Pressure Loss Equations Research Articles

Improving drilling\xa0hydraulics estimations-a case study

Accurate pressure drop estimation is important for drill string and bit nozzles design and optimized fluid circulations as well as identifying the drilling problems such as bit nozzle(s) washout or plugging. In this study, the Bingham Plastic model has been modified by applying a coefficient to its turbulent pressure loss calculations. This coefficient encompasses the effects of the drill pipe tool joints and other effects in estimation of pressure losses. The range of the coefficient was determined in field applications for different hole sizes and mud types. The results showed that applying a correction coefficient of 1.08–1.12 to turbulent pressure loss equations (depending on borehole size and mud type) improves the pressure loss estimation. By applying this coefficient, the estimated pressure losses are increased to compensate the under-estimation of the Bingham Plastic model. This is considered a significant contribution to accurate calculation of borehole hydraulics and in-time detection and identification of borehole problems and reduction of invisible lost time. The findings also showed that this enhanced effect is independent of the mud type. The use of this coefficient removes the necessity of using rather complex mud rheological models such as the Herschel–Bulkley model.

Optimal power and gas flow for large-scale transmission systems

The integrated modeling of power and gas systems gains importance as a result of increasing interdependencies due to bidirectional coupling in renewable energy systems through power-to-gas and gas-fired power plants. The optimal power and gas flow problem (OPGF) aiming to minimize system dispatch costs is mostly applied to small test systems. However, to investigate system-wide effects of sector coupling, large-scale transmission grids must be considered. Due to nonlinearities especially in the pressure loss equation, a nonlinear optimization problem results. This paper aims to demonstrate that successive linear programming, in contrast to other discussed approaches, is suitable for solving large-scale and multi-period OPGF-problems. The presented approach shows high solution quality despite short computing time even for large-scale systems such as the German power and gas transmission grid.

Research on the change law of annulus flow pressure loss under the condition of arc concave borehole in cementing

The exact calculation and control for cementing annulus flow pressure is very important, especially for formations with narrow density windows. It is easy to form belly shaped arc concave boreholes because of the uneven hole enlargement rate in the process of practical drilling. Research on the change law of annulus flow pressure loss in an arc concave borehole is helpful for controlling the annulus pressure profile accurately. The structure of flow pressure loss is analyzed through the establishment of a flow pressure loss equation in an arc concave borehole; the fluid flow control equation is established, the solving method is studied, the analysis software is developed, the flow pressure loss is calculated, the influence law of hole enlargement rate and fluid displacement on the flow pressure loss are analyzed, and the results are verified by numerical simulation software, Fluent. The results show that the flow pressure loss in arc concave borehole sections is less than that in normal boreholes within the scope of common hole enlargement rates. The offset between software calculation results and numerical simulation results are in the scope of engineering allowable error. The conclusions provide a powerful technical reference for analyzing cementing annulus pressure characteristics accurately.

Numerical Study of Viscous Fluid Flows in a Kenics Static Mixer

Since many years static mixers find usage in chemical, food, cosmetic and pharmaceutical industry. One of the most commonly used is the Kenics type static mixer. In a framework of the current work the CFD simulation for Kenics static mixer were performed. In food or cosmetic industry one must deal very often with non-Newtonian fluids. Therefore this work concerns the numerical study of non-Newtonian fluid flux in a kenics km static mixer with laminar flow using the Navier-Stocks equation governing the phenomenon and the pressure loss equation. This simulation was made using the computational fluid dynamic software (CFX 12.0). In this paper we studied the influence of the Reynolds number, the viscosity of the fluid, aspect ratio and the number of helical elements fixed on the pressure drop. It was found that the CFD results of pressure drop for non-Newtonian power law was similar to literature data (the correlation of C.D.GRACE 1971 and the numerical simulation of E.SAATDJIAN 2012).

