Analytical model of leakage through an incomplete-sealed well

Abstract

This study presents a new analytical model to predict the pressure changes in a monitoring well and the leakage rate due to the leakage through an incomplete-sealed well in a closed system. Different from previous analytical models, herein we develop a new model to simulate the leakage of a leaky well which is incomplete-sealed and connects with the storage aquifer in a certain segment. Based on the problem description and assumptions, the governing equations with corresponding definite conditions are presented and solved by means of Laplace transform, Fourier cosine transform and Duhamel's principle. Verification of the developed model is achieved by comparing with existing analytical model. Then, the leakage rates and pressure changes are calculated for different key factors and sensitivity analyses are conducted. Obviously, a higher permeability accelerates the fluid exchange between the storage aquifer and the monitoring aquifer. Thus, with the increase of the leakage permeability, the leakage from the storage aquifer is more intensive but the ultimate leakage rate is invariable. With the decrease of the dimensionless distance, the seepage resistance along the leakage path is decreasing, resulting in the greater leakage between the two aquifers. Similarly, the dynamic equilibrium is unaffected by the position of the leakage segment. The incomplete seal of the leaky well only affects the spherical flow stage and this effect is relatively small. Therefore, the dimensionless leakage height has no obvious effect on the leakage. The increase of the storativity ratio enlarges the pressure difference between the two aquifers and increases the ultimate leakage rate to achieve the dynamic equilibrium. The leakage in the case with greater storativity ratio increases more significantly. This paper presents a simple and efficient analytical solutions for the leakage through an incomplete-sealed well and extends the applicability of the previous models.