Generalized Rowlins–Shellhardt equation and its application for optimization of well operation modes

Relevance. The need to improve the accuracy and reliability of forecasting the productivity of gas and gas condensate wells in the long-term planning of gas production enterprises. To improve the accuracy and reliability of calculations of forecast flow rates, it is necessary to take into account changes in the filtration and capacitance properties of the formation in bottom-hole zones caused by the values of reservoir pressure and depression changing over time.

Aim. To determine the equations of real indicator curves of fluid inflow to a gas well, taking into account the dependence of the reservoir filtration and capacitance properties in bottom-hole zones on changing values of reservoir pressure and depression. To achieve this aim, the authors apply the working hypothesis that, firstly, in a hidden form, all the physical patterns of gas filtration to the well are contained in the accounting geological and field documentation accumulated during the operation of the well. Secondly, the equations of all real indicator curves can be approximated by the generalized Rawlins–Shellhardt equation proposed by the authors. Based on the results of processing real geological and field data from a number of wells, a new effect was discovered, showing that real indicator curves, unlike classical theoretical situations, can be described by non-monotonic dependences of flow rate on depression. The discovered new effect has important theoretical and practical significance for the oil and gas industry.

Objects. Equations of gas inflows to wells, approximated in the form of a generalized Rawlins–Shellhardt equation.

Methods. Methods of interpolation and approximation of field data, numerical integration, mathematical modeling methods, correlation and regression analyses, least squares method.

Results. For real indicator curves describing, in contrast to classical filtration laws, including non-monotonic dependences of the flow rate on depression, an approximation model is constructed in the form of the proposed generalized Rawlins–Shellhardt equation. This model opens up a new approach to forecasting the flow rates of gas wells, improves the efficiency of gas production and contributes to the sustainable development of the energy sector. For example, it greatly simplifies planning of geological and technical measures and optimizes the development of gas fields.