A Hierarchical Model Calibration Approach with Multiscale Spectral-Domain Parameterization: Application to a Structurally Complex Fractured Reservoir

Abstract

A hierarchal history matching algorithm is proposed that sequentially calibrates reservoir parameters from the global-to-local scale in consideration of parameter uncertainty and the resolution of the data. Parameter updates are constrained to the prior geologic heterogeneity and are performed parsimoniously, or only to spatial scales that can be resolved by the historical data. In the first step of the workflow, a genetic algorithm (GA) is used to calibrate and assess the uncertainty in global parameters (e.g., regional fracture properties, aquifer strength) that influence reservoir energy and field-scale flow behavior. To identify the reservoir volume over which each parameter region is applied, a novel heterogeneity segmentation technique is developed from spectral clustering theory. After an ensemble of calibrated model realizations is identified using the GA, the ensemble is reduced via a cluster analysis to define a variance-preserving subset of the members for the second step of local, higher-resolution parameter calibration. Each member of the subset is calibrated to well-level phase rate and pressure data using a sensitivity-based scheme. To improve the ill-posedness of each high-resolution inverse problem, the heterogeneity field is parameterized in the spectral domain using the Grid Connectivity-based Transform (GCT) to provide a compressed representation that captures only the sensitive geologic trends. The GCT concurrently imposes geological continuity during calibration and promotes minimal changes to each prior ensemble member. The proposed calibration workflow is applied to a structurally complex, fractured reservoir located offshore Peru. The reservoir is modeled as dual porosity and single permeability (DPSP). In the global calibration step, the field water production rates, gas rates and average reservoir pressure are matched using the GA together with zonal multipliers that represent spatial variation in aquifer strength, fracture porosity and a matrix-fracture coupling parameter. In the subsequent local step, the well-by-well production histories are matched through calibration of the most uncertain grid-cell parameter, fracture permeability, which is characterized using the GCT parameterization. The final calibrated models are consistent with geologic interpretation and are currently being applied for field development strategies.

Calibrate complex fracture model for subsurface flow based on Bayesian formulation

“…For instance, the sparse randomized maximum likelihood method was advanced to solve the high-dimensionality problem in the inversing process for subsurface flow (Khaninezhad and Jafarpour 2014). The two-stage procedure based on simultaneous perturbation stochastic algorithm (SPSA) (Zhang et al 2016a) was proposed to improve the efficiency for inversing reservoir field models, and a hierarchal calibration framework with multiscale spectral-domain parameterization was used for complex fractured reservoirs (Kang et al 2014). The ensemble Kalman filter (ENKF) to subsurface flow model calibration being capable of resolving nonlinear problems has also been extensively studied in the past decade (Aanonsen et al 2009;Chen and Zhang 2006).…”