The Tube

In order to find rj and r, we will pick a chain and explore its tube in more detail. The tube is created by other chains. If they come into contact with the test chain, they act as obstacles to the chain s motion. However, we have seen that only a small proportion of such contacts can really limit the chain s choice of conformations. This proportion is of the order of 1/Ng. These are the contacts which can be regarded as effective cross-links. 

Notice that this result for the length of the tube is much less than the full length of the chain NL This is because Ne 1. 

7 The Dependence of the Longest Relaxation Time on the Chain Length 

Now let s calculate the longest relaxation time t for a polymer melt. As we have said, it is the time that a reptating chain takes to leave its original tube. To do this, the chain obviously has to diffuse along the tube axis by a distance of order A. 

When a chain moves in a dense system (like a polymer melt), the frictional forces acting on each monomer are totally independent. Hence, the total frictional force experienced by the moving chain is simply the sum of the frictional forces on each individual monomer. How can we find these frictional forces on the monomers Let s focus on one monomer suppose it has a velocity v. This is the velocity of diffusion, so it is not too high. (To be more precise, it is of the same order as the thermal velocity of the monomer.) This gives us the right to take the force f of viscous friction to be proportional to the velocity f = —pv. Here p is the coefficient of friction for a single monomer. Since the total friction is the sum over all the monomers, the same must be true for the coefficients of friction. The 

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In situations where a low concentration of suspended solids needs to be separated from a liquid, then cross-flow filtration can be used. The most common design uses a porous tube. The suspension is passed through the tube at high velocity and is concentrated as the liquid flows through the porous medium. The turbulent flow prevents the formation of a filter cake, and the solids are removed as a more concentrated slurry. 

Molisch s test A general test for carbohydrates. The carbohydrate is dissolved in water, alcoholic 1-naphthol added, and concentrated sulphuric acid poured down the side of the tube. A deep violet ring is formed at the junction of the liquids. A modification, the rapid furfural test , is used to distinguish between glucose and fructose. A mixture of the sugar, 1-naphthol, and concentrated hydrochloric acid is boiled. With fructose and saccharides containing fructose a violet colour is produced immediately the solution boils. With glucose the appearance of the colour is slower. 

In oil bearing formations, the presence of polar chemical functions of asphaltenes probably makes the rock wettable to hydrocarbons and limits their production. It also happens that during production, asphaltenes precipitate, blocking the tubing. The asphaltenes are partly responsible for the high viscosity and specific gravity of heavy crudes, leading to transport problems. 

For Jet Al, the pressure drop should be less than 33 mbar, and the visual observation of the tube should correspond to a minimum of three on the scale of reference. 

In the refinery the salts deposit in the tubes of exchangers and reduce heat transfer, while in heater tubes, hot spots are created favoring coke formation. 

While the long chain hydrocarbons (above 18 carbon atoms) may exist in solution at reservoir temperature and pressure, they can solidify at the lower temperatures and pressures experienced in surface facilities, or even in the tubing. The fraction of the longer chain hydrocarbons in the crude oil are therefore of particular interest to process engineers, who will typically require a detailed laboratory analysis of the crude oil oomposition, extending to the measurement of the fraction of molecules as long as C3Q. 

If the reservoir pressure remains above the bubble point then any gas liberated from the oil must be released in the tubing and the separators, and will therefore appear at the surface. In this case the producing gas oil ratio (Rp) will be equal to R. i.e. every stock tank barrel of oil produced liberates Rs scf of gas af surface. 

A well known example of capillary-buoyancy equilibrium is the experiment in which a number of glass tubes of varying diameter are placed into a tray of water. The water level rises up the tubes, reaching its highest point in the narrowest of the tubes. The same observation would be made if the fluids in the system were oil and water rather than air and water. 

