New Method In Predicting Groundwater Flow System

Due to the development of human society and expansion of the production scales, the global water resources crisis began to surface. During the process of utilizing and exploitation of the ground water in the world, dreadful environmental problems prevail. For example, because of the over exploitation and inappropriate utilization of the ground water, not only has it intensified the demand and supply imbalance, it has also set off a series of geological problems, such as ground-surface settlement and collapse, seawater invasion, ground fissure, mining area geological catastrophic events etc.The importance of the appropriate utilization and protection of the ground water has gradually become known to the world community. The quantitative assessment of groundwater resources has become the center topic in water resource management. The groundwater numerical simulation started to evolve after the development of the quantitative assessment of groundwater resources. Through the improvement of the calculation methods and technologies, numerical simulation has become the mainstream method in quantitative assessment. The numerical simulation not only can simulate the ground water flow problems, it can also be used to simulate the water quality problems or problems occur in other models. The ground water numerical simulation has turned into an effective tool for ground water quantitative assessment management.Although there is a vast development of the calculation methods and technologies of ground-water numerical simulation, it has the following limitations in its theories and practicalities and needs to be further researched and resolved. For examples: the uncertainty of the simulation results, the limitation of the numeric calculations, problems incurred in the input data requirements, the assumptions to the models, and the assessment of the boundary condition, as well as some other uncertainties caused by the non-heterogeneous of aquifer. Therefore, the groundwater modeling process is still permeated with all kinds of uncertain factors. It is one of the biggest challenges in this research field to fully utilize and improve the technologies on hand to eliminate the modeling uncertainty, promote the validity of the numerical simulation process and the reliability of the forecasted results.Looking from the aspect of the water resource management and considering the stress changes (such as, new wells, changes in rainfall filtration rate, new reservoirs), people are probably more concerned with the net change incurred in the groundwater system. If we are using the traditional groundwater modeling process to predict the influences to the groundwater system caused by the local stress changes, we need to build a model first, followed by modifying the model to satisfy the existing conditions, manipulating the model to obtain the distribution of the groundwater water table before the stress changes, reworking the model to get the distribution after the changes, eventually calculating the difference between the two distribution values to obtain the net change. Constructing the groundwater modeling requires inputting tremendous amount of field data to modify the model. The difficulties in model calibration caused by the lack of field information, the measurement errors, and natural environmental variables all affect the uncertainty of the field data which in turn causes the parameter uncertainty and the inaccuracy of the modeling predictions.Under some circumstances, the net change only depends on a few parameters. If we can build a mathematical modeling to simulate the net change directly, we can reduce the need for field data, and the ill effects of the uncertain factors found in the traditional modeling in order to raise the efficiency and accuracy of the modeling process. For example: If we are only concerned with the environment impact caused by a groundwater pumping stress, we can regard river stage and recharge changes equal to zero. The boundary could be set far from the impact area and set to no flow. The only parameters we need to know then are the aquifer hydraulic conductivities and leakance of surface water features. Since we calculate the change from zero, the preliminary conditions of the modeling can be set to zero. By reducing data requirements and moving the boundaries away from the impact area of local stresses, the uncertainties related to the data and boundary conditions can be reduced.According to what have been discussed, this study, based on the traditional groundwater numerical modeling, has developed a new groundwater modeling to make direct predictions on the groundwater system changes caused by the local stress fluctuations. The proposed new modeling reduces the requirement of input data in the modeling processes, simplifies the boundary conditions, at the same time, and introduces the iteration method in solving the governing equation. The change governing equations related to confined and unconfined aquifer have been developed. It was verified that the simulation process for confined aquifer is as the same as those of traditional numerical simulation process. Otherwise, it is only approximation for unconfined aquifer. The predicted error will be increased as long as the increase of the absolute value of net change. This study introduced an iteration scheme which can improve the perturbation results.There are seven chapters in this paper.Chapter One is the introduction. Referencing through a large quantity of documents, literatures, surveys and researches, it illuminates the importance of the groundwater resources quantitative assessment in water resources management and utilization. It summarizes the development of the groundwater numerical modeling, its present function and exiting issues. It points out the limitations, the requirement for larger amount of raw data and the outcome uncertainty caused by the different variables in the existing numerical modeling. The available research results are inadequate in predicting warnings for the highly concerned issue of groundwater net change caused by local stress fluctuations. Chapter Two is a study of the governing equations and numerical simulations. This chapter gives an introduction to governing equation used in traditional modeling and numerical solutions. In most groundwater models, these equations are solved numerically using finite difference schemes. There are an array of multifunctional software developed abroad for groundwater modeling and are widely adopted for their modularization, visualization, interactivities and variety in simulation method.Considering the geological parameters and head changes caused by local stress fluctuations, we developed the groundwater head change governing equation for the fluctuating component of variables by decomposing the variables in the governing equation into an initial term and a perturbation term. The format of groundwater head change governing equation for confined aquifer is similar with that of traditional governing equation. Theoretically, therefore, we can use the same numerical schemes to directly model the hydraulic head perturbation in confined aquifers.The perturbation governing equation for unconfined aquifer is different from traditional governing equation. Theoretically, if the change in head is small