Performing non-aggregate range queries over encrypted data stored on untrusted clouds has been considered by a large body of work over the last years. However, prior schemes mainly concentrate on improving query performance while the scalability dimension still remains challenging. Due to heavily pre-processing incoming data at a trusted component such as encrypting data and building secure indexes, existing solutions cannot provide a satisfactory ingestion throughput. In this paper, we overcome this limitation by introducing a framework for secure range query processing, FRESQUE, that enables a scalable consumption throughput while still maintaining strong privacy protection for outsourced data. Our experiments on real-world datasets show that FRESQUE can support over 160 thousand record insertions in a second, when running on a 12-computing node cluster. It also significantly outperforms one of the most efficient schemes such as PINED-RQ++ by 43 times on ingestion throughput.