Application of Engineering Principles - Assignment Example

Question a If the velo profile of a fluid over a plate is a parabolic with a vertex 20 cm from the plate, where the velo gradients and shear stresses at a distance of 0,10,and 20 cm from the plate, if the velocity of the profile is 850 centipoise. Answer: U=850 centipoise du/dy=? & at y = 0, 10, 20 cm As we know that …………………..(1) And we also know that for Newtonian fluids ……………………..(2) By differentiating the equation 2 we get At y =0 = 0 and =0 At y =20 = -0.1275 and =-0.153 N/m2 At y = 10 Assuming there is uniform distribution of velocity over the plate So by interpolation we can assume that At y=10 =-0.06375 Integrating the above expression we get, u = -0.06375y now putting y=10 u =-0.6375m/sec = 0.0406N/m2 Question 1 (b): Dynamic viscosity of some common fluids as a function of temperature: Dynamic viscosity is the resistance to flow encountered when one layer or plane of fluid attempts to move over another identical layer or plane of fluid at a given speed. Dynamic viscosity is also called absolute viscosity. As illustrated in the figure viscosity is very sensitive to temperature. For example, as the temperature of water changes from 60 to 100oF the density decreases by less than 1% but the viscosity decreases by 400%. It is thus clear that particular attention must be given to temperature when determining viscosity. Figure shows in more detail how the viscosity varies from fluid to fluid and how for a given fluid it varies with temperature, whereas for gases an increase in temperature causes an increase in viscosity. This difference in the effect of temperature on the viscosity of liquids and gases can again be traced to the difference in molecular structure. The liquid molecules are closely space, with strong cohesive forces between to these intermolecular forces. As the temperature increases, theses cohesive are reduced with a corresponding reduction in resistance to motion. Since viscosity is an index of this resistance, it follows that the viscosity is reduced by an increase in temperature. In gases, however, the molecules are widely spaced and intermolecular forces negligible. In this case resistance to relative motion arises due to the exchange of momentum of gas this case resistance to relative motion arises due to the exchange of momentum of gas molecules between adjacent layers. As molecules are transported by random motion from a region of bulk velocity to mix with molecules in a region of higher bulk velocity (and vice versa), there is an effective momentum exchange which resists the relative motion between the layers. As the temperature of the gas increases, the random molecular activity increases with a corresponding increase in viscosity. The effect of temperature on viscosity can be closely approximated using two empirical formulas. For gases the sutherland equation can be expressed as Where c and s are empirical constants and T is absolute temperature. Thus, if the viscosity is known at two temperatures, c and s can be determined. Or, if more than two viscosities are known, the data can be correlated with above equation by using some type of curve fitting scheme. For liquids an empirical equation that has been used is Where D and B are constants and T is absolute temperature. This equation is often referred to as andrade’s equation. As was the case for gases, the viscosity must be known at least for two temperatures so the two constants can be determined. Question 1 (c): Oil flows through a pipe AB of 2.5 m diameter at 5m/s and then passes through a divergent pipe BC of 3.25 diameter. Another pipe of 3m diameter is connected at point D to increase flow rate by 3 times. Then oil is allowed to discharge equally through 2 pipes using continuity equation. (i) As given VAB= 5 m/sec at dab = 2.5 m DBC=3.25m and dD=3m Using the continuity equation A1V1=A2V2 (2.5)2 x 5 x 3 = (3)2 x V2 V2 =10.41 m/sec (ii) Dimensions of pipe CE=? (2.5)2 x 5 x 3/2 = d2 x 4 d = 2.42 m (iii) if the flow direction in pipe CE is reversed then flow rate in pipe CF will be Q = (2.5)2 x 5 x 3 - (2.5)2 x 5 x 3/2 Q =46.875 m3/sec Question 2 : The pressure of mud measured between degasser inlet and outlet are 0.0981 N/cm2 (vacuum) and 4 N/cm2 (gauge). Neglect datum head. The specific gravity of mud is recorded by hydrometer for 100 seconds with equal time interval as 0.84, 0.85, 0.83, 0.84, 0.83, 0.83,0.85, 0.83, 