Statistical modelling of expanding cement slurry

Abstract

Questions of statistical processing of results of laboratory studies of expanding cement slurry are considered. Calcium oxide with inhibitors of a hydration reaction and calcium oxide with dicalcium ferrite are used as expansion additives. Six types of expansion additives are tested. Studies are performed at the two temperature regimes such as 22 and 75 °C. Series of results is obtained. At the first stage of mathematical processing of data evaluation of differences in mean values of linear expansion values by the Student's criterion were estimated. Comparison of mean values by certain options showed that maximum influence of temperature among studied parameters belongs to CaО + ferrochrome lignosulfonate (FCLS) (99/1), minimum influence belongs to CaСО3 + FeSO4 (2:1). To consider joint influence of concentration of the expanding additive and temperature on the value of linear expansion multidimensional models are built. Model values of linear expansion were calculated from multidimensional models and then compared with experimental values. Comparisons are made in two ways. The first way is based on the total number of all the data. The second way is based on six models built on different additives. As a result, two correlation fields are obtained. Each filed has three subfields (classes). Distinguished classes are described by linear discriminant functions with help of linear discriminant analysis. An analysis of obtained discriminant functions showed that values of linear expansion in classes are formed in accordance with different mechanisms. Therefore, refined multidimensional models and linear discriminant functions are built to calculate the values of linear expansion with three distinguished classes considered. A performed analysis showed that values of linear expansion in the range of 1-6 % are formed depending on concentration of the additive and temperature. Then in the range of 6-10 % the process proceeds due to a synergistic effect of the joint influence of concentration of an additive and temperature.

Keywords

• expanding cement slurry
• regression analysis
• correlation analysis
• mathematical model
• well
• expanding additives