consists of changing model parameters until a set that produces a result that satisfies the data provided for calibration. This is usually a daunting procedure, particularly for those unfamiliar with the geological conditions in the area being modeled or for beginners in the art of modeling.

To speed up the calibration process, a model calibration approach is recommended that uses an inverse technique to achieve rapid convergence between the model and actual data. Many of these so-called inversion techniques involve some form of simulated annealing to achieve rapid convergence; a method that has its origins in statistical mechanics. It finds optimal or near-optimal solutions of complex systems and uses a statistical sampling approach to select the criteria. It also includes a strategy of what to do when the results are either improved or degraded. Although this method does speed up the trial and error process of model calibration considerably, it often results in a set of unrealistic model parameters. For example, in pore pressure modeling, five variables are considered to be of primal importance in pressure generation, retention, and dissipation. One of these is the initial porosity of the sediment before burial. When simulated annealing is applied to match the definitive porosity and pore pressure curves established from petrophysical analysis, it often provides a solution in which the initial porosity is unrealistically high or low. Therefore, the modeler must exercise some constraints regarding the range of values considered reasonable for each variable included in the model, thus introducing the element of personal bias into the model. Unfortunately, the introduction of biases at this early stage of model building is difficult to assess at the end of the process.

Several examples of geological models from different areas of the world have been constructed to study pressure behavior within a volume of sediment. These models were used to predict pressure in a proposed wellbore lying within the sediment volume. These pressure predictions are then applied. Predicting wellbore stability and an accompanying drilling program are presented to illustrate the proper design and calibration of a purpose-built geological model. Recommendations are made regarding the examination of uncertainties accompanying these predictions. Aspects of these models are presented to illustrate the various aspects of model calibration and its influence on the final model and predictions achieved from them.

AAPG Search and Discovery Article #90091©2009 AAPG Hedberg Research Conference, May 3-7, 2009 - Napa, California, U.S.A.