Longitudinal Pressure Drop Research Articles

A Computer Simulation Model of a Horizontal Wellbore Cleaning Using a Transverse Axial-travelling Dynamic-pressure Jets System

Abstract The upsurge in horizontal wellbore drilling technology in the present decade underscores its importance in radically increasing the productivity of hydrocarbons. Secure horizontal wellbore drilling cannot be divorced from efficient wellbore cleaning. However, conventional horizontal wellbore cleaning, which involves a reduction of the cuttings concentration in the wellbore annulus by the circulation of drilling fluid using controlled longitudinal pressure drop, suffers from the lack of independent and controlled transverse dynamic pressure drop. For a broader approach to remedy this impediment, this paper presents a computer simulation model for enhancing horizontal wellbore cleaning by inducing controlled dynamic suspension of cuttings in the wellbore annulus. The process involves a transverse axialtravelling dynamic-pressure jets system (TAD-Jets system) in collaboration with conventional axial laminar flow in multiple variant conduits, orbitally-cascaded and embedded in the drillstring annulus. The simulated results were found to be very promising. Introduction The process of cleaning a horizontal wellbore is carried out under varied conditions of uncertainty. Conventional wellbore cleaning involves a number of input variables, whose estimated probability distribution and interrelationships have not yet been fully derived mathematically or otherwise. The first attempt to establish a single multivariable mathematical relationship among major input variables involved in horizontal wellbore cleaning, using a transverse axial-travelling dynamic-pressure jets system, was described in the paper by Mutua and Changirwa(1). The present study is a computer simulation model of their previous work. It is geared to evaluating and establishing stochastically the optimum operational conditions of TAD-Jets system. Formulation of Simulation Model The development of the simulation model herein is based on the best available knowledge of the actual horizontal wellbore cleaning and TAD-Jets system. Figure 1 shows that the TAD-Jets system is an integral part of the drilling string. It's function is to dynamically suspend the solids in the annulus. To clarify the mechanism of the TAD-Jets system function, a section of the wellbore annulus is illustrated by Figure 3. In the system approach of problem solving employed in this paper, a conscious attempt has been made to understand the relationship between various input parameters of the system. The objectives and pertinent constraint: and restraints which govern the solution of horizontal wellbore cleaning have been identified and classified into major processes and forces (Table 1). The model formulation consists of a set of equations describing (1) two-phase heterogenous axial flow in the horizontal wellbore eccentric annuli, (2) two-phase heterogenous transverse flow in the horizontal wellbore eccentric annuli, (3) material balance of cuttings in the eccentric annuli. Assumptions: Cuttings The cuttings (drill cuttings in Figures 1 and 2) compact bed forms in wellbore sections where the drilling fluid upward radial flow velocity Vr is less than the cuttings slip velocity Vs (Figure 1). The cuttings-drilling fluid mixture is not sticky and does not block the transverse jet nozzles. The cuttings do not react with the drilling fluid. Transverse Jets Flow Transverse jets flow is turbulent and localised in a given well- bore section and does not affect the neighbouring sections substantially.

Analysis of pig's coronary arterial blood flow with detailed anatomical data.

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: one asymmetric model satisfies all anatomical data (including the mean connectivity matrix) and the other, a symmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.

EFFECTS OF AXIAL PRESSURE DROP ON THE LENGTH-AVERAGED PERMEATE FLUX IN CROSSFLOW MICROFILTRATION

Abstract A hydrodynamic model is presented which predicts the dependence of the steady-state, length-averaged permeate flux on the longitudinal pressure drop during crossflow microfiltration in both flat slit and tubular channels. The integral approach described by Romero and Davis (1988) has been extended to predict the axial variation of the transmembrane pressure drop along with that of permeate flux and cake layer thickness. The mechanism of shear-induced diffusion is employed in the analysis, which is restricted to particles with diameters of approximately 0.5–20μm (Davis, 1992), but the procedures may be extended to other particle transport mechanisms. The model predictions have been compared to the corresponding values calculated using a constant transmembrane pressure drop set equal to the arithmetic mean of those at the channel entrance and exit. The simulation results show the axial pressure drop to have the most significant effect on the average, steady-state permeate flux predictions for long,...

