The traditional trial and error approach of history matching to obtain an accurate model requires engineers to control each uncertain parameter and can be quite time consuming and inefficient. However, automatic history matching (AHM), assisted by computers, is an efficient process to control a large number of parameters simultaneously by an algorithm that integrates a static model with dynamic data to minimize a misfit for improving reliability. It helps to reduce simulation run time as well.
Particle Swarm Optimization (PSO) is a population based stochastic algorithm that can explore parameter space combined with the least squares single objective function. The process of AHM can adopt parameterization and realization methods to reduce inverse problems. In this study, realizations of various reservoir properties such as porosity, net to gross, relative permeability, horizontal and vertical permeability, and aquifer size were chosen for controlling throughout the AHM. History matching was conducted to validate the efficiency of each method. The guidelines for optimized AHM with a stochastic algorithm are also disccussed.
The realization and parameterization methods improved matching results in a full-field application with resulting in a reduced misfit and in less. A stochastic algorithm generates multiple models to deduce control parameters to reduce a misfit. In this study we identified that PSO converged effectively with updated control parameters. The optimized AHM improved the accuracy of a full-field model although some misfit remained in the match to bottomhole pressure.
We found that updating with too many parameters makes the problem difficult to solve while using too few leads to false convergence. In addition, while the simulation run time is critical, a full-field simulation model with reduced computational overhead is benefitial.
In this study, we observed that the PSO was an efficient algorithm to update control parameters to reduce a misfit. Using the parameterization and realization as an assisted method helped find better results. Overall this study can be used as a guideline to optimize the process of history matching.
Wheeler, Mary F. (The University of Texas at Austin, USA) | Srinivasan, Sanjay (Pennsylvania State University, USA) | Lee, Sanghyun (Florida State University, USA) | Singh, Manik (Pennsylvania State University, USA)
Optimal design of hydraulic fractures is controlled by the distribution of natural fractures in the reservoir. Due to sparse information, there is uncertainty associated with the prediction of the natural fracture system. Our objective here is to: i) Quantify uncertainty associated with prediction of natural fractures using micro-seismic data and a Bayesian model selection approach, and ii) Use fracture probability maps to implement a finite element phase-field approach for modeling interactions of propagating fractures with natural fractures.
The proposed approach employs state-of-the-art numerical modeling of natural and hydraulic fractures using a diffusive adaptive finite element phase-field approach. The diffusive phase field is defined using the probability map describing the uncertainty in the spatial distribution of natural fractures. That probability map is computed using a model selection procedure that utilizes a suite of prior models for the natural fracture network and a fast proxy to quickly evaluate the forward seismic response corresponding to slip events along fractures. Employing indicator functions, diffusive fracture networks are generated utilizing an accurate computational adaptive mesh scheme based on a posteriori error estimators.
The coupled algorithm was validated with existing benchmark problems which include prototype computations with fracture propagation and reservoir flows in a highly heterogeneous reservoir with natural fractures. Implementation of a algorithm for computing fracture probability map based on synthetic micro-seismic data mimicking a Fort Worth basin data set reveals consistency between the interpreted fracture sets and those observed in the reference. Convergence of iterative solvers and numerical efficiencies of the methods were tested against different examples including field-scale problems. Results reveal that the interpretation of uncertainty pertaining to the presence of fractures and utilizing that uncertainty within the phase field approach to simulate the interactions between induced and natural fracture yields complex structures that include fracture branching, fracture hooking etc.
The novelty of this work lies in the efficient integration of the phase-field fracture propagation models to diffusive natural fracture networks with stochastic representation of uncertainty associated with the prediction of natural fractures in a reservoir. The presented method enables practicing engineers to design hydraulic fracturing treatment accounting for the uncertainty associated with the location and spatial variations in natural fractures. Together with efficient parallel implementation, our approach allows for cost-efficient approach to optimizing production processes in the field.
Acidizing in un-fractured carbonate reservoirs has been well studied through modeling and simulation. Since carbonate reservoirs are often naturally fractured, fractures should be modeled for realistic acidizing operations. We present adaptive enriched Galerkin (EG) methods to simulate acidizing in fractured carbonate reservoirs. We adopt a two-scale continuum model for the acid transport. The coupled flow and reactive transport systems are spatially discretized by EG methods. Fractures are introduced using local grid refinement (LGR) technique. Adaptive mesh refinement (AMR) is implemented around wormhole interfaces. Simulation results show that acidizing in fractured carbonate reservoirs is largely dependent on the fracture system while acidizing in unfractured carbonate reservoirs is mainly determined by operation parameters such as acid injection rate. Computationally, the proposed EG scheme has less numerical dispersion and grid orientation effects than standard cell center finite difference/volume methods. AMR is very efficient to track the wormhole growth and speed up acidizing simulations.
We present and analyze a multirate fixed stress split iterative coupling scheme for coupling flow and geomechanics in a poroelastic medium involving fracture propagation modeled with a phase field approach. The novelty of this work lies in the efficient integration of the fixed-stress split coupling scheme with phase-field fracture propagation models. The multirate coupling algorithm utilizes different time-scales of the flow and mechanics problems, by allowing for multiple finer time steps for flow within one coarse mechanics time step. When applied to production scenarios, the multirate scheme results in massive reductions in the number of mechanics linear iterations, without jeopardizing the accuracy of the obtained results. A number of numerical simulations substantiate our algorithmic developments. These tests include prototype computations, multiple propagating fractures, and fractures initialized by a microseismic probability map.