Approximate Solutions For Well Flows With Variable Rates

The well flow with pumping test plays an important role in groundwater research,which can intuitively understand and explain the groundwater movement.Under the pumping test with constant rate,the well flow model has been well studied.With the extension of the problem and the advancement of the actual situation,it is necessary to consider the pumping test with variable rate.It can describe the change of groundwater level more precisely and provide an effective calculation method for groundwater prediction.This paper mainly studies the approximate solution of the well flow model driven by pumping test variable rate and estimates the aquifer hydraulic transmissivity and storativity according to the simplified formula of the series solution for the model.The first chapter introduces the development background of well flow model and the related advancement.The second chapter provides the mathematical knowledge involved in this paper,such as well flow equation,Bessel function,exponential integral,Laplace transform and inverse Laplace transform,series product,Gaussian noise model and properties,signal-to-noise ratio,etc.In the third chapter,the approximate solution of well flow model with variable rate is studied.The series solutions in short time and long time for a general pumping function is given.When the pumping test function changes exponentially and periodically,the series expansions of the solution in small time and at infinity are studied in detail.We also discuss how to join these two series expansions to satisfy the given accuracy.In order to confirm the accuracy of the formulas,they are applied to three actual groundwater scenarios for analysis.In the fourth chapter,the parameter estimations are studied in the well flow model with variable rate.By adding Gauss white noises to the calculated values to simulate the real data and substituting the data into the fitting formula,the transmissivity and storativity are inverted.The results obtained in this paper are verified by theoretical derivation and experiment,which provides a new method for the calculation of groundwater flows by pumping test with variable rate.