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.

An Analysis for Simulating Reservoir Performance Under Pressure Maintenance by Gas and/or Water Injection

1968 ◽  
Vol 8 (04) ◽  
pp. 331-340 ◽  
Author(s):  
K.H. Coats
Keyword(s):  
Gas Injection ◽  
Water Injection ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Gas Density ◽  
Flow Equations ◽  
Flow Problems ◽  
Dimensional Flow ◽  
Three Phase ◽  
Compressibility Effects

Coats, K.H., Member AIME, The U. of Texas, Austin, Texas Abstract This paper describes a generalized analysis for calculating three-phase, three-dimensional flow in reservoirs. The analysis handles pressure maintenance type problems where fluid compressibility effects are negligible. A separate analysis for depletion type problems is described in another paper. The calculations consist of numerical, simultaneous solution of the three-flow equations using the iterative alternating direction technique of Douglas and Rachford. The mathematical details are fully described in the Appendix. The analysis is a computerized mathematical model that accounts for gravity, and capillary and viscous forces, and allows arbitrary reservoir heterogeneity, geometry, well locations and rates. A unique aspect of the analysis is the simultaneous solution of only as many difference equations in each grid block of the reservoir as there are mobile phases present. Thus, while the analysis handles phases present. Thus, while the analysis handles three-phase flow, the efficiency of the calculations (in a typical problem where three phases actually coexist only in a minor portion of the reservoir) is four to eight times greater than that of an analysis solving three equations in every block. The program may be applied to two-phase flow problems and to one-, two- or three-dimensional flow problems with negligible loss in efficiency, compared to programs specifically written for these sub cases. This paper also describes several applications of the analysis which illustrate some effects of gravitational and capillary forces in waterflooding of a heterogeneous reservoir. Another application indicates the utility of the program in simulating the fillup stage of water injection into a reservoir containing an initial free gas phase. Computer times and costs for the applications performed are given to indicate the current expense performed are given to indicate the current expense of three-dimensional, three-phase reservoir simulation. Introduction Under pressure maintenance by water and/or gas injection, fluid compressibility effects are generally negligible in producing operations. Although gas compressibility may be appreciable, the maintenance of pressure results in negligible time variation of gas density. In addition, the spatial variation of gas density is usually small in relation to the gas density itself. Producing schemes of pattern or flank waterflood and/or crestal gas injection, therefore, may be simulated with an analysis which presumes fluid incompressibility. presumes fluid incompressibility. The computing efficiency of a numerical model for simulating incompressible fluid flow is as much as 50 percent greater than that of a compressible flow model. Therefore, an analysis for numerically simulating three-dimensional flow of three incompressible, immiscible phases was developed and programmed. programmed. THE MODEL The equations describing three-phase, incompressible flow are the continuity equation and Darcy's law for each flowing phase. Combining these equations and introducing capillary pressures gives the three flow equations: ................ (1a) ............... (1b) SPEJ p. 331

scholarly journals Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods

1997 ◽  
Author(s):  
Wei Ning ◽  
Li He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Nonlinear Effects ◽  
Euler Method ◽  
Time Averaging ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Perturbation Equations

An quasi three-dimensional time-linearized Euler method has been developed to compute unsteady flows around oscillating blades. In the baseline method, unsteady flow is decomposed into a steady flow plus a linear harmonically varying unsteady flow. Both the steady flow equations and the unsteady perturbation equations are solved using a pseudo time-marching method. Based upon this method, a novel nonlinear harmonic Euler method has been developed. Due to the nonlinearity of the aerodynamic governing equations, time-averaging generates extra “unsteady stress” terms. These nonlinear effects are included by a strongly coupled approach between the perturbation equations and the time-averaged equations. Numerical results demonstrate that nonlinear effects are very effectively modelled by the nonlinear harmonic method.

Partial Integration of Equations of Multiphase Flow

1968 ◽  
Vol 8 (04) ◽  
pp. 370-380 ◽  
Author(s):  
John C. Martin
Keyword(s):  
Three Dimensional ◽  
Two Dimensional ◽  
Flow Equations ◽  
Vertical Equilibrium ◽  
The Third ◽  
Dimensional Flow ◽  
Three Phase ◽  
Capillary Pressures ◽  
Third Dimension ◽  
Partial Integration

