| Authors |
Alex DE BEER, Michael GRAVATT, Theo RENAUD, Andrew POWER, Joris POPINEAU, Ruanui NICHOLSON, Oliver MACLAREN, Ken DEKKERS, John O\'SULLIVAN, Michael O\'SULLIVAN |
| Abstract |
Reservoir modeling is a vital tool in the sustainable management of geothermal reservoirs. A key component of the modeling process is model calibration, in which parameters, including permeabilities and mass upflows, are adjusted until there is an adequate match between the model outputs and collected data. The Bayesian approach to model calibration is gaining increasing use in the context of reservoir modeling. A key element of the Bayesian approach is the use of a prior distribution, which acts as a mathematical representation of expert knowledge on the likely values of the model parameters prior to data being collected. Once data is collected, it is combined with the prior to form the posterior probability distribution, which defines the solution to the calibration problem. Characterizing the prior is a subjective process. Common practice in geothermal modelling is to use a log-normal distribution to represent the permeabilities associated with each rock type in each formation within the model. This approach, however, disregards geological principles which dictate what the relative values of the permeabilities of different rock types within a given formation can be. For instance, the permeability of a fault rock type in the direction across the fault may not exceed the permeability of the surrounding formation; a prior constructed in the traditional, naïve manner, however, assigns a non-zero probability to this situation. In this paper, we demonstrate how a prior that adheres to simple geological principles can be characterized. We then perform several comparisons, by running a natural-state model with parameters sampled from both a geologically consistent prior and a prior constructed in a naïve manner, to determine whether adhering to geological principles when characterizing the prior improves the quality of the model outputs. These tests include quantitative analysis of the agreement between reservoir simulation results and geophysical data such as inferred alteration and downhole temperature profiles, as well as a qualitative analysis of the shapes of the convective plumes produced. Our analysis suggests that there are differences in the temperature profiles produced by running the model with parameter sets sampled from each type of prior. It is difficult, however, to identify the prior that produces the more realistic set of modeled temperatures based on these comparisons. By contrast, our analysis of the convective plumes produced suggests that the plumes produced using parameters sampled from a geologically consistent prior interact with the fault structures of the system in a way that is more aligned with how we would expect the system to behave in reality. We conclude by discussing some directions for future investigation of the effectiveness of geologically consistent priors. |