An Efficient and Practical Workflow for Probabilistic Forecasting of Brown Fields Constrained by Historical Data

Abstract

Brown fields are fields with significant production history. Probabilistic forecasting for brown fields requires multiple history-matched models that are conditioned to available field production data. This paper presents a systematic and practical workflow to generate an ensemble of simulation models that is able to capture uncertainties in forecasts, while honoring the observed production data.The proposed workflow employs the Bayes theorem to define a posterior Probability Density Function (PDF) that represents model forecast uncertainty by incorporating the misfit between simulation results and measured production data. Previous workflows use the Markov Chain Monte Carlo (MCMC) sampling method, which requires an extremely large number (thousands) of simulation runs. To alleviate this drawback, a Proxy-based Acceptance-Rejection (PAR) sampling method is developed in this study to generate representative simulation models that characterize the posterior PDF using hundreds of simulation runs. The proposed workflow can be summarized in five key steps:1. Run an initial set of reservoir simulations by simultaneously varying multiple uncertain parameters using an experimental design method. 2. Construct a proxy function using a Radial-Basis Function (RBF) neural network to approximate the posterior PDF calculated from the initial set of simulation results. 3. Sample the posterior PDF using the PAR sampling method and run an ensemble of new simulation models using the sample values. 4. The new simulation results obtained in step 3 are added to the training datasets generated in step 1 to improve the accuracy of the proxy function. Steps 3 and 4 are repeated until a predefined stop criterion is satisfied. 5. Filter all simulation runs generated in step 3 using appropriate tolerance criteria for various history-match quality indicators. The selected filtered cases constitute the final ensemble of simulation models that can be further used for uncertainty quantification in forecasting.The proposed workflow is demonstrated on two reservoir simulation models:1. Synthetic case. The forecast uncertainty of the ninth SPE Comparative Solution Project (SPE9) simulation model is investigated with a synthetic production history and 32 uncertain parameters. 2. Unconventional oil field case. The workflow is applied to an Eagle Ford shale oil well to determine P90 (conservative), P50 (most likely), and P10 (optimistic) cases of estimated ultimate recovery (EUR).Results of the workflow are compared to those obtained using the Metropolis-Hasting MCMC sampling method. The comparison shows that the proposed workflow only requires 800 simulation runs to obtain results as accurate as the MCMC method with 8000 simulation runs. This translates into a 10times speedup, which makes the proposed workflow practical for many real reservoir simulation studies.

Comparison of Numerical vs Analytical Models for EUR Calculation and Optimization in Unconventional Reservoirs

“…In a recent study, Yang et al (2015) proposed a systematic and practical workflow for probabilistic forecasting of brown fields in the framework of Bayesian inversion, which takes a statistical approach to the history matching problem. That is, rather than trying to find the best parameter values, it computes a probability density for the parameters by calculating the simulation modeling error with respect to the actual measured data.…”

“…The selected subset of history-matched models is then carried forward to the forecast period to quantify the uncertainties of production forecasts. Furthermore, Yang et al (2015) developed a Proxy-based Acceptance-Rejection (PAR) sampling method to alleviate large number of simulation runs required when using Markov Chain Monte Carlo (MCMC) sampling methods.…”

A Mathematical Modelling for Workflows

“…Historically, a model that has been adopted in workflow analysis is the strictly empirical model, in which mathematical methods with discrete variables such as Petri Nets and Milner [21][22][23], or other methods, analyze information with qualitative characteristics [11,18,24,25] and extract indicators [18,24,26,27] that can serve as a reference for a team of managers or professionals responsible for analysis of workflows or research in various fields of work. Other workflow approximations or causality-based concepts have a much more labor-intensive mathematical model [28][29][30][31][32][33] and although useful for some purposes, they may be costly for firms looking for more streamlined process of workflow analysis solutions, but without spending a lot of time required to complete the analyses. ese methods, in some cases, are very useful for analyzing agents and operational procedures from a previous theoretical model or an inductive/intuitive model based on empirical evidence [5,7].…”

Productivity Equation and the m Distributions of Information Processing in Workflows

“…Since an individual might process information given in several different forms (ad hoc expressions), the complex adaptive system can reach a possible margin of work performances (index of performances). The non-linearity of the complex adaptive systems prevents the possibility of comparing a group of individuals with specific and indeterminate cognitive patterns naturally [5,6], and their forms of work, to generate patterns of execution in the workflows of linear or non-linear dimensions [7][8][9][10]. For this empirical limitation, in order to arrange the best productivity, theoretical control methods can be mandatory to conceive the phenomena in its complex nature.…”