A two‐dimensional model has been developed to solve for the problem of thermal injection into confining aquifer with a caprock of finite thickness and a bedrock of infinite thickness. Heat transfer by horizontal convection within the aquifer and by vertical conduction in the caprock and bedrock is considered. The model also incorporates variable temperatures on the surface of the caprock. Thus it can be used to study problems in connection with aquifer thermal energy storage, heat recovery from, and cold water injection into aquifers near the surface. The derived analytical solutions show that the caprock thickness is important only in long‐time periods and at greater distance from the injection well. The application of this model to cold water injection into an aquifer with 1.75‐m caprock thickness shows that the influence of seasonal variations of the surface temperature on the aquifer is nearly ±2°C.

Productivity impairment in tight-gas formations is a typical phenomenon for fractured wells. Processes responsible for this behavior are related to the characteristics of the porous media, and are induced as a consequence of the fracturing process. Fracture damage has been discussed in the literature for decades. In almost all cases, effects were considered in isolation. This is often not appropriate since natural effects such as stress dependency, fracture closure, and non-Darcy flow are interdependent. The same applies for the cleanup process where the back production of the load-water from the leakoff zones can be influenced by mechanical damage caused during the fracturing process, or by capillary forces and the gel residues of unbroken fracturing fluids within the fracture plane. This study analyzed the most common damage mechanisms by means of both generic and real field data. The latter was taken from German Rotliegend gas wells, which were history-matched and used for the evaluation of their cleanup and long-term production behavior. The results obtained were used to rank the individual processes for their damage potential. In addition to a commercial model, a customized in-house simulator was required in order to capture the specific physics. Results suggest that the consequences of processes independent of the reservoir conditions are not negligible when compared to the damage induced by the fracturing itself. In particular, in tight-gas, the stress dependency of the reservoir rock and fracture closure both tend to have a significant impact on the long-term productivity. Furthermore, inertial non-Darcy flow can cause much higher production impairment than, for example, hydraulic damage. It also shows that low permeability reservoirs are more affected by non-Darcy flow effects in both the fractures and the reservoir than is generally assumed. Introduction A wide variety of studies have been published in the literature dealing with damage mechanisms in fractured wells. A realistic cleanup scenario can imply, among others,complex three phase flow,the formation of a load-water invasion zone accompanied by hydraulic and mechanical damage in the fracture vicinity,filtercake buildup and erosion,gel residue damaging the proppant pack, incorporating complex non-Newtonian rheology,viscous fingering through the proppant pack, andunbroken fracturing fluids within the proppant pack.1,2,3,4,5,6,7,8,9 In the course of the subsequent production, inertial non-Darcy flow and geomechanical effects, e.g., stress dependency of reservoir permeability and fracture closure, additionally impact the behavior of the fractured well. These mechanisms are often neglected in analytical or numerical studies for the sake of simplicity. Unlike mechanical or hydraulic formation damage they are not "artificially induced", but rather a natural process. Many publications deal with these effects in isolation. This is often not appropriate since mechanisms such as stress dependency, fracture closure, and non-Darcy flow are interdependent. The same applies for the cleanup process where the back production of the loadwater from the leakoff zones can be influenced, for example, by mechanical damage caused during the fracturing process, or by capillary forces and the gel residues of unbroken fracturing fluids within the fracture plane. This study analyzed the most common damage mechanisms by means of both generic and real field data. The latter was taken from German Rotliegend gas wells, which were history-matched and used for the evaluation of their cleanup and long-term production behavior. The results obtained were then used to rank the individual processes for their damage potential under typical conditions. In addition to a commercial model, the use of a customized in-house reservoir simulator was necessary in order to capture the specific physics.

One of the main difficulties in transport modeling and calibration is the extraordinarily long computing times necessary for simulation runs. Improved execution time is a prerequisite for calibration in transport modeling. In this paper we investigate the problem of code acceleration using an adaptive grid refinement, neglecting subdomains, and devising a method by which the Courant condition can be ignored while maintaining accurate solutions. Grid refinement is based on dividing selected cells into regular subcells and including the balance equations of subcells in the equation system. The connection of coarse and refined cells satisfies the mass balance with an interpolation scheme that is implicitly included in the equation system. The refined subdomain can move with the average transport velocity of the subdomain. Very small time steps are required on a fine or a refined grid, because of the combined effect of the Courant and Peclet conditions. Therefore, we have developed a special upwind technique in small grid cells with high velocities (velocity suppression). We have neglected grid subdomains with very small concentration gradients (zero suppression). The resulting software, MODCALIF, is a three-dimensional, modularly constructed FORTRAN code. For convenience, the package names used by the well-known MODFLOW and MT3D computer programs are adopted, and the same input file structure and format is used, but the program presented here is separate and independent. Also, MODCALIF includes algorithms for variable density modeling and model calibration. The method is tested by comparison with an analytical solution, and illustrated by means of a two-dimensional theoretical example and three-dimensional simulations of the variable-density Cape Cod and SALTPOOL experiments. Crossing from fine to coarse grid produces numerical dispersion when the whole subdomain of interest is refined; however, we show that accurate solutions can be obtained using a fraction of the execution time required by uniformly fine-grid solutions.