Geologic Model Optimization via Response Surface Gradient Search
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Solution Overview
Problem
Existing optimization methods for geologic modeling in hydrocarbon exploration face challenges in finding global optima due to the presence of local minima, especially when dealing with complex problems involving many independent parameters, where iterative sampling and response surface modeling are used but often get trapped in local minima.
Innovation Solution
A method that combines global and local optimization techniques by using a numerical model to predict outcomes and their gradients, constructing a geometric approximation of the parameter space through Voronoi tessellation or Delaunay triangulation, and iteratively updating the response surface model to select parameter values, allowing for both deterministic and stochastic selection of new parameters based on cost and gradient information.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If iterative sampling of parameter space is performed to find optimal parameters, then the method can handle complex problems with many independent parameters, but the solution gets trapped in local minima rather than finding the global optimum
Solution Approach 1:
The algorithm dynamically adapts its search behavior by adjusting the probability of accepting worse solutions based on iteration count and temperature parameters. Early in the process, it explores more aggressively; later, it exploits promising regions more intensively. This dynamic adjustment allows the method to both handle complex parameter spaces and avoid getting trapped in local minima.
Solution Approach 2:
The simulated annealing algorithm changes the acceptance criterion parameter (temperature) over time according to a cooling schedule. By systematically varying this parameter from high to low values, the algorithm transitions from broad exploration to focused exploitation, enabling it to navigate complex parameter spaces while converging to global optima rather than settling for local minima.
2Loss of information
If systematic sampling of parameter space is performed to construct response surface, then approximate response surface can be built, but the process is prohibitive for more than just a few free parameters
Solution Approach 1:
Instead of systematically sampling the entire parameter space, the algorithm performs partial sampling by evaluating the cost function only at the current parameter set and its neighbors. This selective evaluation maintains sufficient response surface information for effective optimization while avoiding the prohibitive computational cost of exhaustive sampling in high-dimensional spaces.
3Productivity
If gradient-based optimization is used to find downhill directions, then the method can efficiently navigate the response surface, but it guarantees only local optima rather than global optimum
Solution Approach 1:
The algorithm applies preliminary anti-action by intentionally accepting worse solutions with probability exp(-ΔE/T) during early iterations when temperature is high. This counterintuitive move against the gradient direction prevents premature convergence to local minima, while still allowing efficient downhill navigation when temperature decreases later in the process.
Data Source
AI summary
A method of improving a geologic model of a subsurface region. One or more sets of parameter values are selected. Each parameter represents a geologic property. A cost and a gradient of the cost are obtained for each set. A geometric approximation of a parameter space defined by one or more formations is constructed. A response surface model is generated expressing the cost and gradient associated with each formation. When a finishing condition is not satisfied, at least one additional set is selected based at least in part on the response surface model associated with previously selected sets. Parts of the method are repeated using successively selected additional sets to update the approximation and the response surface model until the finishing condition is satisfied. Sets having a predetermined level of cost to a geologic model of the subsurface region and/or their associated predicted outcomes are outputted to update the geologic model.