In a solid solution random displacements of the solute and solvent ions from the mean crystal lattice are produced by the elastic strkins associated with their different sizes.A prediction of the effects on the X-ray spectrum is based on a model which treats the solute ions as centres of dilation in a finite isotropic elastic continuum. The resultant theory shows that the addition of solute atoms produces a mean lattice parameter change upon which are superimposed random displacements of the ions. These displacements result in a decrease in the integrated X-ray intensities of the high-order diffraction lines of the form associated with thermal vibrations. The effect is particularly marked in the copper-gold solid solution and comparison of the measured X-ray intensities from copper and a 15 atomic % solution of gold in copper enable one to deduce a value for the root mean square displacement ~/(~) due to distortion, when that due to thermal vibration has been allowed for.Measurements of the X-ray spectra were made using a Geiger-counter spectrometer from which it is deduced that ~/(~2) = 0.11 ~. This value compares favourably with the value predicted from the elasticity theory, namely V(~ ~) = 0.13 A.
The Pettit formation in Carthage Field is predominately a gas reservoir. At reservoir pressure and temperature, no free liquids are produced. However, water and condensate will drop out of the gas stream as the gas cools on the path to the surface.When the production rate declines below the critical velocity these fluids can accumulate and cause the well to load up and eventually cease flowing. Heating the wellbore to reservoir conditions is a new method of eliminating fluid condensation in the wellbore. This paper discusses the first successful application of wellbore heating to prevent fluid condensation and eliminate liquid loading. This application is in the Carthage Field. Introduction The Pettit formation in Carthage Field was discovered in 1936. The formation is limestone with an average permeability of 10–50 md and porosity ranging from 8% to 17%. The average cumulative production per well is 16 BCF, with current reservoir pressure ranging from approximately 120 to 200 psi across the field. Well tests indicate an average produced water ratio of 7.7 bbls/mmcf and produced condensate ratio of 7.5 bbl/mmcf. Typical completion depth for this reservoir is 6,100' with a reservoir temperature of 200 degrees Fahrenheit. Due to the low pressures in the reservoir, backpressure caused from liquid loading can significantly impact production rates. Bottom-hole pressure surveys and down-hole video show that produced reservoir fluids are initially dissolved in the gas stream. As the mixture travels to the surface the water and condensate begin to condense due to the temperature reduction associated with the geothermal gradient. As more and more fluids condense several distinct flow patterns begin to form which include; mist, annular, and slug flow. In wells where the gas velocity is below the critical velocity these fluids accumulate and can cause the well to load up and even cease flowing. Numerous lift applications have been tested on the Pettit Formation in Carthage Field, which include; coiled tubing velocity strings, foamer injection, plunger lift and conventional rod pumping. These methods all attempt to lift fluids that have already dropped out of the gas stream. An alternative lift option is to heat the wellbore to reservoir temperature. This method prevents fluids from condensing and eliminates the pressure problems associated with loading. This method also allows for the use of larger tubing sizes, which reduce friction pressures by increasing flow area. Another benefit is the reduction in the abandonment pressure of the reservoir. With no fluid accumulation and limited friction pressures, lower abandonment pressures and higher production rates can be achieved. This paper discusses the first application of wellbore heating to prevent liquid loading in the Pettit formation, by reviewing the principals of the heater cable itself, the selection of the first installation candidate and reviewing the results. Gas Well Thermal De-watering Background. Gasses entering a well bore will contain water in a vapor state.This evaporated water does not consist of tiny particles of liquid held in suspension in the gas but is itself a gas as invisible as the gas with which it mixes. Gas temperature, pressure and composition dictate the quantity of evaporated water that can be held in a gas. When the evaporated water limit is reached the gas is said to be "saturated" or at its "dew point". Any decrease in temperature or increase in pressure will cause some of this evaporated water to condense out as liquid water. Background. Gasses entering a well bore will contain water in a vapor state.This evaporated water does not consist of tiny particles of liquid held in suspension in the gas but is itself a gas as invisible as the gas with which it mixes. Gas temperature, pressure and composition dictate the quantity of evaporated water that can be held in a gas. When the evaporated water limit is reached the gas is said to be "saturated" or at its "dew point". Any decrease in temperature or increase in pressure will cause some of this evaporated water to condense out as liquid water.
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