compared to the saturated thickness, we can use the same numerical method as for traditional groundwater modeling to estimate hydraulic head change. However, if the change in head is large compared to the saturated thickness, the numerical schemes employed in traditional groundwater equations cannot be directly used.For the more complicated case of unconfined aquifers, we introduced an iteration scheme which improved the perturbation results. We compiled finite difference scheme programs for iteration scheme in MATLAB which can be combined with those exiting software, such as MODFLOW and IGW, in solving the unconfined aquifer perturbation equation.Chapter Three: Considering the geological parameters and head changes caused by local stress fluctuations, we developed the flux change governing equation by decomposing the variables in the governing equation into an initial term and a perturbation term. The format of change governing equation for confined aquifer is similar with that of traditional governing equation. Theoretically, therefore, we can use the same numerical schemes to directly model the flux perturbation in confined aquifers.The flux change governing equation for unconfined aquifer is different from traditional governing equation. Theoretically, if the change in head is small compared to the saturated thickness, we can use the same numerical method as for traditional groundwater modeling to estimate flux change. However, if the change in head is large compared to the saturated thickness, the numerical schemes employed in traditional groundwater equations cannot be directly used. We derive finite difference scheme for solving flux change governing equation in unconfined aquifer.Chapter Four: We use a 1D groundwater model for which an analytical solution existed to verify the results obtained from perturbation equations and to verify the improvements through the iteration scheme. The verification results show that the perturbation solution is exactly as the same as the analytical solution in confined aquifer. In unconfined aquifer, the iteration solutions converged to the analytical solution. We also found out that when the relative change in head is small, it takes lesser iterations to converge to the analytical solution and vice versa.Chapter Five: New method application. The aim of new method is to directly calculate the change caused by local stress fluctuations without having to separately model pre-and post-stress conditions. To test this methodology, we created a one-layer groundwater model for an unconfined aquifer. We simulated a typical scenario in which more groundwater pumping is required for a certain new development in an area; the development also creates impervious surfaces reducing recharge rates; and, the water levels drop in the surface reservoirs due to droughts/climate change etc. We first ascertained the net changes in aquifer levels using the traditional modeling approach, i.e., separately modeling pre- and post-conditions and then calculating the net change by subtracting one from the other. After ascertaining the change using traditional modeling approach we set up a 'perturbation model' to directly calculate the 'change'. Theoretically, the model should give us the same change as the traditional models as long as change in head is small relative to saturated thickness of the aquifer. However, that not being the case in our example model, the two solutions did not match. The difference can be minimized by iterating it several times using the iteration scheme. As expected, the results of 'modeling change only' improved with every iteration step until the solution converged to the traditional modeling solution.We have already seen that the new method solution converges to the analytical one for a 1D situation. It is difficult to ascertain an analytical solution for a relatively more complicated (2D or 3D) groundwater situation where different kinds of stresses change simultaneously. However, using a traditional modeling approach with very fine model discrete grid we obtained a solution close to the analytical one and demonstrated that 'modeling the change only' can converge to this solution after a few iterations.Chapter Six: Using statistics to analyze the differences between the new method and the traditional method in model calibration.In order to build up the credibility of the model calibration, we have created a relatively complex groundwater conceptual model based on experiences and set a relative large density of discrete grid. We simulated the net change by employing finite difference numerical simulation method in traditional way and using the results as calibration targets. Reset the model with less density of discrete grid for calibration. We then calibrated the model respectively in traditional method and new method. From the calibration results we can see that applications of groundwater models do require extensive field information for input data and for calibration. The uncertainties in data due to measurement errors and natural variability translate into the uncertainty of estimated parameters which further translates into uncertainty in model predictions. The groundwater modeling process is marred by uncertainties all along. Our new approach is more efficient in terms of time and resources required to build the model and also reduce uncertainties related to data, parameter estimation and boundary conditions leading to reduced uncertainty in model predictions.Chapter Seven: Conclusions. This chapter points out the distinct concept of the new method and the simplicity and efficiency of the iteration scheme .By programming the new method into the traditional numerical modeling software, we can obtain fast and efficient predictions on the groundwater head net change caused by local stress fluctuations.Perturbation method not only can be used to predict the groundwater head net change caused by local stress fluctuations, it can also associate the obtained net change to the groundwater level distribution to compute the system groundwater head distribution after the stress fluctuations. By using this method, we avoid the complexity of the traditional modeling in making predictions. When we put the results into practical use, it will increase our ability to make such predictions. This research and its payoffs will bring great contributions to the water resources management.The innovations of this study are as follows:1. Based on the traditional groundwater numerical modeling, this study introduces the perturbation theory to derive the change governing equation to directly reflect the groundwater head or flux net change caused by local stress fluctuations. This new approach is more efficient in terms of time and resources required to build the model and also reduce uncertainties related to data, parameter estimation and boundary conditions leading to reduced uncertainty in model predictions. 2. This study introduces an iteration scheme which improves the simulation results and compiles finite difference scheme programs which can be combined with those existing software in solving the unconfined aquifer head change governing equation.3. Making validation using analysis solution and the predictions from the outcomes, quantifying the iteration steps requested by convergence, providing guidance in making practical applications.