Velocity profiles measured for airflow through a large-scale model of the human nasal cavity.

An anatomically accurate, x20 enlarged scale model of a healthy right human adult nasal cavity was constructed from computerized axial tomography scans for the study of nasal airflow patterns. Detailed velocity profiles for inspiratory and expiratory flow through the model and turbulence intensity were measured with a hot-film anemometer probe with 1 mm spatial resolution. Steady flow rates equivalent to 1,100, 560, and 180 ml/s through one side of the real human nose were studied. Airflows were determined to be moderately turbulent, but changes in the velocity profiles between the highest and lowest flow rates suggest that for normal breathing laminar flow may be present in much of the nasal cavity. The velocity measurements closest to the model wall were estimated to be inside the laminar sublayer, such that the slopes of the velocity profiles are reasonably good estimates of the velocity gradients at the walls. The overall longitudinal pressure drop inside the nasal cavity for the three inspiratory flow rates was estimated from the average total shear stress measured at the central nasal wall and showed good agreement with literature values measured in human subjects.

Non-invasive evaluation of segmental pressure drop and resistance in large arteries in humans based on a Poiseuille model of intra-arterial velocity distribution

The aim of the study was to evaluate in hypertensive subjects the longitudinal pressure drop and segmental resistance in a large artery in relation to shearing forces of the circulating blood column at the arterial wall. Arterial diameter, blood velocity, and flow were measured in the brachial artery using pulsed Doppler apparatus. Blood viscosity was measured at 96 s-1 with a low shear viscometer. Segmental resistance per unit arterial length was calculated using the basic Poiseuille resistance expression from the ratio between blood viscosity and the fourth power of arterial diameter. Longitudinal pressure drop was deduced as the product between segmental resistance and blood flow. The Poiseuille model of velocity distribution also enabled wall shear rate and stress to be calculated from the ratio between blood velocity and arterial diameter and from the product between shear rate and blood viscosity respectively. 19 ambulatory male patients with mild to moderate hypertension and 11 normotensive male controls of similar age were studied. Compared to controls, hypertensive patients had higher arterial diameter (p less than 0.001) lower blood velocity (p less than 0.05), higher blood viscosity (p less than 0.01), lower segmental resistance and pressure drop (p less than 0.001, p less than 0.01) and lower shear rate and stress (p less than 0.01, p less than 0.05). A negative correlation existed in the overall normotensive and hypertensive population between pressure drop and mean blood pressure (r = -0.55, p less than 0.01). The hypertensive state is associated with a clear reduction in large artery segmental resistance and longitudinal pressure drop concomitantly with a decrease in shear conditions at the arterial wall. The mechanisms of reduced resistance and pressure drop are related to decreased wall shear and increased diameter of the artery, both of which reduce the frictional forces at the blood-arterial wall interface.

Calculation of pressure pulsation intensity and gas content in an adiabatic two-phase flow

A calculation technique is developed for evaluating the intensity of pressure pulsations, longitudinal pressure drop, and gas content in a two-phase adiabatic flow. Calculations are compared to experimental data.

Effect of radial electric field on heat and momentum transfers in dielectric organic liquid for laminar flow through concentric annuli

Experiments were conducted to investigate changes in convective heat transfer in flows of dielectric organic liquids in annuli between copper tube and concentric wires. Also investigated was longitudinal pressure drop in the flow which could be induced by applying electric fields of direct current between the wall of the tube and the central wire electrode. In the laminar range of Reynolds number, heat transfer rates at the outer wall increased in the thermally well-developed region, and the thermal development was advanced. On the other hand, pressure drops were also increased in liquids of small Prandtl number. In the transitional and turbulent range, however, neither changes of heat nor momentum transfer were noticeable. To express these results in the low Reynolds number range a semi-empirical formulation in non-dimensional terms was derived from the similarity principle.