Reservoir Uncertainty Quantification Using Probabilistic History Matching Workflow

Abstract

Understanding and capturing the uncertainty of the reservoir are keys to predicting its performance and making operational decisions. Conventional industry practices with a single or three (high-mid-low case) models have little ability to describe the full complexity of subsurface uncertainty and often yield poor performance in forecasting. To improve our understanding of the effect of reservoir uncertainty in performance, we need to use an ensemble of models which spans the full space of the uncertain parameters. These parameters may range widely from global parameters, such as water-oil contact and fault transmissibility, to cell-based properties, such as heterogeneous permeability and porosity. While it is ideal to explore all the possible parameter combinations, doing so can easily result in millions of models and become impractical for history matching and forecasting purposes. In this work we present a two-step history matching workflow where the uncertainties in the local heterogeneity and global parameters are investigated sequentially and yet in a manageable manner. The workflow begins with a geological model built based upon available information. The local geological heterogeneity, which cannot be readily determined from the information such as seismic images or well logs, is examined in the first step of the workflow. We create an ensemble of 103 to 105 models which span the uncertainty space for properties like permeability, porosity and/or net-to-gross but all are constrained to geostatistical data such as ranges, standard deviations and variograms. To effectively reduce the ensemble size, we implement the dynamic fingerprinting technique, a method based on streamline information (time of flight or drainage time), to screen and cluster the models. The concept behind this methodology is that for each distinct property realization, a given production schedule will generate a flow pattern which, like a fingerprint, is unique to that realization. This method is highly efficient since the time required to obtain the characteristic flow pattern is significantly shorter than the time of interest (typically the whole production history). The fingerprints from individual realizations are collected and clustered according to their principal flow pattern through single value decomposition. Each cluster aggregates a set of model realizations that despite their apparent difference in the model space, all correspond to similar principal flow trends. A single representative is then chosen from each cluster. The second step of the workflow aims to examine the uncertainties of the global parameters. For each representative obtained from the first step, we implement the standard workflow for Design of Experiment and proxy modeling to construct response surfaces as functions of global parameters. Algorithms such as Markov Chain Monte Carlo are then implemented to perform vast sampling and condition the models to the history data. The end result is a small set of models that are based on realistic geology, preserve flow-relevant subsurface uncertainty, and are conditioned to production data. The proposed workflow, which can be referred to as the probability history matching (PHM) workflow, provides an efficient and effective way to select representatives and condition to historical data. The selected models can be used for making forecasts and support development planning under uncertainty. An application of this workflow is shown on a real-world field example.

Flow-based dissimilarity measures for reservoir models: a spatial-temporal tensor approach

“…The SVD-based approach presented in Section 2 has been adopted in industrial practice, [41], but it has some limitations. Through the vectorized form in which flow variables are stored, the spatial-temporal structure of the reservoir is lost.…”

“…Compact representations of s(x, t k ) are important for an efficient and fast numerical calculation of distance measures, see [41]. A typical way to construct lower dimensional representations of s(x, t k ) is obtained by utilizing a basis function expansion for the set of flow variables over all grid cells:…”

“…While streamline simulators have been used to generate a fast characterization of the cumulative production rates (see, e.g., [27,32], and [30]), they have also led to a technique called dynamic fingerprinting ( [41]), where streamline information (time-of-flight (TOF) or drainage time) is used to generate flow patterns that are, like a fingerprint, unique to each realization. Then, fingerprints are used to screen and cluster reservoir realizations with similar dynamical performance.…”

“…The large dimensionality of these structures would make them unsuitable to serve as a dissimilarity measure for performing model discrimination and clustering, and therefore reduced-order representations are necessary. Previously, [9,26] and [23] have used the singular value decomposition (SVD) and POD model order reduction techniques to arrive at low dimensional representations of flow variables, while [41] have used SVD to represent the fingerprints through a reduced set of basis functions. However, the SVD approach has some limitations.…”

Assisted History Matching of Channelized Models by Use of Pluri-Principal-Component Analysis

“…With nodes of the triangles representing the surface of a channel, Rahon et al (1997) conditioned geological bodies to production data. By parameterizing the location of the central line, the width, and the thickness of a channel all along the channel length, Bi et al (2000) and Zhang et al (2002) investigated methods of conditioning 3D stochastic channels to pressure data by use of the gradientbased optimization methods. Their methods worked quite well for a reservoir with a single channel.…”