Probabilistic Flows Research Articles

Optimal Transport in Systems and Control

Optimal transport began as the problem of how to efficiently redistribute goods between production and consumers and evolved into a far-reaching geometric variational framework for studying flows of distributions on metric spaces. This theory enables a class of stochastic control problems to regulate dynamical systems so as to limit uncertainty to within specified limits. Representative control examples include the landing of a spacecraft aimed probabilistically toward a target and the suppression of undesirable effects of thermal noise on resonators; in both of these examples, the goal is to regulate the flow of the distribution of the random state. A most unlikely link turned up between transport of probability distributions and a maximum entropy inference problem posed by Erwin Schrödinger, where the latter is seen as an entropy-regularized version of the former. These intertwined topics of optimal transport, stochastic control, and inference are the subject of this review, which aims to highlight connections, insights, and computational tools while touching on quadratic regulator theory and probabilistic flows in discrete spaces and networks.

4D Seismic With Reservoir Simulation Improves Reservoir Forecasting

This article, written by JPT Technology Editor Judy Feder, contains highlights of paper SPE 191521, “Quantitative Integration of 4D Seismic with Reservoir Simulation,” by Sarath Pavan Ketineni, SPE, Subhash Kalla, SPE, Shauna Oppert, SPE, and Travis Billiter, SPE, Chevron, prepared for the 2018 SPE Annual Technical Conference and Exhibition, Dallas, 24–26 September. The paper has not been peer reviewed. Standard history-matching work flows use qualitative 4D seismic observations in reservoir modeling and simulation. However, such work flows lack a robust framework for quantitatively integrating 4D seismic interpretations. Four-dimensional, or time-lapse, seismic interpretations provide valuable interwell saturation and pressure information. Quantitatively integrating these data can help constrain simulation parameters and improve the reliability of production modeling. This paper outlines the value of 4D for reducing uncertainty in the range of history-matched models and improving the production forecast. Introduction Reservoir-simulation models play an essential role in generating optimal field-development strategies, but they need to be history-matched before they can be used for reliable forecasting. Traditional history matching of a reservoir involves matching observed production and pressure data at well locations by changing the uncertain parameters in the reservoir model within the acceptable range. The parameters can be classified broadly as static and dynamic. Static parameters include permeability, porosity, and net to gross, among many others. Dynamic parameters may include oil/water contacts, fault transmissibilities, relative permeability curves, and flow pathways. Deterministic modeling focuses on a single scenario of the reservoir model, ignoring the effect of uncertainty in the parameters considered. Probabilistic history matching is the process of selecting non unique and multiple history-matched reservoir models by altering the uncertain static and dynamic parameters to obtain a range of possible forecasts. Typically, in probabilistic work flows, objective functions composed of a combination of differences in measured and simulated bottomhole pressure data and individual fluid-phase flow rates are used to identify significant factors or uncertainties. The functions are typically based on surveillance data obtained at well locations and therefore may not be sensitive to key reservoir uncertainty away from wells. A good match with production data for a given reservoir model does not ensure robustness in making performance forecasts. Reservoir heterogeneities—high-permeability pathways, barriers and baffles, or vertical connections forged from geologic erosion—can significantly affect drainage and swept patterns and well-production forecasts. Especially during early stages of field production, history matching to pressure and fluid-rate production data often lacks information necessary to resolve these critical heterogeneities fully, which may significantly affect production. Even a well-posed probabilistic history-matching approach cannot incorporate the variety and complexities of heterogeneities that are yet to have a strong imprint on future production because of insufficient data away from wells and the sheer number of static and dynamic uncertainties that can affect production.

Implications of medium-range numerical weather model output in hydrologic applications: Assessment of skill and economic value

Integrating medium-range numerical weather model output into hydrologic models has been shown to yield useful information. The emphases in this study were to (i) develop effective mechanisms for integrating meteorological ensemble systems into hydrologic forecasts; and (ii) evaluate the skill and economic values of the subsequent hydrologic forecasts. The general framework was demonstrated under a number of conditioning paradigms for the Chute-du-Diable watershed located in Quebec, Canada. For this purpose, two downscaling models were employed to generate station total daily precipitation and average daily temperature. The performances of the downscaled outputs were compared against the raw model output using suites of diagnostic measures. The comparative results indicated that the downscaled outputs yielded more accurate and realistic forecasts than the raw model output. These outputs were then forced into an HBV hydrologic model in order to generate flow forecasts up to 14 days ahead. The approach effectively generated deterministic and probabilistic flows. The subsequent simulation results revealed that the downscale-based flows yielded greater skill values than the raw-based flows. The potential economic values of flow forecasts were assessed based on a simple optimal decision-making, cost–loss analysis technique. The principal outcomes emerging from the analyses include: (i) the economic benefits associated with probabilistic flow forecasts were more useful than their deterministic counterparts; and (ii) the downscale-based flow forecasts offered greater benefits, which are applicable to a much wider range of users, than the raw-based flow forecasts. The findings of the present study clearly illustrate the potential added value that may be obtained as a result of adequate downscaling, as opposed to using the raw model output, for hydrologic applications.

Generalized flow-interception facility location models with probabilistic customer flows

Flow-intercepting facilities are facilities such as gas stations and advertising billboards, which provide “service” to passing-by customer flows. Customers that pass by such facilities are said to be intercepted. A typical objective in locating these facilities is the maximization of the total customer flow intercepted. We consider two new models for locating flow-intercepting facilities on a network. Both models use only information on the fraction of customers travelling from any node to any adjacent nodes and the fraction of customers that start their travel at any given node. This information is more practical to obtain than the complete path flow information required by existing models. The trade-off for using this reduced data set is the loss of equivalence with the path-flow based models. However, a set of computational experiments shows that the proposed models can be regarded as an approximation of the existing ones. In the first model, repeat visits by a customer to the facilities (e.g., billboards) increase the value of the objective function, but at smaller rates each additional time. In the second model, only the first visit by a customer to any facility contributes to the objective function (e.g., gas stations), and only a fraction of customers travelling through a facility node can be intercepted by the facility. The models are initially formulated as nonlinear integer programs. By employing the theory of total-reward Markov decision processes with side constraints, much more tractable formulations as linear integer programs are derived. The paper also contains some additional results on the efficient solution for a special case of the first model, and on the connections between the two models

Optimal Screening Plans for Nonserial Production Systems

Quality control screening programs are defined and evaluated for the general n-stage nonserial production process. A total expected cost criterion, developed as a function of the screening applied at each inspection station, embraces the various costs of inspection, defect repair and defects passing through the process undetected. Absorbing Markov chains aid in the identification of probabilistic flows of defective materials through the production network. Minimum cost screening programs are developed, giving the optimal level of screening at every potential inspection station. For a quasi-concave cost structure, it is shown that the optimal screening program will employ either zero or 100 percent effective screening throughout. A standard branch and bound “backtrack” strategy readily identifies optimal screening programs for the unconstrained (0, 1) nonlinear integer programming problem. An illustrative problem is presented.