Reservoir history matching using constrained ensemble Kalman filtering

Abstract

The high heterogeneity of petroleum reservoirs, represented by their spatially varying rock properties (porosity and permeability), greatly dictates the quantity of recoverable oil. In this work, the estimation of the spatial permeability distribution, which is crucial for predicting the future performance of a reservoir, is carried out through a history matching technique based on constrained ensemble Kalman filtering (EnKF). The main contribution in this work is the novel implementation of hard and soft constraints in the recursive EnKF estimation methodology for petroleum reservoirs. Hard data is obtained from the actual values of the reservoir parameters at discrete locations obtained by core sampling and well logging, while the soft data considered is obtained from correlograms, which characterize the spatial correlation of the rock properties in a reservoir. In each time update, the parameter estimates obtained from the unconstrained EnKF are modified by one of two novel algorithms. In the first, the correlation matrix obtained after the unconstrained EnKF update is transformed to honour the true correlation structure from the correlogram by applying a projection-based method. The second algorithm involves the use of a technique for soft constrained covariance localization. We observe that the soft data constrained localization method results in the best estimates of the permeability and also reduces the computational time significantly. We quantify the improvement in estimation performance of each of the constrained methods over unconstrained estimation. The method, while developed for estimation in petroleum reservoirs, is also generally applicable to systems with spatial heterogeneity and underlying spatial correlations.

Constrained State Estimation -- A Review

“…Raghu et al introduced two algorithms to incorporate the constraints into the EnKF [78]. The first algorithm uses the projection-based method.…”

Modelling temperature dynamics of the SAGD process in an oil reservoir by the discovery of parametric partial differential equations

“…Geostatistical simulation packages use algorithms to generate spatial properties. [23] They can be classified as geostatistical estimation algorithms and geostatistical simulation algorithms. The estimation algorithms are used to obtain unbiased estimates of the reservoir properties such as porosity and permeability using interpolation techniques.…”

Wavelet-Based Kalman Smoothing Method for Uncertain Parameters Processing: Applications in Oil Well-Testing Data Denoising and Prediction

“…It is not only widely used in the fields of medical [ 25 ], aviation [ 26 ], geology [ 27 ], and disaster prediction [ 28 ], but also plays an important role in evaluating oil well reservoir parameters [ 29 , 30 ], model parameter correction [ 31 , 32 ], and reservoir dynamic monitoring [ 33 , 34 ]. To improve the performance of reservoir prediction, Raghu [ 35 ] used a Kalman filter to estimate the spatial permeability distribution. Xue [ 36 ] used the Kalman state-space model to correct the triaxial parameters near the bit.…”