0.84 and 0.84. Assume that flow rate of mud is same as the flow rate in stand pipe. (i) As total number of observations are 10 so by using the definition of the median the average specific gravity of mud will be 0.83. (ii) using the bernouli equation with inlet and outlet of same size we get, Putting values in above equation gives 6.3 X10-4 m (iii) As we can see from tables there are some variations in manometer pressure readings which may be due to one of the reasons listed Parallex error Zero error of the manometer Environmental effects Carelessness in measuring the time interval Slight change in the desnity due to temperature Non smooth surface of the manometer tube (vi) As we know that As for given condition the flow rate is same for both flow meters 91406.25(1-)=d2 by solving the quadratic equation we get d=29.93mm (b) In a well control stimulator, three pumps A,B, and C are connected parallel between mud tank and stand pipe through pipe lines to increase the discharge. The diameter of pipe connected with pump A is 7.5 cm. the mud flows through at 15 cm/sec in pump A. (i) let us say that the equivalent pipe is D. and according to the given conditions Qb=1.2Qc and also we know that QD=QB + Qc QD =2.2 Qc By putting in values in above equation we get D= 5.056 cm (ii) Power input to the pump = power transmitted through pipe P =0.522H (iii)various minor losses occurring at the drill pipe tip during cutting: (a) Loss due to sudden enlargement (b) Loss due to sudden contraction (c) Loss of head at inlet of pipe (d) Loss of head at outlet of pipe (iv) Application of laminar and turbulent flow in drilling operations: Laminar flow: The most common annular flow regime is laminar. It exists from very low pump rates to the rate at which turbulence begins. Characteristics useful to drilling engineer are low friction pressures and minimum hole erosion. Laminar flow can be described as individual layers, or laminae moving through the pipe or annulus. The center layers usually moves at the rates greater than the layers near the well bore or pipe. The flow profile describes the variations in the layer velocities. These variations are controlled by the shear resistant capabilities of the mud. A high yield point of the mud tends to make the layers move at more uniform rates. Cutting removal is often discussed as being more difficult with laminar now. The cutting appears to be more outward from higher velocity layers to more acquiescent areas. These outer layers have very low velocities and may not be effective in removing the cuttings. A common procedure for minimizing the problem is to increase the yield point, which decreases layer velocity variations. An alternative is to pump a 10-20-bbl high-viscosity plug to “sweep” the annulus of cuttings. Turbulent flow: Turbulence occurs when increased velocities between the layers create shear strengths exceeding the ability of the mud to remain in the laminar flow. The layered structure becomes chaotic and turbulent. Turbulence occurs mainly in the drill string and occasionally around the drill collars. Much published literature suggests that annular turbulent flow increases the hole erosion problems. The flow stream is continuously swirling into the walls. In addition, the velocity at the walls is significantly greater than the wall layer in laminar flow. Many industry personnel believe that the turbulent flow and formation type are the controlling parameters of erosion. (3) A storm grain has the cross section shown in the fig, and is laid on the slope 1.5m/km. if it is constructed of brick work, find the normal discharge, when it is exactly half full of the water. First of all finding the area of the fig, that is given by So Now since the velocity of the fluid is not given, so assuming it as V = 1 m/sec So normal discharge when it is exactly half full of the water is By putting values in above equation we get, Question 3: (i) Identify and discuss the various rig components in which heat exchange mechanism takes place. Following are the various rig components Degasser: This vessel is used for gas contamination removal. It consists of a vessel which has inclined flat surfaces in thin layers and a vacuum pump. The mud is allowed to flow over the inclined thin layers which helps break out entrained gas in the mud. The vacuum pump reduces the pressure in the vessel to about 5 psia which extracts the gas from the mud. This device is