This paper presents a dimensionless number and its critical value for predicting the onset of instability during immiscible displacement in porous media. The critical dimensionless number obtained from a stability theory for a cylindrical system successfully predicted the onset of instability in laboratory floods. Therefore, this number can be used to classify the stability of two-phase incompressible displacements in homogeneous porous media. Introduction When a fluid displaces a more viscous fluid, the displacement front may become unstable, resulting in viscous fingering. This phenomenon raises both practical and theoretical concerns. Apart from further reducing the displacement efficiency of an already inefficient displacement arrangement, instability may invalidate the usual method of simulating immiscible displacement performance based on relative permeability and capillary pressure concepts. Also, it introduces an additional scaling requirement for using model tests to forecast prototype displacement results. Therefore, it would be most beneficial to predict the onset of instability, so as to avoid viscous fingering, or, where it is unavoidable, to be able to recognize it as a factor in the displacement.The onset of instability call be predicted by a stability analysis of the displacement. The objective of such an analysis is to determine the conditions under which small disturbances or perturbations of the displacement front will grow to become viscous fingers. Ideally, the analysis should give a universal dimensionless scaling group together with its critical value above which instability will occur. The stability classification then would entail no more than the calculation of one dimensionless number in a manner analogous to the calculation of a Reynolds number to distinguish between laminar and turbulent flow.Several stability studies of immiscible displacement have been reported in the literature. Collectively, they show that these variables are pertinent to the stability problem:mobility (or viscosity) ratio,displacement velocity, system geometry and dimensions,capillary and gravitational forces, andsystem permeability and wettability. However, none of the previous studies have combined these variables into one dimensionless number that can be used to quantify the stability classification.The objective of this study was to obtain, by means of a stability analysis, a universal dimensionless scaling group and its critical value for predicting the onset of instability during immiscible displacement in porous media. This paper shows how the stability theory of Chuoke et al. was extended to achieve this objective and presents the results of laboratory floods that confirm the predicted onset of instability in cylindrical cores. Theory The pertinent dimensionless number for predicting the onset of instability was obtained by extending the stability theory of Chuoke et al. Their theory was based on a piston-like unperturbed displacement model in which the oil and water zones are separated by a planar interface. Details of the theory and our extension of it are presented in the following sections. SPEJ P. 249^

The importance of miscible displacements in the petroleum industry makes their understanding and quantitative prediction critical in decisions on the applicability of certain recovery techniques. In this study, scaling miscible displacements in porous media was investigated using a general procedure of inspectional analyis. The procedure was used to derive the minimum number of dimensionless scaling groups which govern miscible displacements. It was found that scaling miscible displacements in a two-dimensional, homogeneous, anisotropic vertical cross-section requires the matching of nine dimensionless scaling groups. A numerical sensitivity study of the equations was performed to investigate the effects of some of the scaling groups on the performance of miscible displacements. Through this sensitivity study, it was found that one of the groups is insensitive to the results over all practical values. Hence, the problem can be scaled by only eight dimensionless scaling groups. The prediction of the recovery efficiency for miscible EOR processes can be achieved solely by analyzing these scaling groups. Preliminary results indicate that when the groups are used as inputs to an artificial neural network, the efficiency of the displacement can be accurately predicted.

A compositional material-balance model was used to predict the densities of diesel-and mineral-oil-based muds at elevated pressures and temperatures. We measured the densities of diesel oil, two mineral oils, and calcium chloride solutions from 78 to 350°F and from 0 to 15,000 psig. The measured densities were used in an existing compositional material-balance model to predict the densities of 11-and 17-lbm/gal oil-based muds. We also measured the densities of these muds at elevated pressures and temperatures and compared them with the predicted values. The results show excellent agreement between measured and predicted densities. The experimental density data were used to predict downhole densities and static wellbore pressures for the oil-based muds. Results show that the mineral-oil muds are not only more compressible than the diesel-oil muds, but also more susceptible to thermal expansion. Therefore, all the oil-based muds tend to give essentially the same static-wellbore-pressure profile.

5PE )47/3 summary.A study was undertaken to investigate how instability would affect the oii[water relative permeability curves bhtained by the. dynamic-displacement method. In this method, stable Buckley-Leverett displacement theorj is used to calculate relative permeability cuties from coreflood dsta, Thus, to obtain the true relative permeability curves by the dynarnic-disp~cement method, the coreflocd must he stable. However, the method frequently has been applied to umstable core ftoods. The consequence of this aPPlimtion of the method has not been previously reponed.We compared~illwater relative permeability cw-vis from steady-state a"d dyqamic-dkplacement experiments at several levels of in.stsbility. The results 'showed that tbe dynamicdkplacement relative permeability curves deviated "significantly from the steadystate cu'i-ves as the degree of instabili~increased. This observation indicates the need to scale Iaboratow Tel?ive pe~eability measurements to account for instabili~. To obtain representative relative permeability curves for numerical modeling of. a resetvoir, laboratory displacement experiments should be conducted at the same degree of instabili!qr as that iu the reservoir.