A Strongly Coupled, Fully Implicit, Three Dimensional, Three Phase Reservoir Simulator

1979 ◽  
Author(s):  
P.P. Bansal ◽  
A.E. McDonald ◽  
E.E. Moreland ◽  
R.H. Trimble
Keyword(s):  
Three Dimensional ◽  
Strongly Coupled ◽  
Fully Implicit ◽  
Three Phase ◽  
Reservoir Simulator

A Strongly Coupled, Fully Implicit, Three-Dimensional, Three-Phase Well Coning Model

1981 ◽  
Vol 21 (04) ◽  
pp. 454-458 ◽  
Author(s):  
Russell H. Trimble ◽  
A.E. McDonald
Keyword(s):  
Strong Coupling ◽  
Three Dimensional ◽  
Operating Conditions ◽  
Stable Model ◽  
Data Input ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Regulatory Constraints ◽  
Reservoir Flow ◽  
Three Phase

Abstract WELCOS is a robust, three-dimensional, three-phase well coning simulator that couples the well rate equation to the reservoir flow equations. This strong coupling allows well rate to be determined simultaneously with reservoir pressures and saturations. The flexibility obtained permits the use of dynamic constraints on well rates, resulting in a highly stable model. The model may be used to obtain the maximum well productivity for a given set of physical limitations and regulatory constraints e.g., minimum surface pressure, maximum allowed GOR, WOR, water rate, gas rate, etc. The model can function either as a production well or an injection well and, in general, may be used to study any single-well behavior. This paper describes a strongly coupled formulation and discusses its utility in relation to other implicit models. The linearization of the nonlinear finite difference equations and solution of the resulting linear equations are discussed. Example field applications are included to show the utility of user-supplied production constraints in determining well performance. Introduction A number of well coning simulators have been reported in the literature. 1–6 This paper describes a three-dimensional, three-phase well coning simulator that has been in extensive use in our company since 1972. A primary consideration in the development of WELCOS was easy usage by inexperienced users working difficult problems. This demands freedom from stability problems and algorithmic parameters requiring user intervention. This paper emphasizes stability and flexibility of a strongly coupled algorithm. Strong coupling of the production and reservoir flow terms requires simultaneous solution for all unknowns, without auxiliary side calculations or approximations to bring the well rate terms to a desired level of accuracy. This algorithm is computationally more expensive than a sequential formation7,8 but it has several offsetting advantages. Increased stability permits larger time steps than sequential methods, especially for difficult problems. The coupling of the well constraints yields a very reliable model. The user can forecast well potential under assigned operating conditions with a single simulation run. Several trial-and-error runs may be required when operating constraints are uncoupled from the flow equations. The utility of WELCOS is enhanced further by modern concepts of well flow equations.9,10 These include the pseudogas potential function,11 skin factor to account for damage or improvement, non-Darcy flow effect, flow restriction due to restricted entry such as partial penetration, flash surface separation, gas lift calculations, and tubing string pressure losses. Simplicity and flexibility are key features of the data input and output systems. Data input has free-field formatting with a standard structure for all cards. Each card has a mnemonic field for data identification, a control field for processing instructions, and six data fields. Data need not appear in specific columns within fields. All input cards are read and checked for validity (proper mnemonic card names, valid numbers, etc.) and for inconsistencies (such as monotonic table values, negative numbers, etc.). A data processing run will not be aborted when the first error is detected. Processing will continue until as many errors as possible have been found.

scholarly journals A Three-Phase Fundamental Diagram from Three-Dimensional Traffic Data

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 17
Author(s):  
Maria Laura Delle Delle Monache ◽  
Karen Chi ◽  
Yong Chen ◽  
Paola Goatin ◽  
Ke Han ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Time Estimation ◽  
Travel Time Estimation ◽  
Traffic Data ◽  
Fundamental Diagram ◽  
Model Based Clustering ◽  
Three Phase ◽  
Characterization Of Solutions ◽  
Two Phases

