Abstract
Because facies are nominal variables, their modeling methods are different from the modeling methods for continuous variables. Kriging and stochastic simulation methods presented in Chaps. 16 and 17 cannot be directly used for construction of a facies model; they can be modified for facies modeling, or totally different methods are used. Although facies are often modeled before modeling petrophysical variables, modeling methods for continuous variables were presented in the earlier chapters because it is easier to understand facies modeling methods after understanding kriging and stochastic simulation for continuous variables. This chapter presents several facies modeling methods, including indicator kriging, sequential indicator simulation and its variations, object-based modeling, truncated Gaussian and plurigaussian simulations, and simulation using multipoint statistics.
There are no routine statistical questions, only questionable statistical routines.
D.R. Cox
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Appendix 18.1: Simulated Annealing for Honoring Multiple Constraints in OBM
Appendix 18.1: Simulated Annealing for Honoring Multiple Constraints in OBM
The method and use of simulated annealing in object-based modeling can be found in Holden et al. (1997) and MacDonald et al. (1995). Here we show the main principle of the simulated annealing for handling multiple constraints in fluvial channel OBM using an example of balancing the honoring of various inputs (Fig. 18.17). The soft conditioning data and target NTG ratio are honored as a function of the simulated-annealing iteration number when well data are not used to condition the model. The algorithm first generates a certain number of channels to approximately honor the target NTG ratio. That usually takes a few dozen iterations. Then it begins to honor the soft (secondary) data component while allowing the honoring of the net-to-gross ratio (N/G) to fluctuate. As the iteration increases, the soft data component is reduced, implying that the algorithm is attempting to honor more and more of the soft data.
Simulated-annealing curves for honoring the well data, N/G ratio, and soft conditioning data. Temperature is a parameter in simulated annealing. The low values for soft data honoring implies better honoring in the plot
When well data are integrated into the model, they are generally honored before the honoring of the soft data. However, although most well data are honored at an early stage of iteration, some well data may be very difficult to honor. Therefore, as the iteration keeps increasing, the algorithm attempts to simultaneously honor the soft data and the remaining, not-yet-honored, well data. It happens that, at a certain iteration, the well data are honored at a high rate, but at the expense of honoring the soft data. For instance, in Fig. 18.17, when the iteration reaches 18,000 and 25,000, sudden jumps in the soft data honoring are due to the honoring of the well data.
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Ma, Y.Z. (2019). Geostatistical Modeling of Facies. In: Quantitative Geosciences: Data Analytics, Geostatistics, Reservoir Characterization and Modeling. Springer, Cham. https://doi.org/10.1007/978-3-030-17860-4_18
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