«Oilfield engineering»

New mathematical model of water, oil and gas inflow to a well

UDC: 622.276.2.001.57
DOI: 10.33285/0207-2351-2023-1(649)-5-24

Authors:

¹ National University of Oil and Gas "Gubkin University", Moscow, Russia

Keywords: flow, filtration, water, oil, gas, minimum flow rate, minimum pressure, maximum pressure, maximum flow rate, experience, experiment, reservoir thickness, productive reservoir, well, initial conditions, ordinary differential equations

Annotation:

The article briefly analyzes the known dependencies that determine the total inflow of liquid Q_w and gas Q_g to the well in radial flow, which are determined on the basis of the mass conservation law, the driving forces law and Darcy filtration law.

The presented formulas contain two important parameters – the radius of the supply circuit r_e and the pressure on the supply circuit p_e, the values of which are uncertain; there exist recommendations (M. Masket, et al.) that the distance r_e is completely arbitrary, it should be taken from the center of the well to a point where there is every reason to obtain well-founded pressure values p_e; the arguments of Professor N.E. Zhukovsky, who already in 1888 noted the shortcomings of the doctrine of the radius of influence, based on the filtration law in the form of Darcy.

Examples of calculations are considered that show good agreement between the experimental and calculated (predicted) values of the flow rate (pressure) of water, oil and gas and indicate the adequacy of the new mathematical model for different processes of water, oil and gas flow in natural reservoirs.

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