Abstract Equations for three-phase, three-dimensional, compressible flow (including capillarity) are reduced to two-dimensional relations by a partial integration. This reduction allows three-dimensional flow problems to be treated with mathematics for only two spatial dimensions. The results can be used to formulate flow equations for two-dimensional reservoir simulators i-n which the effects of capillarity and fluid segregation in the third dimension are represented. Such reservoir simulators would retain many of the advantages of two-dimensional simulators while simulating three-dimensional effects. The principal restriction of the method is that the thickness of the reservoir should be small, compared to the distance across the reservoir. Introduction In recent years, computers have been used to calculate performances of many reservoirs. Most of the detailed calculations, however, are based on finite difference solutions of the flow equations, and present day computers are seldom able to handle a sufficient number of cells to produce entirely satisfactory solutions, even for produce entirely satisfactory solutions, even for reservoirs represented by two-dimensional arrays of cells. The simulation becomes much worse when one wishes to approximate the reservoir by a three-dimensional array. A great saving in computation or a more detailed solution can be obtained for many reservoirs by using the partial integration of the equations of flow, presented in this paper. The integration reduces the three-dimensional equations to two-dimensional relations; ant for studies of two-dimensional flows in vertical cross-sections, the equations are reduced to one-dimensional relations. Most reservoir performance calculations currently are based on one- or two-dimensional flow relations. In some cases flow in the third dimension is approximated by assuming a particular type of vertical saturation distribution, such as gravity segregation. The relations developed in this paper approach those for segregated flow as the capillary pressures approach zero, and they approach those for uniformly distributed saturations as the capillary pressures are increased. For this analysis, the ratio of the reservoir's thickness to the maximum distance across it must be small. The capillary pressures between the oil and water should also be small compared to the maximum pressure difference in the reservoirs. It is requirement is met by most reservoirs. It is assumed that the capillary-pressure curves are well defined, whether or not hysteresis effects are included. Also, the reservoir must have sufficient vertical permeability to allow the fluids to segregate. The results presented here provide a firm theoretical foundation to Coats' et al. assumption of vertical equilibrium and extend the relations to three-phase flow. Coats' assumption of vertical equilibrium, which he verified by calculations and experiment, is developed here mathematically from basic flow equations. Discussion SATURATION AND PRESSURE DISTRIBUTIONS Appendix A presents a mathematical analysis of fluid flow in reservoirs where the ratio of thickness to maximum distance across the reservoir is small. The results indicate:that the fluids along any line perpendicular to such a reservoir's upper surface are in antic capillary equilibrium (vertical equilibrium);that, to a first approximation, the fluid pressures and properties are functions of only areal position in the reservoir and time; andthat hydrostatic pressure gradients exist along any line perpendicular to the reservoir's upper surface. The results might be expected after studying several physical considerations. First, no flow is allowed normal to the upper and lower reservoir boundaries, which are relatively close together. SPEJ P. 370

scholarly journals CFD Study of Industrial FCC Risers: The Effect of Outlet Configurations on Hydrodynamics and Reactions

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Gabriela C. Lopes ◽  
Leonardo M. Rosa ◽  
Milton Mori ◽  
José R. Nunhez ◽  
Waldir P. Martignoni
Keyword(s):  
Catalytic Cracking ◽  
Flow Model ◽  
Numerical Study ◽  
Three Dimensional ◽  
Kinetic Scheme ◽  
Operating Conditions ◽  
Fluid Catalytic Cracking ◽  
Geometric Configurations ◽  
Three Phase ◽  
Three Phase Flow

Fluid catalytic cracking (FCC) riser reactors have complex hydrodynamics, which depend not only on operating conditions, feedstock quality, and catalyst particles characteristics, but also on the geometric configurations of the reactor. This paper presents a numerical study of the influence of different riser outlet designs on the dynamic of the flow and reactor efficiency. A three-dimensional, three-phase flow model and a four-lump kinetic scheme were used to predict the performance of the reactor. The phenomenon of vaporization of the liquid oil droplets was also analyzed. Results showed that small changes in the outlet configuration had a significant effect on the flow patterns and consequently, on the reaction yields.

Computation of Unsteady Flows Around Oscillating Blades Using Linear and Nonlinear Harmonic Euler Methods

1998 ◽  
Vol 120 (3) ◽  
pp. 508-514 ◽  
Author(s):  
W. Ning ◽  
L. He
Keyword(s):  
Unsteady Flow ◽  
Steady Flow ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Nonlinear Effects ◽  
Euler Method ◽  
Time Averaging ◽  
Strongly Coupled ◽  
Flow Equations ◽  
Perturbation Equations

A quasi-three-dimensional time-linearized Euler method has been developed to compute unsteady flows around oscillating blades. In the baseline method, unsteady flow is decomposed into a steady flow plus a linear harmonically varying unsteady flow. Both the steady flow equations and the unsteady perturbation equations are solved using a pseudo-time-marching method. Based upon this method, a novel nonlinear harmonic Euler method has been developed. Due to the nonlinearity of the aerodynamic governing equations, time-averaging generates extra “unsteady stress” terms. These nonlinear effects are included by a strongly coupled approach between the perturbation equations and the time-averaged equations. Numerical results demonstrate that nonlinear effects are very effectively modeled by the nonlinear harmonic method.

