Development of Surrogate models for CSI probabilistic production forecast of a heavy oil field

Abstract

The aim of this work is to present the development of a Surrogate Reservoir Model capable of accurately predicting cumulative oil production of a heavy oil field in Mexico considering variables with uncertainty. Five numerical models of wells were considered for the numerical model of the field. Four input uncertain variables (the dead oil viscosity with temperature, the reservoir pressure, the reservoir permeability and oil sand thickness hydraulically connected to the well) were selected as the ones with more impact on the initial hot oil production rate according to an analytical production prediction model. The central composite experimental design technique was selected to capture the maximum amount of information from the model response with a minimum number of reservoir models simulations. Twenty five runs were built to be run with the STARS simulator for each well type on the reservoir model. The results show that Surrogate Reservoir Models are an ideal tool to perform real-time probabilistic production forecasting of the reservoir.

Introduction

One of the objectives of reservoir engineers is to build reliable reservoir models to be used by reservoir managers in order to make decisions. The modeling and simulation of reservoirs is a critical step in the planning and development of oil fields. Numerical reservoir simulation has become an industry standard tool for hydrocarbon reservoir management. It is now used in all phases of field development in the oil and gas industry.

Before a reservoir model can be accepted for the forecast of future production, the model has to be updated with historical production data. On the other hand, the quality of the data used to construct the reservoir model is most of the time poor, leading to a high uncertainty of production forecasts.

As the reservoir models (RMs) run in a wide variety of time scales, several hours or even days, the problem intensifies when we realize that in many cases, the uncertainty of several variables has to be considered in order to make reliable forecasts. Then sensitivity analysis of uncertain variables and probabilistic forecasting and risk analysis become a must and several RMs runs must be made for different combinations of uncertain variables values.

Typical uncertainty analysis techniques require many realizations and runs of the reservoir model. In the day and age that reservoir models are getting larger and more complicated, making hundreds or sometimes thousands of simulation runs can put considerable strain on the time and computational resources to make these types of analyses.

Surrogate Reservoir Models (SRMs) are prototypes of the RMs that can run in fractions of a second rather than in hours or days. If properly designed, they can mimic the capabilities of the RM with high accuracy. SRMs are attractive tools to be used as an efficient substitution of RMs. The SRM is built on the basis of modeling the response of the reservoir simulator with a limited number of cases chosen intelligently. It is not necessary to know how the simulation code operates (or even to understand it), only the input–output behavior of the reservoir model is important. SRMs can be developed regularly off-line as new versions of the RMs become available, and can efficiently be used for forecasting behavior under uncertainty conditions as well as for real-time decision making.

Consequently, to improve the confidence of production forecasts, a methodology is introduced, based upon Surrogate Reservoir Models, to build replacements for the reservoir model.

The aim of this work is to present the construction and use of Surrogate Reservoir Models (SRMs) capable of accurately predicting cumulative oil production for every well stimulated with cyclic steam injection (CSI) at any given time in a heavy oil reservoir in Mexico considering variables with uncertainty. There is extensive literature (from 1992 to 2017) on surrogate models in petroleum area concerning the use of SRMs as prototypes of the RMs. In the appendix A a survey of some publications [1], [5], [8], [9], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38] related to the aim of this work is presented. Also the main results known so far in some of them are shown. Section 2 describes the reservoir in terms of crude oil type, API density, viscosity, depth and pressures. Additionally, the numerical models of wells considered are listed (conventional CSI, selective CSI and horizontal CSI for an extra heavy and a heavy reservoir). Section 3 is dealing with the variables that have the greatest influence on the production behavior (the dead oil viscosity with temperature, the reservoir pressure, the reservoir permeability and oil sand thickness hydraulically connected to the well). Section 4 details the numerical model associated to each well type to be performed with the STARS simulator [10]. Section 5 describes the construction of the surrogate reservoir models. The central composite experimental design technique was selected to capture the maximum amount of information from the model response with a minimum number of reservoir models simulations. Also, the relative error in norm 2 on how the surrogate model approximates the reservoir model for all the runs and for each of the well models is reported. Section 6 discusses the construction of the field-to-study model, based on the surrogate reservoir model of each well type and the activity of the wells for a period of 15 years. Finally, in Section 7, the conclusions of this work are listed.