From the above plot, it can be seen that the recovery factor for gas reservoirs depends upon how low an abandonment pressure can be achieved. To produce at a specified delivery pressure, the reservoir pressure has to overcome a series of pressure drops the drawdown pressure (refer to Figure 9.2), and the pressure drops in the tubing, processing facility and export pipeline (refer to Figure 9.12). To improve recovery of gas, compression facilities are often provided on surface to boost the pressure to overcome the pressure drops in the export line and meet the delivery pressure specified. 

A static bottom hole pressure survey (SBHP) is useful for determining the reservoir pressure near the well, undisturbed by the effects of production. This often cannot be achieved by simply correcting a surface pressure measurement, because the tubing contents may be unknown, or the tubing contains a compressible fluid whose density varies with pressure (which itself has an unknown profile). 

Having reached the wellbore, the fluid must now flow up the tubing to the wellhead, through the choke, flowline, separator facilities and then to the export or storage point each step involves overcoming some pressure drop. 

Monitoring and control of the production process will be performed by a combination of instrumentation and control equipment plus manual involvement. The level of sophistication of the systems can vary considerably. For example, monitoring well performance can be done in a simple fashion by sending a man to write down and report the tubing head pressures of producing wells on a daily basis, or at the other extreme by using computer assisted operations (CAO) which uses a remote computer-based system to control production on a well by well basis with no physical presence at the wellhead. 

Tubing corrosion due to FIgS (sour corrosion) or COg (sweet corrosion) may become so severe that the tubing leaks. This would certainly require a workover. Monitoring of the... 

The relationship between the tubing performance and reservoir performance is more fully explained in Section 9.5. 

Sand production from loosely consolidated formations may lead to erosion of tubulars and valves and sand-fill in of both the sump of the A/ell and surface separators. In addition, sand may bridge off in the tubing, severely restricting flow. The presence of sand production may be monitored by in-line detectors. If the quantities of sand produced become unacceptable then downhole sand exclusion should be considered (Section 9.7). 

To verify the modelling of the data eolleetion process, calculations of SAT 4, in the entrance window of the XRII was compared to measurements of RNR p oj in stored data as function of tube potential. The images object was a steel cylinder 5-mm) with a glass rod 1-mm) as defect. X-ray spectra were filtered with 0.6-mm copper. Tube current and exposure time were varied so that the signal beside the object. So, was kept constant for all tube potentials. Figure 8 shows measured and simulated SNR oproj, where both point out 100 kV as the tube potential that gives a maximum. Due to overestimation of the noise in calculations the maximum in the simulated values are normalised to the maximum in the measured values. Once the model was verified it was used to calculate optimal choice of filter materials and tube potentials, see figure 9. 

The accuracy of the calculated solution is highly depending of realistic values for conductivity and permeability of the tube material. While the conductivity can be found in the literature for most materials, the right permeability is harder to determine. In the RFEC technique the exciter current and thus the exciter field strength is often to high to assume a... 

A ring specimen is cut from the tube. Two coils are wrapped around this ring, one exciter coil and one receiver coil. The exciter coil N1 should cover the entire ring so that there are no field losses when ring is saturated. The sinusoidal exciter current which can be measured at... 

The development of Remote Field Eddy Current probes requires experience and expensive experiments. The numerical simulation of electromagnetic fields can be used not only for a better understanding of the Remote Field effect but also for the probe lay out. Geometrical parameters of the prohe can be derived from calculation results as well as inspection parameters. An important requirement for a realistic prediction of the probe performance is the consideration of material properties of the tube for which the probe is designed. The experimental determination of magnetization curves is necessary and can be satisfactory done with a simple experimental setup. 

Inside the tube near the driver coil there is a high level of field, but this is rapidly attenuated by the eddy currents generated in the inside wall. 

At the location at the pick-up coil system (some 2.5 tube diameters away from the driver) the net field inside the tube is primarily due to the external field. See Fig.3. 

The probe receives a signal when either the driver or detector coil passes a flaw or other feature in the tube A signal is produced over the full length of the flaw. It is affected by geometry and permeability changes which cause the instrument zero to wander. 

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