Mathematical programming for process optimization problems in well drilling

Optimization problems solved by means of linear programming are presented in the form of equalities or inequalities, the target function being linear. Linear programming methods are widely used in solving problems for engineering, food industry, and chemical industry. This prevalence is due to the availability of the software for solving high-dimensionality linear programming problems and the possibility to analyze the problems when varying the source data. Constructing a linear programming model includes determining the variables of the problem, setting constraints in the form of inequalities, and representing the solution objective as a linear function. The article presents the description of the problem’s’ mathematical formulation and the specific realization of the description for the so-called ‘mixture’ problems: the mixture is the drilling mud, its technological quality being a function of the ingredients, and the preparation cost should be minimal. The construction of the problem model is realized by solving it with the semigraphical method using a program code for graphing and a special code for solving linear programming problems in the MATLAB environment. The problem solution is analyzed, and the ways to improve the solution by reorganizing the mixture composition are suggested.

constraints, target function, problem model, feasible region