Homework_C14 - Homework Set # 14: Unsteady-state transfer...

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Homework Set # 14: Unsteady-state transfer of species Due Date: 12-05-05 Problem #1: Recall the example of the unsteady state evaporation of component A contained in a test tube in the lecture note (or see Example 20.1-1, 2 nd edition). Extend this example to account for interphase transfer of both species A and B. Show how to obtain Eqs. 20.1-23 to -25. Problem #2: For flow in porous media, the interstitial velocity v (velocity of fluid averaged over the void space of a porous, permeable volume element) is related to the discharge velocity u (velocity of fluid averaged over the volume element) as follows φ = u v In the attached article, derive Eq. (1) using the expressions for convection and dispersion fluxes of fluid in porous media and species molar balance in the lecture note.
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, ‘Spz. L47 Dead-End Pore Volume and Dispersion in Porous Media K. H, COATS JL?IICIR MEMBER AIME B. D. SMITH* I JERSEY PRODUCTION RESEARCH CO. TULSA, OKLA. ABSTRACT Experiments in ‘wbr’cb calcium chloride displaced sodi~m chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on bow validly the mixing process is modeled by a differ- ential “(i.e., not finite-stage) capacitance matbernat- ical model. The effluent concentration profile from two consolidated cores exhibited corisidera ble asymmetry, while two unconsolidated cores yielded nearly symmetrical profiies. All runs resulted in brea~tbrough of the SO per cent concerztratio~ significantly before one pore volume was injected In addition, velocity appreciably afiected the efiluent concentration profile irom a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion ‘modeL The capacitance model allows det erminat ion o{ the amount oi dead-end pore space in a porous matrix and tbe eifect of velocity on the rate oi diifusion into tbis SPace. An experimental program yielding insight into the physical validity oi the capacitance eifect is described. INTRODUCTION Axial dispersion the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relatively recent studies l-ls and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemicaI reactors, and the adsorption of solutes from a flowing stream onto the ayrface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption psrdmeters are deter- mined from the nature of concentration profiles. In general, early studi& of dispersion assumed applicability of a simple diffusion equation and were concerned with cortel.ation of the experimentally determined ~{effective $* di ffusion coefficient with OriKinal manuscript received in Society of” Petroleum Engi-” neere office Sept. 5, 1963. Revised manuscript received Jan. 19, 1964. PaPer rmesented at Annual SPE Fall Meeting held Oct.
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Homework_C14 - Homework Set # 14: Unsteady-state transfer...

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