This paper uses empirical traffic data collected from three locations in Europe and the US to reveal a three-phase fundamental diagram with two phases located in the uncongested regime. Model-based clustering, hypothesis testing and regression analyses are applied to the speed–flow–occupancy relationship represented in the three-dimensional space to rigorously validate the three phases and identify their gaps. The finding is consistent across the aforementioned different geographical locations. Accordingly, we propose a three-phase macroscopic traffic flow model and a characterization of solutions to the Riemann problems. This work identifies critical structures in the fundamental diagram that are typically ignored in first- and higher-order models and could significantly impact travel time estimation on highways.

scholarly journals Prandtl Number in Classical Hard-Sphere and One-Component Plasma Fluids

Molecules ◽  
2021 ◽  
Vol 26 (4) ◽  
pp. 821
Author(s):  
Sergey Khrapak ◽  
Alexey Khrapak
Keyword(s):  
Prandtl Number ◽  
Hard Sphere ◽  
Solid Phase ◽  
Freezing Point ◽  
Three Dimensional ◽  
Order Unity ◽  
Strongly Coupled ◽  
Dielectric Fluids ◽  
Weakly Coupled ◽  
Component Plasma

The Prandtl number is evaluated for the three-dimensional hard-sphere and one-component plasma fluids, from the dilute weakly coupled regime up to a dense strongly coupled regime near the fluid-solid phase transition. In both cases, numerical values of order unity are obtained. The Prandtl number increases on approaching the freezing point, where it reaches a quasi-universal value for simple dielectric fluids of about ≃1.7. Relations to two-dimensional fluids are briefly discussed.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

Effects of Wheel-Shaft-Fluid Coupling and Local Wheel Deformations on the Global Behavior of Shaft Lines

2002 ◽  
Vol 124 (4) ◽  
pp. 953-957 ◽  
Author(s):  
D. Lornage ◽  
E. Chatelet ◽  
G. Jacquet-Richardet
Keyword(s):  
Three Dimensional ◽  
Fluid Film ◽  
Global Behavior ◽  
Three Dimensional Model ◽  
Fluid Films ◽  
Strongly Coupled ◽  
Proposed Model ◽  
Structural Deformations ◽  
Time Marching ◽  
Fluid Coupling

Rotating parts of turbomachines are generally studied using different uncoupled approaches. For example, the dynamic behavior of shafts and wheels are considered independently and the influence of the surrounding fluid is often taken into account in an approximate way. These approaches, while often sufficiently accurate, are questionable when wheel-shaft coupling is observed or when fluid elements are strongly coupled with local structural deformations (leakage flow between wheel and casing, fluid bearings mounted on a thin-walled shaft, etc.). The approach proposed is a step toward a global model of shaft lines. The whole flexible wheel-shaft assembly and the influence of specific fluid film elements are considered in a fully three-dimensional model. In this paper, the proposed model is first presented and then applied to a simple disk-shaft assembly coupled with a fluid film clustered between the disk and a rigid casing. The finite element method is used together with a modal reduction for the structural analysis. As thin fluid films are considered, the Reynolds equation is solved using finite differences in order to obtain the pressure field. Data are transferred between structural and fluid meshes using a general method based on an interfacing grid concept. The equations governing the whole system are solved within a time-marching procedure. The results obtained show significant influence of specific three-dimensional features such as disk-shaft coupling and local disk deformations on global behavior.

Mixed potential type YSZ-based NO2 sensors with efficient three-dimensional three-phase boundary processed by electrospinning

2022 ◽  
Vol 354 ◽  
pp. 131219
Author(s):  
Siyuan Lv ◽  
Yueying Zhang ◽  
Li Jiang ◽  
Lianjing Zhao ◽  
Jing Wang ◽  
...  
Keyword(s):  
Phase Boundary ◽  
Three Dimensional ◽  
Mixed Potential ◽  
Potential Type ◽  
Three Phase ◽  
Three Phase Boundary
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