about 99% efficient. Mud Gas Separator: This is generally the first device available to extract gas from the mud. It consists of a tower with baffle plates, which are flat plates that force the fluid through a certain path. The mud is allowed to flow in the tower over the baffle plates which separates some of the entrained gas. This device generally can extract 50% to 60% of the gas. Bag-Type Preventers (Annular Preventers): This preventer is used the most because the rubber sealing element can conform to any shape or size conduit in the hole. The annular preventer can further collapse completely and seal the annulus with no conduit to the hole. (This is not recommended.) The annular preventers consist of a rubber-covered, metal-ribbed sealing element. This element is caused to collapse and seal by allowing the pressurized hydraulic fluid from the accumulator to move a tapered, form-fitted cylinder against the rubber which causes collapse. Ram Preventers: This type BOP is used mainly as a backup to the bag-type preventer or for high-pressure situations. Diverter System: The diverter system is used in conjunction with the annular preventer to divert the path of mud flow either overboard or through the mud gas separation facilities. This system is generally only used when drilling at shallow depths where the formation has a weak fracture gradient. HCR Valve: The HCR valve is a hydraulically operated gate valve. This valve is used on diverter systems and choke lines leading from the blow out preventers. The advantage of the valve is that it can be operated remotely. Pods and Control Lines: The pods and control lines are used in subsea operations; the control lines run from the accumulator to the pods which are located on the subsea BOP stack. These two devices are responsible for transmitting the hydraulic pressure from the accumulator to actuate the various functions of the subsea BOP stack. (ii) Discuss the reasons why drill bit temperature is maintained (>50C) above the atmospheric conditions. There are several reasons why the drill bit temperature is maintained 50oC above atmosphere. The drill bit’s performance is optimum at this temperature. There is less problem of stuck pipe condition At this temperature less chance of oil sticking to drill bit. Recommended by the manufacturer At this temperature it is easier to operate rather than at lower temperatures. (iii) Explain thermodynamically how diesel based mud helps the drill string to avoid stuck pipe conditions. Diesel based muds have traditionally been used to improve lubricity, minimize the problems associated with water-sensitive formations and deal with other site specific conditions for which other drill muds are not suited. Drill based muds have been the drilling fluid choice for a range of special situations, including high temperatures, hydratable shales, high angle, extended-reach wells, high density muds, and drilling through salt. Because of their enhanced lubricity, are also used as spotting pills during drilling operations with water based muds when drill pipe becomes stuck in the hole. A spotting fluid is a substance added to an existing circulating mud system to free stuck drill pipe. Typically it is applied as a discrete dose known as spotting pill. Stuck drill pipe is a problem for many operators while performing their duties. The inability of water based muds to effectively suppress the hydrational tendencies of some water sensitive formations can result in hole enlargement or collapse. This problem can only be very well controlled with diesel based muds, which do not hydrate the shale and maintain hole stability. References Reid,R.C., prausnitz, J.M.m and Sherwood, T.K, The Properties of Gases and Liquids 3rd Ed,. McGraw-Hill,New York, 1977. Benedict, R.P., Fundamentals of Temperature, pressure, and Flow Measurements, 3rd Ed,. Wiley, New York, 1984 Holman, J.P., Experimental Methods for Engineers, 4th Ed., McGraw-Hill, New York, 1983. Tipler, P.A., physics, Worth, New York, 1982 Riley, W.F., and Sturges, L.D.m Engineering Mechanics: Dynamics, 2nd Ed,. Wiley, New York, 1996 Goldstein, R.J., Fluid Mechanics, 8th Ed,. McGraw-Hill, New York, 1985. Streeter, V.L., and Wylie, E.B., Fluid Mechanics, 8th Ed,. McGraw-Hill, New York,1985. Ayers, R.C, Jr., et al., 1985, “The General mud concept for NPDES Permitting of offshore Drilling Discharges,” Journal of petroleum Technology, p. 475. Read More