A = a = = ideal gas state Subscripts c = critical property i, i, k = component identifications o = reference state A group contribution molecular model is developed for the thermocluding energy of vaporization, pVT relations, excess properties, and activity coefficients. The model is based on the cell theory in which the repulsive forces of molecules are expressed with a modified cell partition function derived from the Carnahan-Starling equation of state for hard spheres. The attractive forces are made u p of group pair interaction contributions. Group and interaction properties have been determined for methyl, methylene, hydroxyl, and carbonyl. Extensive comparisons are School of Chemical Engineering made of predictions of the model with data for pure liquids and their solu-Purdue University tions. West Lofayette, Indiana 47907 1. To develop a comprehensive theory of group contribution for the estimation of various thermodynamic
y z X = ratio of R2 to R1 = ratio of the derivative time constant to y l / y z ; = positive constant.used to multiply each process see Equation ( 7 4 time constant in a set = defined by Equation (7b) = defined by Equation ( 7 c ) , s = product of the process time constants; T 1 ' 7 2 . 7 3 , s = sum of process time constants; 71 + 72 + T3, s = smallest process time constant, s = second largest process time constant, s = largest process time constant, s = reset or integral action time constant, s = derivative action time constant, s Greek Letters al a2 y1 y3 TI Q TS vi TD T~Z -N ; T D Z -N = values of 7 1 and T D suggested by the Zieg-7 2 = 7172 + 7173 + 72T.3, s2 ler-Nichol's rules, s rib = all lower values of Ti will lead to operation in the split stability region; defined by Equation = lowest value of T~ for z = 1 for which any value = critical frequency (that is, 180 deg phase lag), (lo), s T~~ oC of K , will lead to stable operation, s
This work presents the results of a one-dimensional experimental investigation of contaminant transport in heterogeneous porous media. The usual transport equations fail to adequately predict dispersion in such systems, and new theories to account for the distinctions have not yet been examined experimentally. We use a one-dimensional porous media which is heterogeneous on the scale of observation to determine if the phenomena predicted by the new theories are observable.The experimental media are constructed from distinct layers of spherical glass beads packed into cylindrical columns of Lucite. Flow was in the direction perpendicular to the layers. Dispersion was measured by recording the concentration of a chloride tracer as a function of time and position. The scale of measurement was finer than the scale of the heterogeneity. The results show that the mixing between miscible fluids was affected by transitions in the system parameters, before the transitions were encountered by the mixing zone. This newly observed phenomenon has been interpreted as a nonlocal effect, and it begins to verify the new predictive theories.
A new method of reservoir evaluation called pulse-testfng has been developed for describing formation properties between webs. Pulse-testing utilizes a sensitive dif7erentiai-pressure gauge at a responding well to measure and record the response generated by a series of ffo w rate changes (pulses) at an adjacent or pulsing well. Since the pulse-test instruments have a senst!ivity of about 0.001 psi, pulses of several hours or less iz duration will generate a measurable response in most reservoirs. For this reason, many well pairs can be tested in a short period of time with li?-tie inter fere~ce in field operations.Comparison of pulse-test results to conventional testing tnethods shows that the pulses obey unsteady-state, compressible-j?ow *heory and thus provide a measure of both transmissibility (kb/ p) and storage (~ch). In addition, the metitod c'an be used qualitatively to describe communication across faults and between zones, wtd~irection and mrz,qnitude of fracture trends.
Thisis a state-of-the-art review of dispersion in real porous media to examine present knowledge and to indicate research directions.We limited the discussion to macroscopic mixing caused by uneven cocurrent laminar flow exemplified by flow of petroleum in reservoirs, movement of fresh water and waste fluids in aquifers, and flow of fluids in fixed beds. Countercurrent gas-liquid, liquid-liquid, and fluidized systems are not considered. Further, the discussion is directed at dispersion in nonideal media.We do not pretend to be exhaustive in this reviewrather, we attempt to cover selected papers which illustrate the major directions of research. The interested reader can find more material in the bibliography than can be given fair treatment within the scope of this paper.We start with definitions of dispersion and of the three nonidealities, heterogeneity, nonuniformity, and anisotropy. After a brief general introduction, we consider statistical models of dispersion, continuum models of dispersion, and data which apply to systems containing nonidealities.
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