Abstract
This paper presents the use of scaling and dimensional analysis to assess the viability of conventional modelling of immiscible displacement occurring when water is injected into the oil-saturated, porous rock—a conventional secondary oil-recovery method. A brief description of the laboratory tests of oil displacement with water performed on long core sets taken from wells operating on a Polish oil reservoir was presented. A dimensionless product generator based on dimensional analysis and Buckingham Π theorem was used to generate all possible combinatorial sets of dimensionless products for physical variables describing the phenomenon. The mathematical model of the phenomenon was transformed to its dimensionless form, using a selected set of the products. The results of the laboratory tests were analyzed as functions of the products. Statistically verified quantities describing both dependent and independent experiment variables were subject to a regression analysis to study dependencies of the experimental results upon selected dimensionless products. The degrees of the dependencies were determined and compared with the model coefficients. The conclusions are drawn for the purposes of model application to correctly describe the laboratory and, consequently, field scale processes of immiscible oil displacement by water.
Highlights
Immiscible displacement is a phenomenon occurring, e.g., during the process of water injection to an oil field as a secondary method of oil recovery [1,2]
This paper presents a unique report on the subject with regard to the carbonate rocks and reservoir fluids found in Polish petroleum formations
Buckingham Π theorem allows for the reduction of the most general equations of physical variables that describe the phenomenon to equations involving only sets of dimensionless products (Π’s) constructed from the original variables
Summary
Immiscible displacement is a phenomenon occurring, e.g., during the process of water injection to an oil field as a secondary method of oil recovery [1,2]. This paper presents a unique report on the subject with regard to the carbonate rocks and reservoir fluids found in Polish petroleum formations Both small- and large-scale modelling are conventionally performed by an approximate description of the real-world phenomena. Buckingham Π theorem allows for the reduction of the most general equations of physical variables that describe the phenomenon to equations involving only sets of dimensionless products (Π’s) constructed from the original variables. The significance of the dimensionless Π products is analyzed with respect to their influence upon experimental results and confronted with the dependencies of the model If it is positively verified, the model can be applied to the large-scale problems, according to the similarity theory [10]. A detailed description of the procedure is presented, and the appropriate conclusions are drawn
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