Geostatistical History Matching Under Training-Image Based Geological Model Constraints

Abstract

Abstract History matching forms an integral part of the reservoir modeling work-flow process. Despite the existence of many history matching tools, the integration of production data with seismic and geological continuity data remains a challenge. Geostatistical tools exists for integrating large scale seismic and fine scale well/core data. A general framework for integrating production data with diverse types of geological/structural data is largely lacking. In this paper we develop a new method for history matching that can account for production data constraint by prior geological data, such as the presence of channels, fractures or shale lenses. With multiple-point (mp) geostatistics prior information about geological patterns is carried by training images from which geological structures are borrowed then anchored to the subsurface data. A simple Markov chain iteratively modifies the mp geostatistical realizations until history match. The method is simple and general in the sense that the procedure can be applied to any type of geological environment without requiring a modification of the algorithm. Introduction Production data brings an important, yet indirect constraint to the spatial distribution of reservoir variables. Pressure data provides information on the average pore volume and permeability connectivity near wells, while fractional flow data informs the extent of permeability connectivity between wells. Production data rarely suffice however to characterize heterogeneous reservoirs, a large amount of uncertainty still remains after history matching of geostatistical models [1]. History matching is an ill-posed inverse problem attempting to invert reservoir properties from measured flow and pressure data. Solutions to such inverse problems are rarely unique which allows imparting other sources of data such as provided by seismic surveys and geological interpretation. The nonuniqueness of the history matching problem is well-known and various techniques have been developed that allow integrating production data with geological continuity information in fine scale geostatistical models2,3,4,5,6,7. Most of these prior geological models reproduce only the covariance as a measure of geological continuity. Covariance models are rarely sufficient to depict patterns of geological continuity consisting of strongly connected, curvi-linear geological objects such as channels or fractures, see for example [8] and [9]. Ideally one would like to possess a single history matching algorithm that can handle diverse type of geological structures. We propose a pixel-based history matching method that can account for a large variety of styles of geological continuity, not necessarily limited to the two-point statistics of a variogram model, or to simplistic Boolean shapes. For that purpose, we borrow ideas from the area of multiple-point (mp) geostatistics. mp-Geostatistics relies on the concept of a training image. The training image quantifies, explicitly, patterns of geological heterogeneity relevant for the subsurface reservoir. A fast sequential simulation algorithm, termed snesim (single normal equation simulation), has been developed that borrows those patterns from the training image and anchors them to local subsurface data. Next, a simple one-parameter Markov chain process to changes the mp realizations until a history match. The transition matrix of this Markov chain is parameterized by a single parameter and modifies gradually and iteratively an initial geological consistent geostatistical realization to match better the production data. The Markov chain is implemented such that the final model honors the imposed training-image based geological structure. We first review some important concepts in mp geostatistics that allows defining a large variety of prior geological models, then develop the proposed history matching methodology.