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The pressure drop across the skin can be computed from Eq. In a completely analogous manner to previous build-up theory, Eqs.
In many cases, conventional plotting of pressure or pressure squared leads to plots which are not linear, although the m p plot is linear as it should be. One 'example given in the Appendix yields reasonable straight lines for both m p and pressure- squared plotting Fig. In other cases, it has been observed that the pres'sure-log time plot and m p -log time plots are excellent straight lines, although a pressure-squared plot shows considerable curva- ture.
In all oases tried to date, the m p -log time plot has produced reasonable st,raight lines.
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Often, it is necessary to analyze a variable-rate draw- down-such as Russell's8 test, or to account for wellbore storage effects: This requires superposition of constant rates to generate variable-ralte cases. In other cases, it has been observed that the pres'sure-log time plot and m p -log time plots are excellent straight lines, although a pressure-squared plot shows considerable curva- ture. In all oases tried to date, the m p -log time plot has produced reasonable st,raight lines.
Often, it is necessary to analyze a variable-rate draw- down-such as Russell's8 test, or to account for wellbore storage effects: This requires superposition of constant rates to generate variable-ralte cases. An important question at this poinJt is whether the real gas flow solutions offer a worthwhile improvement over 'existing gas flow solutions currently used in well test analysis? In addition to the problem of gas physical property variation, use of the real gas flow solutions offers an important improvement over existing gas flow theory that is particularly important for low permeability for- mations.
That is, the solution in terms of real gas pseudo- pressure includes the second-degree pressure gradient term neglected by methods based on eitiher liquid flow or ideal gas flow solutions.
In the case of low-permeability gas well testing, current well test imerpretation methods can lead to formation capacity or deliverability estimates that can be grossly in error. In this so-called hybrid model, the conduction of heat in the cylinder block and other solid components is solved via the finite volume method using a commercial CFD package The in-cylinder compression model and the CFD model are coupled via the continuity of temperature of heat fluxes at the cylinder walls.
The methodology is complemented by steady-state energy balance equations for each compressor component suction muffler, discharge muffler, discharge line, compressor shell, electric motor, radial bearings , as described in Kremer et al.
A time step of 3 s was employed in the explicit formulation of the differential equations of the in-cylinder vapour compression model. The simulation is initiated with the piston at the bottom dead centre, with the initial cylinder vapour pressure and temperature set equal to those at the suction plenum.
The instants at which droplet families are atomized in the cylinder are evenly distributed along the turn of the crankshaft angle. At each time step, an implicit calculation of the droplet radius and temperature is performed.
The instantaneous interfacial temperature is equal to the saturation temperature at the instantaneous gas pressure in the cylinder.
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The droplet temperature profile for each family is solved numerically via the finite volume method, since the boundary conditions are non-homogeneous. The interfacial heat fluxes are calculated via eqs.
Convergence of this inner loop is assumed to have been attained when the variation of the droplet radius is less than 0. The valve dynamics and the instantaneous suction and discharge mass flow rates are calculated and, with the rate of change of the droplet radius calculated as above, eq. The new vapour temperature and pressure are then calculated with eqs.
The procedure is repeated until a cyclic steady-state is achieved, i.
The calculation procedure described above was incorporated into the hybrid model, which is responsible for updating the vapour temperature at the suction port and the temperature of the cylinder walls.
The iterative procedure is repeated until all temperature variations calculated in the model are below 0.
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The average mass flux of atomized droplets is such that 40 families with an initial droplet radius of 7.Influence of the number of droplets specified boundaries. In the case of low-permeability gas well testing, current well test imerpretation methods can lead to formation capacity or deliverability estimates that can be grossly in error.
This is a way of life. In other words, it is improbable that high grade energy in the form of liquid refrigerant, capable of producing a cooling effect in the system, can be used for compressor cooling at the expense of added compression work without a performance penalty.
If producing time t is long enough that the radius is stabilized hefore the well is shut in, approximation for pressure huild-up is: and the dimensionless producing time is defined as: Or using standard conditions of An important question at this poinJt is whether the real gas flow solutions offer a worthwhile improvement over 'existing gas flow solutions currently used in well test analysis?
The decrease of the in-cylinder temperature resulting from the latent heat transfer to the atomized droplets is illustrated in Fig.
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