New mathematical models for production and pressure behavior of a well producing at constant bottomhole pressure

Abstract

New mathematical models are developed in this study to forecast the production and pressure behavior of a centered well producing at constant bottomhole pressure from a circular closed boundary reservoir and the pressure buildup performance after shut-in. Both of transient flow and boundary dominated flow are considered. The results of the proposed models are validated by CMG simulation. The new models are based on single phase fluid flow of constant compressibility, viscosity and formation volume factor in homogeneous 2D reservoir with uniform thickness. A fully analytical solution is obtained through combinations of Dirac delta function, Bessel functions, Laplace transform, Green's function and inverse Laplace transform. Stehfest's method is used to convert the obtained solution from the Laplace domain into the real domain. Gaussian quadrature with 100 points is used to approximate the integral of a function. The complete procedure of governing equations is described in details to allow verification. During transient flow, the dimensionless pressure in the reservoir is graphed vs. the logarithm of radial distance to generate straight lines; with the increasing of producing time, the pressure gradient along the radial distance drops; and the decline of the flow rate is shown to be a power law nature and the cumulative production increases linearly with respect to producing time; it is found that the decline rate, Dt, is independent of bottomhole pressures; for the pressure buildup following a period of constant bottomhole pressure production, it indicates that the bottomhole pressure displays a linear relationship with Horner time. During boundary dominated flow, the flow rate declines exponentially; the logarithm of flow rate is graphed versus time to produce a semi-log straight line; and the Cartesian plot of flow rate versus cumulative production also generates a straight line. Both of these two graphs can be verified by Arps' empirical decline model; it is found that the decline coefficient, Db, is independent of bottomhole pressures but depends on reservoir size, it decreases as the reservoir size increases. A CMG simulation is ran to verify the production decline and pressure buildup performance following constant bottomhole pressure production. The results of the simulation coincides with those of the models. Finally, the mathematical models proposed in this work are efficient to forecast the production and pressure behavior of a well producing at constant bottomhole pressure.

Date of Award	2016
Original language	American English
Supervisor	Jing Lu (Supervisor)