The application of intelligent algorithms that use clever simplifications and methods to solve computationallycomplex problems are rapidly displacing traditional methods in the petroleum industry. The latest forward-thinking approaches inhistory matching and uncertainty quantification were applied on a dynamic model that has unknown permeability model. The original perm-poro profile was constructed based on synthetic data to compare Assisted History Matching (AHM)approach to the exact solution. It is assumed that relative permeabilities, endpoints, or any parameter other than absolute permeability to match oil/water/gas rates, gas-oil ratio, water injection rate, watercut and bottomhole pressure cannot be modified.
The standard approach is to match a model via permeability variation is to split the grid into several regions. However, this process is a complete guess as it is unclear in advance how to select regions. The geological prerequisites for such splitting usually do not exist. Moreover, the values of permeability and porosity in different grid blocks are correlated. Independent change of these values for each region distortscorrelations or make the model unphysical.
The proposed alternative involves the decomposition of permeability model into spectrum amplitudes using Discrete Cosine Transformation (DCT), which is a form of Fourier Transform. The sum of all amplitudes in DCT is equal to the original property distribution. Uncertain permeability model typically involves subjective judgment, and several optimization runs to construct uncertainty matrix. However, the proposed multi-objective Particle Swarm Optimization (PSO) helps to reduce randomness and find optimal undominated by any other objective solution with fewer runs. Further optimization of Flexi-PSO algorithm is performed on its constituting components such as swarm size, inertia, nostalgia, sociality, damping factor, neighbor count, neighborliness, the proportion of explorers, egoism, community and relative critical distance to increase the speed of convergence. Additionally, the clustering technique, such as Principal Component Analysis (PCA), is suggested as a mean to reduce the space dimensionality of resulted solutions while ensuring the diversity of selected cluster centers.
The presentedset of methodshelps to achieve a qualitative and quantitative match with respect to any property, reduce the number of uncertainty parameters, setup ageneric and efficient approach towards assisted history matching.
