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PREDICTION OF MOLECULAR DIFFUSION AT RESERVOIR

CONDITIONS. PARTI---MEASUREMENT AND PREDICTION O

BINARY DENSE GAS DIFFUSION COEFFICIENTS

P.M. SIGMUND

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RECOVERY TECHNOLOGY JCPT76-02-05 JCPT-12 Prediction of Molecular Diffusion At Reservoir Conditions. Part I Measurement and Prediction of Binary Dense Gas Diffusion Coefficients Phillip M. Sigmund, Petroleum Recovery Institute, Calgary, Alberta Abstract Diffusion coefficients in binary dense fluid systems are measured and used along with data available in the literature to obtain a generalized correlation for predicting binary molecular diffusion coefficients in dense gases over a broad range of conditions. Introduction ATTEMPTS to quantify

porous media are often, encountered in desi gn studies of processes(@ related to petroleum re covery. Dispersion, an important part of mixing pheno mena, can be related to the distribution in travel times tha t results when a fluid passes through a porous media"1. On a micro- scopic scale, the two most important mechani sms con- tributing to dispersion are variation s in velocity be- tween fluid elements flowing in neighb ouring pores or groups of pores (often referred to as convect ive mixing) and molecular diffusion",' , ". Although there is some controversy over the magnitudeffects, it has been thought that in vertical gravity- stabilized miscible floods, such as those carried out in the carbonate pinnacle reefs of Alberta, molecular diffusion played an important role in the mixing of the solvent bank with drive gas and oil('-, In other pro- cesses, such@h -as gas, solvent or C02 horizontal 'miscible floods, the effects of molecular diffusion are difficult to quantify, but are thought to be important in the recovery of non-flowing oil by mass transfer", ', "'. The estimation of molecular diffusion coefficients in low-pressure gChapman @@sk ?g Theory"." is adequate for a wide variety oi singie- Phillip M. Sigmund graduated from the University of Waterloo with a B.A.Sc. (c emical engineering) in 1963 and a M.A.Sc. (chemical en- gineering) in 1964. After obtaining his Pb.D. (chemical engineering) from the University of Texas in 1969, he joined the Petroleum Recovery Re- search Institute, where he is cur- rently employed as a senior research engineer. H e has been involved in Institute research projects dealing _ with retrograde phenomena in porous media, diffusion and dispersion phenomena

from car- bonate reservoirs, and the use of CO, and SO, for en- hanc4@d oil recovery. Dr. Sigmund is a member of CIM, CIC, AIME and the Association of Professional Engineers of Alberta. 4a@ component and binary gases ... .... In liquids, the success of theoreticil models has been more limited, perhaps because of ilhe complex nature of molecular interac- tions in the liquid state. N evertheless, except in the critical region, liquid diffusion coefficients can at present be predicted by empirical correlations, with sufficient accuracy for many engineering pur-

critical or dense fluid state, there are few exp@@rimental studies of diffusion coefficients inbinary mixtures. This has made it difficult t.o assess predictive t(@chniques, which have so far been tested largely on l-,he basis of self-diffusion data and are generally considered unreliable(',"). The pres(@nt two-part paper describes Petroleum Re(!overy Institute work that was directed toward de- veloping improved predictive methods for molecular diffusion coefficients in the high-pressure dense gas state which is commonly encountered under reservoir conditions. @rhe

previously unob- tained data on binary diffusion coefficients for fluids in the dens(! gas state, and a general correlation for binary molecular diffusion coefficients at conditions ranging from ambient to those likely to exist in Alberta reservoirs. 'r he second part presents a method., for using the binary correlation to estimate diffusion in multicompolient systems and shows how the effects of convection and diffusion can be combined to calculate concentration profiles for flu id mixtures flowing in porous media. Experimental APPARATUS AND PROCEDURE A Loschrriidused in the experi- ments. It consisted of three ball valves joined together wit h stainless steel tubing to form the upper and lower half cells. I'he ball valves were modified slightly to prov ide for circulation of dense gas mixtures above their upp er dew point. The cell lengths in this version of the Loschmidt apparat us could be easily changed by using different lengths of tub ing, allowing a broad range of pressures to be studied in gas system s. The diffusion cell was held in a vertical position by ring clamp s and placed in a chromatographic air oven, which served a

illustration of the cell is shown in Figure 1. Diffusion was studied between mixtures of gases over some desired mole fraction interval (approxim- ately 0.20). The two mixtures of approximately desired composition were generated by metering appropriate amounts of each pure component into two storage ves- sels equipped with floating pistons. The volume and hence pressiire of each fluid was adjusted to ensure _ The Jburfial'of Canadian Petroleum

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