A dynamic model for the oscillatory regime of liquid rise in capillaries

The oscillatory regime for liquid rise in vertical capillaries has been observed but the analytical solution that can be applied for this regime is still in shortage. Some lack terms in the existing analytical solutions make them show deviations when predicting the oscillatory behavior of liquid rise. An improved dynamic model is built in this work for the oscillatory regime. Two main contributions are made, concerning the non-equal pressure losses at the entrance for liquid rise and fall, and the receding dynamic contact angle for the regions with negative capillary numbers. Experiments are performed to correlate the empirical parameters in the submodels and to validate the combined dynamic model. Good accuracies of the present model are obtained by comparing with the experimental data both in literature and from the present study. Inclusion of the non-equal pressure loss equations for the end effect makes the model well capture the high asymmetry of oscillations, while the two-stage dynamic contact angle models correct the local bouncing of the meniscus. The dynamics of liquid in the oscillatory regime is discussed by comparing the contribution of each pressure force. Occurrence criteria of the oscillatory regime is obtained through a non-dimensional analysis. It is shown that the oscillatory regime is affected not only by the combined parameter (ω), but also by the immersed height of tube (H0) and the pressure head loss coefficients (ξ).

Design of Pneumatic Rotor Pump Mechanism and Dynamics Analysis

To meet the special needs of the bolting and shotcreting work environment of coal mine, a new pneumatic spring-piston mechanism was designed. The derivation process of the pressure loss equation was described based on S.Morinaga formula. The concrete pumping machanism kinetic model was constructed and analysed using Lagranges Equation. The work of this paper lays a theoretical foundation for optimization design of wet spraying machine system.

Discharging Behavior of Single and Two-Phase Flow through Safety Valve

The discharging flow rate from safety or relief valves is restricted with the minimum flow area between disk and seat. The flow rate is usually smaller than the calculation with the minimum flow area due to the vena contraction. The discharging flow rate of water was measured at different valve lifts and seat configurations. The water flow rate was affected with the lift and seat configuration due to the different formation of vena contraction. The air and air-water two-phase discharging flow rate were also measured and compared with the non-equilibrium or slip flow model. The air flow rate was affected not only with the vena contraction but also with the delay of expansion. The two-phase flow rate was affected with the slip velocity between air and water. It was suggested that the vena contraction of two-phase flow was mitigated with the oscillatory flow behavior. The two-phase discharging flow rate was well correlated with the simple pressure loss equation. The single and two-phase discharging behavior was carefully observed by using the transparent disk.

An Effective Method for Modeling Non-Moving Stagnant Liquid Columns in Gas Gathering Systems

Abstract Gas gathering system modeling is often complicated by the presence of localized pressure losses that are not easily explained by traditional pressure loss correlations. The tendency is to assume the pressure loss correlation must be tweaked to match measured operating conditions. This often leads to inappropriate manipulation of tuning factors (efficiency factor or roughness). A more appropriate approach is to recheck the validity of the input data and, most importantly, visit the field prepared to gather additional data to resolve the causes of the localized pressure losses. The objectives of this paper are to discuss one of the causes of localized pressure losses —Stagnant Liquid Columns —and to present several cases where localized pressure losses were interpreted to be caused by stagnant liquid accumulations. Introduction The maturation of the gas gathering systems throughout North America has resulted in the majority of systems being operated well below their original design conditions. Consequently, it is common to encounter pressure losses that exceed those predicted by steady-state single-phase and two-phase correlations. The reasons for these pressure losses are varied and most often relate to measurement issues, poor understanding of the pipeline and facility connections and sometimes non-moving liquid accumulations called stagnant liquid columns. Liquid accumulations are a concern because their continuous removal is difficult and they increase backpressure for all upstream wells, which reduces well deliverability and can result in localized pipeline corrosion. One would think that the traditionally used steady-state two-phase pressure loss equations would be capable of predicting the pressure loss that occurs in these liquid accumulations. However, the steady-state flow of fluid must be, by definition, continuous: inlet rate equal to outflow rate. If the liquid enters the conduit and accumulates while the gas continues through, we no longer have steady-state flow and the validity of the correlation no longer holds. It has been the authors' experience that localized pressure losses are often associated with liquid accumulations. Typically, field staff usually know there is a problem and may or may not have already realized that it is due to liquids, but it is usually a surprise for head-office staff because there is little or no liquid production reported. This leads to the question, how do we reliably identify stagnant liquid columns and how should they be modeled? To answer this question, a discussion of recommended modeling procedures is required. Discussion Pressure Loss Categorization The existing steady-state pressure loss correlations generally do a very good job of estimating pressure losses when used appropriately. Consequently, a comparison of simulated line pressures with field measured line pressures should result in a reasonable match within a preset tolerance. Measured line pressures that do not match modelled line pressures must be scrutinized closely to determine the cause of the mismatch, rather than relying primarily on tweaking tuning factors such as pipeline roughness or flow efficiency. For wells or groups of wells where a reasonable match is not initially obtained, it is good practice to begin by attempting to classify the unmatched pressure losses as either a systemic or localized step pressure loss problem before making changes to the model to force a match.

