A Simple Empirical Pipeline Fluid Flow Equation Based on Actual Oilfield Data

2001 ◽  
Author(s):  
S. Osisanya
Keyword(s):  
Fluid Flow ◽  
Flow Equation ◽  
Fluid Flow Equation

Internal DLA for Cylinders

2014 ◽  
Author(s):  
David Jerison ◽  
Lionel Levine ◽  
Scott Sheffield
Keyword(s):  
Probability Theory ◽  
Fluid Flow ◽  
Continuum Limit ◽  
Free Field ◽  
Flow Equation ◽  
Gaussian Free Field ◽  
Diffusion Limited Aggregation ◽  
Random Lattice ◽  
Diffusion Limited ◽  
Fluid Flow Equation

This chapter discusses the continuum limit of internal Diffusion-Limited Aggregation (DLA), a random lattice growth model governed by a deterministic fluid flow equation known as Hele-Shaw flow. The internal DLA model was introduced in 1986 by Meakin and Deutch to describe chemical processes such as electropolishing, etching, and corrosion. The chapter focuses primarily on fluctuations, and seeks to prove the analogous results for the lattice cylinder. In the case of the cylinder, the fluctuations are described in terms of the Gaussian Free Field exactly. The main tools used in the proofs are martingales. As the chapter shows, the martingale property in this context is the counterpart in probability theory of well-known conservation laws for Hele-Shaw flow.

scholarly journals A mathematical model for identifying the fractional derivative parameter and predicting the results for the fluid flow equation in the well

2021 ◽  
pp. 72-79
Author(s):  
Темирхан Султанович Алероев ◽  
Алла Николаевна Хворова
Keyword(s):  
Mathematical Model ◽  
Fractional Derivatives ◽  
Fractured Reservoirs ◽  
Flow Equation ◽  
Oil Fields ◽  
Coefficient Of Determination ◽  
Experimental Measurements ◽  
Steady State Flow ◽  
Fluid Flow Equation ◽  
The Mathematical Model

В данной статье рассматривается идентификации параметров математической модели, основанной на дифференциальном уравнении с дробными производными. С помощью этой модели описывается установившееся течение в скважине в трещинном деформированном пласте. Рассматриваемая модель может быть использована и при разработке нефтяных месторождений с трещиноватыми коллекторами. Идентификация параметра осуществлялась с помощью оптимизации показателя качества адекватности математической модели - коэффициента детерминации. Также была представлена технология прогнозирования результатов давлений, для области, в которой не проводились экспериментальные измерения. Предлагаемая технология сопровождена расчетами. This article discusses the identification of the parameters of a mathematical model based on a differential equation with fractional derivatives. This model is used to describe the steady-state flow in a well in a fractured deformed formation. The considered model can be used in the development of oil fields with fractured reservoirs. The identification of the parameter was carried out by optimizing the quality indicator of the adequacy of the mathematical model the coefficient of determination. The technology for predicting the results of pressures was also presented, for an area in which no experimental measurements were carried out. The proposed technology is accompanied by calculations.

A Fluid Flow Characterization Device for an Educational Desktop Learning Module

2012 ◽  
Author(s):  
Kirsten L. Peterson ◽  
Marc D. Compere ◽  
Yosef S. Allam ◽  
Bernard J. Van Wie
Keyword(s):  
Fluid Flow ◽  
Core Curriculum ◽  
Volumetric Flow Rate ◽  
Flow Equation ◽  
Control Group ◽  
Fluid Loss ◽  
Educational Goals ◽  
Learning Module ◽  
Hands On ◽  
Volumetric Flowrate

This paper presents the design and testing of a fluid loss characterization device for use in engineering education as a classroom or laboratory demonstration in a core curriculum fluid dynamics course. The design is specifically tailored for clear demonstration of the abstract concept of fluid loss in a way that supports collaborative, hands-on, active, and problem-based learning. This stand-alone device is intended as a prototype for a Desktop Learning Module (DLM) cartridge. The DLM module framework was developed by engineering educators at Washington State University as part of a collaborative NSF-sponsored program. The fluid loss characterization device was sponsored by the Embry-Riddle Aeronautical University Honors Program in Daytona Beach, Florida. The purpose of the experiment is to have students determine the loss coefficients and friction factors of different piping components in a fluid flow system. The experiment involves measuring volumetric flowrate changes in the system due to the introduction of minor and major losses. A pump circulates water at a specified rate tunable by the students to achieve a steady state flow condition. Height sensors report tank heights and a flow meter shows volumetric flow rate which is verifiable with student’s data collection. A graphical computer interface allows students to control pump rate and also reports tank height in real time. The computer and height sensors are not critical to the learning objectives and may be replaced with rulers and a potentiometer for motor control. The educational goals are for students to gain a better understanding of the transition between Bernoulli’s flow equation and the Energy equation, to study major and minor losses, and experimentally determine volumetric flowrate. Fluid flow loss concepts can be reinforced by experimentally verifying these concepts immediately after presenting them on the whiteboard. Educational assessments measuring gains with pre- and post-tests and a conceptual test one week later were performed with a control group and experimental group. Results are presented that allow direct comparison between a hands-on activity versus conventional lecture-based instruction alone. The results indicate no statistically significant differences in gains between control and treatment groups; however the trend indicates improved ability to describe abstract concepts on the material 1 week later in the experiment group. The most promising results show that a greater percentage of students who were actively involved with the demonstration increased their scores from post- to conceptual assessment. This agrees with previously published results on CHAPL [1]. The majority of passive observers showed decreased scores. These results warrant more devices be built and tested to engage the entire class in the hands-on collaborative experiment.

