Many data-intensive sensor network applications are potential big-data enabler: they are deployed in challenging environments to collect large volume of data for a long period of time. However, in the challenging environments, it is not possible to deploy base stations in or near the sensor field to collect sensory data. Therefore, the overflow data of the source nodes is first offloaded to other nodes inside the network, and is then collected when uploading opportunities become available. We call this process data preservation in sensor networks. In this paper, we take into account spatial correlation that exist in sensory data, and study how to minimize the total energy consumption in data preservation. We call this problem data preservation problem with data correlation. We show that with proper transformation, this problem is equivalent to minimum cost flow problem, which can be solved optimally and efficiently. Via simulations, we show that it outperforms an efficient greedy algorithm.