Pressure Loss Equations for Laminar and Turbulent Non-Newtonian Pipe Flow

The equations that define Newtonian pipe flow are well established and used routinely by engineers and scientists throughout the world. The same cannot be said for non-Newtonian flows, which have a higher degree of complexity. This paper presents a coherent set of equations for the laminar and turbulent flow of Herschel-Bulkley fluids. These equations are consistent with those used for Newtonian fluids and previous work on the behavior of generalized non-Newtonian fluids. A numerical model for non-Newtonian flows is discussed and has been compared with experimental measurements from different sources. This model has been used to run a series of simulations to find the coefficients required for a new turbulent friction factor correlation. A new Reynolds number has been defined that represents the conditions in turbulent flows more realistically than the existing Metzner-Reed Reynolds number.

THE EXACT SOLUTION OF AIRFLOWS IN POLYGONAL VENTILATION NETWORKS WITH KNOWN EXTERNAL FLOWS

This paper presents formulas for the exact solution of airflows in a generalized polygonal ventilation network where branch resistances and external airflows are given. To derive the formulas, an equation representing the pressure loss along any mesh or loop is written in terms of the airflow of a single branch. Then a quadratic equation is constructed such that one of its solutions or roots agrees with the solution of the pressure-loss equation. Thus the major computational task of the solution consists of determining the coefficients of the quadratic equation and finding one of its solutions by the well-known quadratic formula. The application of the formulas is illustrated with two problems for quadrilateral networks.

Die Grundlagen der pneumatischen Förderung

AbstractPrinciples of pneumatic conveying. The design of pneumatic conveying systems is critically dependent upon a knowledge of the pressure drop and the minimum necessary velocity of the conveying gas. Starting from the areas of application of pneumatic conveying systems, the conveying states occurring are discussed and appropriately assigned to the diagram of state. The pressure loss equation is reported for conveying in form of a fully suspended flow and strand‐type conveying and the theoretically predicted pressure losses are compared with experimental values for the conveying of coarse and finegrained materials. After mentioning the calculation of the pressure drops due to acceleration and to pipe bends, the article discusses the problem of pipe enlargement for long conveying distances. Equations are also given for the calculation of the so‐called blocking limit and of the conveying gas velocity at which the minimum pressure drop occurs. The influence of the compressor on the choice of the operating point is also discussed. New calculation equations are then given for horizontal and vertical conveying in form of a fully suspended flow conveying and for horizontal strandtype conveying which permit reliable scale‐up. Moreover, a new equation is reported for the blocking limit in horizontal conveying.

高炉滴下帯の気-液向流領域におけるガス圧力損失と液ホールドアップの実験式

The Ergun-type pressure loss equation was extended to the flows in irrigated packed beds on the basis of the assumption that, in the case of irrigated beds, the bed is composed of solid particles and hypothetical liquid droplets. Dimensionless empirical formulae for the quantity and the size of liquid in the bed were obtained by using experimental data on gas pressure drop and liquid holdup obtained under simulating flow conditions of the dropping zone of a blast furnace.Flooding gas velocities as well as gas pressure drop and liquid holdup over entire region of gas velocity up to the flooding could be calculated by use of the above formulae with reasonable accuracy.The pressure loss equation was further extended to the flow of two liquid phases in the dropping zone of a blast furnace. A sample calculation confirmed the result of earlier study that the fluidization of the coke bed would start before the onset of flooding of the slag.