Uncertainty in Production Forecasts Based on Well Observations, Seismic Data, and Production History

Abstract

Summary A stochastic model in a Bayesian setting, conditioned on well observations, seismic amplitude data and production history, is defined. Samples of reservoir characteristics and production forecasts from the posterior model are used to evaluate the impact of various observation types. Well observations are found to be important to production forecasts due to near-well conditioning, while seismic data impact facies geometries but not the production forecasts. Production history contributes significantly only if certain events, such as gas-breakthrough time, are observed in wells. A brute-force rejection sampling approach may work well if proper conditioning on well observations and seismic data is done. Introduction The objective of reservoir evaluation is to forecast production characteristics under various recovery strategies and eventually decide on a management strategy. The forecasts should be as accurate as possible; therefore, both general reservoir knowledge and reservoir-specific observations should be used in the evaluation. General reservoir knowledge includes geologic understanding, physically based models for fluid flow, and insight into the data acquisition procedures. The reservoir-specific observations include well observations, seismic amplitude data, and production history collected from the reservoir under study. In Omre and Tjelmeland,1 a Bayesian approach to integrated reservoir evaluation is presented. Stochastic reservoir modeling based on geologic knowledge and well observations only has evolved over the last two decades. Inclusion of seismic amplitude data has been an active field of research the last few years (see Bortoli et al.2 and Eide et al.3). In order to represent uncertainty, seismic inversion must be a part of the model. History matching of production data has only recently been phrased in a stochastic setting (see Oliver,4 Wen et al.,5 and Hegstad and Omre6). This requires the use of a fluid-flow simulator, which normally needs considerable computer resources to run. The current paper integrates all these sources of information in a framework defined along the lines of Omre and Tjelmeland.1 A graphical model is introduced to communicate the model assumptions more easily to the user. Models and algorithms developed in Eide et al.3 and Hegstad and Omre6 are integrated and applied to a case study inspired by the Troll field in the North Sea. The focus of the paper is to evaluate the contribution of the well observations, seismic-amplitude data, and production history to the reduction of uncertainty in the production forecasts. Conditioning to the production history constitutes a major challenge due to the nonlinearity of the fluid-flow model. The study also sheds some light on which sampling algorithms are suitable for this conditioning. The study is thoroughly documented in Hegstad and Omre,7 in which further details can be found. Reference Reservoir and Production The reference reservoir and the recovery strategy are related to the Troll field in the North Sea offshore Norway (see Eide et al.3). This is a multilayer reservoir with alternating C-sands and M-sands having high- and low-permeability properties, respectively. The reservoir is represented in a 3D domain being 104×104×102 feet3 then discretized into a (50×50×15) - grid termed LD. The primary interest of the study is the future production, being crucially dependent on the reservoir variables of porosity and absolute log-permeability. The acoustic impedances and seismic-reflection coefficients are introduced as support variables. This multivariate spatial reservoir variable, rt, is defined as a high-dimensional vector on the grid LD, with indexes (f,k, z, c) indicating porosity, absolute log-permeability, acoustic impedance, and seismic reflection coefficients respectively. Index t indicates that it is the reference reservoir. The lateral-vertical anisotropy in permeability is 1:600. A more detailed description of the construction can be found in Hegstad and Omre.7 The cross section of the reference reservoir, displayed in Fig. 1, shows distinct layering. The histograms and cross plots of the reservoir variables in Fig. 2 display definite bimodality and clustering. The reference reservoir variables have characteristics far from Gaussian. Initially, oil is assigned every where, and the reservoir is in pressure equilibrium before start of production (i.e., no fluid movements in the reservoir prior to production start). For further details and other fluid characteristics, see Hegstad and Omre. 7 The recovery strategy is based on the injection of gas in one vertical well perforated in the upper layers and the production through two horizontal wells (see Fig. 3.) The reference production is generated by the fluid-flow simulator Eclipse100 (see GeoQuest8) on a (10×10×15) laterally upscaled grid. The permeability characteristics are upscaled by harmonic averaging, while all other variables are upscaled by arithmetic averaging. The oil production-rate and gas-oil ratio in the two producing wells and the bottomhole pressure (BHP) in the injection well are monitored monthly for 16 years, or 5,840 days. This is represented by the time vector on L T (see Fig. 4). Note that gas breakthrough appears after about 3 years and that the plateau production is reached in about 5 years. Stochastic Model and Simulation The stochastic model consists of two components: a prior model for the reservoir and production variables and a likelihood function model for the reservoir-specific observations available. The stochastic model is graphically displayed in Fig. 5. The variables and the relations in this graph will be defined in this section.

Ensemble Kalman filtering with shrinkage regression techniques

“…The example is similar to the reservoir model used in Hegstad and Omre [18], although the prior models for the porosity fields, φ, and ln-permeability, κ, are different.…”

Bayesian calibration of hydrocarbon reservoir models using an approximate reservoir simulator in the prior specification

“…This case study was first introduced in Hegstad and Omre (2001), and later used in Omre and Lødøen (2004). The reservoir under study covers a domain of size 10 4 ×10 4 ×10 2 feet 3 , and is discretised onto a lattice of size 50×50×15.…”

“…The wells operate under a set of constraints, which we discuss below. Hegstad and Omre (2001) define a Bayesian model to evaluate the production forecast conditioned on static data (seismic data and well observations) and dynamic data (observed production history) through a brute-force rejection sampling algorithm. They also useω(·) as an approximation to ω(·) without considering the bias thereby introduced.…”

“…This makes the reflection coefficient non-Gaussian. Details on the construction of the reference reservoir is given in Hegstad and Omre (2001).…”

“…The prior model for the reservoir properties is defined hierarchically, where the prior for porosity and permeability depend on the seismic reflection coefficient. A complete definition of the prior model is given in Hegstad and Omre (2001). The model parameters, including means, correlation lengths and standard deviations, are the same as the ones used by Omre and Lødøen (2004).…”