Fluid flow and optical flow

2008 ◽  
Vol 614 ◽  
pp. 253-291 ◽  
Author(s):  
TIANSHU LIU ◽  
LIXIN SHEN
Keyword(s):  
Fluid Flow ◽  
Optical Flow ◽  
Lagrange Equation ◽  
Fluid Velocity ◽  
Flow Equation ◽  
Flow Computation ◽  
Flow Method ◽  
Optical Flow Method ◽  
Optical Flow Computation ◽  
Particle Images

The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding Euler–Lagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet.

Numerical Investigation of Unsteady Laminar in Oscillated Lid–Driven Cavity Flow

2012 ◽  
Vol 58 (2) ◽  
Author(s):  
Arman Safdari ◽  
Ali Akbari Sheldareh ◽  
Mohammad Poortoosi ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Lattice Boltzmann ◽  
Numerical Scheme ◽  
Flow Behavior ◽  
Flow Characteristics ◽  
Cavity Flow ◽  
Flow Equation ◽  
Driven Cavity ◽  
Fluid Flow Equation ◽  
Multiple Relaxation Time ◽  
Boltzmann Method

This article reports the flow characteristics in an oscillated lid–driven cavity. The mesoscale numerical scheme of the multiple relaxation time lattice Boltzmann method is applied to solve for the fluid flow equation. Our predicted results revealed that the flow behavior is critically dependent on the dimensionless Reynolds number and frequency of the oscillated top lid of the cavity.

The Injection of a Hot Liquid into a Porous Medium

1969 ◽  
Vol 9 (01) ◽  
pp. 100-114 ◽  
Author(s):  
J.E. Cheppelear ◽  
C.W. Volek
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Porous Media ◽  
Fluid Flow ◽  
Theoretical Model ◽  
Heat Flow ◽  
Heat Balance ◽  
Flow Equation ◽  
Hot Water ◽  
Physical Models

Abstract The injection of a hot liquid into initially cool porous media, saturated with the same liquid and porous media, saturated with the same liquid and surrounded by two impermeable but beat conducting media (cap and base rock), bas been studied both experimentally and theoretically. The temperature dependence of the viscosity was included in the theoretical model, but it was assumed that the specific heats and densities of the various materials were independent of the temperature. Solutions to the theoretical model were approximated by numerical methods. Both theoretical and experimental results indicate that centerline temperatures are significantly higher than boundary temperatures. Comparison of experimental and theoretical results with a cold/hot viscosity ratio of 19:1 were in reasonable agreement. Theoretical calculations show, that the effect of the temperature dependence of viscosity was very significant at ratios of 100:1 to 1000:1, which are typical of those that occur when injecting hot water to flood heavy oil reservoirs. Introduction We consider the problem of prediction of fluid flow and temperature distribution in an initially cold-fluid-filled reservoir on the injection of the same hot liquid by the use of mathematical and physical models. The results reported are for a physical models. The results reported are for a two-dimensional rectangular section of the reservoir, as shown in Fig. 1. The injection and withdrawal faces are assumed to be equipotentials for fluid flow. The ultimate purpose of such models would be to predict hot-water injection performance. However, we note that in the work presented here, one of the most significant aspects of the problem - the instabilities resulting from two-phase, water and oil flow - is not included. We will not give a historical review, but refer instead to the paper of Spillette and Nielsen, which contains a rather complete bibliography and critical discussion. The physical problem is exactly the same as Spillette and Nielsen, except for certain simplifications in our assumptions. The mathematical details are somewhat different, and we will present the details of our method here. The mass flow equation, which is elliptic in character, is handled by successive overrelaxation. The heat flow difficulty arose in the over-all heat balance due to by a straightforward explicit approximation. Some difficulty arose in the over-all heat balance due to small errors in the solution of the mass flow equation, and we feel that a different formulation of the heat flow equation would be desirable for future work. In addition to the mathematical solutions for the temperature distributions in a porous medium due to the injection of hot liquids, experimental data are presented to check the validity of these solutions. presented to check the validity of these solutions. A schematic diagram of the model is shown in Fig. 2. Certain qualitative physical conclusions were obtained from our numerical and experimental results These are:Assuming high (infinite) conductivity normal to the bedding plane in the reservoir is a poor approximation, and may lead to overestimates of the total heat losses (to cap and base rock) of as much as 50 percent.More heat is retained in the reservoir (per unit of heat injected) for higher viscosity changes.Any particular temperature isotherm moves more rapidly along the centerline for higher viscosity changes. Consequently, the approximation of temperature independent viscosity is not suitable for obtaining quantitatively correct results. MATHEMATICAL MODEL Our mathematical model is that of a reservoir of thickness 2h. The problem is idealized from that of a linear hot-water drive, and we imagine that the input face is sufficiently far away from the injection wells that the stream lines enter it normally. Similarly the production wells are far enough from the outflow face that the flow lines leave it normally. SPEJ P. 100

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