There is a need to fully utilize the benefits of geothermal water, while avoiding environmental problems in the development process. In this study, the water level, quantity, quality, and temperature of three sub-thermal reservoirs in Kaifeng City urban area, with burial depths of 1600−1800, 1800−2000, and 2000−2200 m, were combined with the local water demand and the actual exploitation and recharge rates, to establish an optimal allocation model of geothermal water considering its temperature, quality, and quantity. The objective function was to minimize the operating cost of the geothermal water supply system, and to overcome the four constraints of the heat supply required to meet the heat demand, single well pumping not exceeding the allowable pumping volume, pumping flow equaling the recharge flow, and water supply meeting the water demand. The model was solved based on the improved whale optimization algorithm and was compared with the results of other algorithms to determine the optimal configuration of geothermal water cascade utilization. The results showed that wells 1, 2, and 3 pumped flow rates of 82.62, 76.54, and 41.17 m/h for heating, respectively. Additionally, 18.40 m/h was used for therapeutic bathing, 9.52 m/h was used for greenhouse cultivation, and 7.74 m/h was used for fish farming. The lowest operating cost of the geothermal water utilization and recharge system was achieved when wells 4, 5, 6, and 7 were recharged with geothermal water at flows of 41.31, 41.31, 40.88, and 41.17 m/h, respectively, and well 6 was also recharged with tap water at a flow rate of 35.66 m/h. Compared with the pre-optimization period, the annual revenue increased by RMB 3.452 million. The study achieved an organic combination of extraction, recharge, and multi-target utilization, which is of great significance for the rational development and utilization of geothermal water and the science-based protection of the resource.

中文翻译：

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深层水库地热水利用的水温、水质、水量优化配置

需要充分利用地热水的优势，同时避免开发过程中出现环境问题。本研究结合开封市城区埋深1600~1800、1800~2000、2000~2200 m的3个次热水库的水位、水量、水质和温度，并结合当地水体结合地热水需求量和实际开采量及补给量，建立考虑温度、水质、水量的地热水优化配置模型。目标函数是使地热水供应系统的运行成本最小化，并克服供热需满足热需求、单井抽水不超过允许抽水量、抽水流量等于回灌流量、和满足用水需求的供水。该模型基于改进的鲸鱼优化算法进行求解，并与其他算法的结果进行比较，确定地热水梯级利用的最优配置。结果表明，1、2、3井供暖抽水流量分别为82.62、76.54、41.17 m/h。此外，18.40 m/h 用于治疗性沐浴，9.52 m/h 用于温室栽培，7.74 m/h 用于养鱼。当4、5、6和7井分别以41.31、41.31、40.88和41.17 m/h的流量回灌地热水时，地热水利用和回灌系统的运行成本达到最低，而6号井则以41.31、41.31、40.88和41.17 m/h的流量回灌地热水。还用流速为 35.66 m/h 的自来水进行补给。与优化前相比，年收入增加345.2万元。该研究实现了提取、回灌和多目标利用的有机结合，对于地热水的合理开发利用和资源的科学保护具有重要意义。