Abstract
This investigation attempts to describe and simulate the alcohol displacement process by means of a cell model, as employed in chemical engineering practice. The proposed model is more simple than previously proposed models, and utilizes parameters chosen on a theoretical basis. The model successfully reproduced the formation of the stabilized bank and the breakthrough of alcohol, the latter depending on one of the model parameters, which may be correlated with the length of the porous medium. Moreover, the effects of the phase behavior of the liquid system involved, as observed in experimental studies, were reproduced. Several variations of the basic model were devised and tested on a digital computer. These included the cases in which:the actual value of fractional flow was used in cell-to-cell computations;the number of cells was varied within the same run; andincomplete rather than complete phase equilibrium was assumed within each cell.
The proposed cell model clarifies the basic mechanism of the process. Detailed concentration profiles obtained for each cell, for instance, showed the mechanism of bank formation in relation to the phase behavior characteristics. The results obtained indicated a varying degree of phase equilibrium concommitant with changes in the velocities of the phases in an actual alcohol displacement. This condition was approximated by changing the number of cells during the simulation. Interesting information was obtained on the influence of path length on the efficiency of alcohol displacement, which has been the subject of some controversy. Certain limitations preclude the use of the proposed model as a substitute for experimental studies. The results obtained were, nevertheless, of value in interpreting the experimental results.
Introduction
During recent years considerable effort has been directed toward an understanding of alcohol displacement, the process whereby oil and water are recovered from a porous medium by the continuous injection of a solvent. The complex nature of the physical process involved has so far defied a complete mathematical treatment. Other methods of approach, amounting to an overall material balance, have been proposed, yielding useful information on certain aspects of the process. Taber et al, in particular, defined the displacement mechanism in terms of the phase behavior of the alcohol-oil-brine system involved. Wachmann reported a mathematical treatment of alcohol displacement subject to certain simplifying assumptions. Donohue proposed the use of a "cell model" for simulating alcohol displacement. The nature of the assumptions involved limited the utility of the model. The present work attempts to examine the variables involved in the simulation of alcohol displacement and discusses several possible versions of the basic cell model. Under certain conditions the model results are similar to the experimental results. In particular, the spontaneous formation of the stabilized bank and the effects of the system phase behavior were successfully reproduced.
PREVIOUS WORK ON CELL MODELS
Cell models and the theoretical plate concept are often used in solving chemical engineering problems in which an explicit mathematical solution may be difficult or impossible to obtain. Examples of such applications occur in distillation, gas-liquid chromatography, reactor technology, absorption, etc. In petroleum engineering, such a model was used by Attra to describe non-equilibrium gas drive, and by Higgins and Leighton to calculate sweep efficiency in water flooding. Aris and Amundsen pointed out the equivalence between the diffusion model and perfectly mixed cells connected in series.
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