scholarly journals Fundamental limitations of the mode temperature concept in strongly coupled systems

2020 ◽  
Vol 75 (8) ◽  
pp. 803-807
Author(s):  
Svend-Age Biehs ◽  
Achim Kittel ◽  
Philippe Ben-Abdallah
Keyword(s):  
Heat Transfer ◽  
Heat Exchange ◽  
Strong Coupling ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Strong Coupling Limit ◽  
Strongly Coupled ◽  
Fundamental Limitations ◽  
Temperature Concept ◽  
Vacuum Gap

AbstractWe theoretically analyze heat exchange between two quantum systems in interaction with external thermostats. We show that in the strong coupling limit the widely used concept of mode temperatures loses its thermodynamic foundation and therefore cannot be employed to make a valid statement on cooling and heating in such systems; instead, the incorrectly applied concept may result in a severe misinterpretation of the underlying physics. We illustrate these general conclusions by discussing recent experimental results reported on the nanoscale heat transfer through quantum fluctuations between two nanomechanical membranes separated by a vacuum gap.

scholarly journals Mutual Information and Meta-Heuristic Classifiers Applied to Bearing Fault Diagnosis in Three-Phase Induction Motors

2020 ◽  
Vol 11 (1) ◽  
pp. 314
Author(s):  
Gustavo Henrique Bazan ◽  
Alessandro Goedtel ◽  
Marcelo Favoretto Castoldi ◽  
Wagner Fontes Godoy ◽  
Oscar Duque-Perez ◽  
...  
Keyword(s):  
Fault Diagnosis ◽  
Mutual Information ◽  
Induction Motors ◽  
Operating Conditions ◽  
Industrial Systems ◽  
Bearing Fault Diagnosis ◽  
Bee Colony ◽  
Three Phase ◽  
C4.5 Decision Tree ◽  
The Time Domain

Three-phase induction motors are extensively used in industrial processes due to their robustness, adaptability to different operating conditions, and low operation and maintenance costs. Induction motor fault diagnosis has received special attention from industry since it can reduce process losses and ensure the reliable operation of industrial systems. Therefore, this paper presents a study on the use of meta-heuristic tools in the diagnosis of bearing failures in induction motors. The extraction of the fault characteristics is performed based on mutual information measurements between the stator current signals in the time domain. Then, the Artificial Bee Colony algorithm is used to select the relevant mutual information values and optimize the pattern classifier input data. To evaluate the classification accuracy under various levels of failure severity, the performance of two different pattern classifiers was compared: The C4.5 decision tree and the multi-layer artificial perceptron neural networks. The experimental results confirm the effectiveness of the proposed approach.

scholarly journals Heat Transfer in Rotating Serpentine Passages With Trips Normal to the Flow

1992 ◽  
Vol 114 (4) ◽  
pp. 847-857 ◽  
Author(s):  
J. H. Wagner ◽  
B. V. Johnson ◽  
R. A. Graziani ◽  
F. C. Yeh
Keyword(s):  
Heat Transfer ◽  
Turbine Blade ◽  
Large Scale ◽  
Flow Direction ◽  
Operating Conditions ◽  
Transfer Model ◽  
Transfer Coefficients ◽  
Flow Equations ◽  
Turbine Blade Cooling ◽  
Heat Transfer Coefficients

Experiments were conducted to determine the effects of buoyancy and Coriolis forces on heat transfer in turbine blade internal coolant passages. The experiments were conducted with a large-scale, multipass, heat transfer model with both radially inward and outward flow. Trip strips on the leading and trailing surfaces of the radial coolant passages were used to produce the rough walls. An analysis of the governing flow equations showed that four parameters influence the heat transfer in rotating passages: coolant-to-wall temperature ratio, Rossby number, Reynolds number, and radius-to-passage hydraulic diameter ratio. The first three of these four parameters were varied over ranges that are typical of advanced gas turbine engine operating conditions. Results were correlated and compared to previous results from stationary and rotating similar models with trip strips. The heat transfer coefficients on surfaces, where the heat transfer increased with rotation and buoyancy, varied by as much as a factor of four. Maximum values of the heat transfer coefficients with high rotation were only slightly above the highest levels obtained with the smooth wall model. The heat transfer coefficients on surfaces where the heat transfer decreased with rotation, varied by as much as a factor of three due to rotation and buoyancy. It was concluded that both Coriolis and buoyancy effects must be considered in turbine blade cooling designs with trip strips and that the effects of rotation were markedly different depending upon the flow direction.

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.

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