Oil spills represent one of the major threats to marine ecosystems. Satellite synthetic-aperture radar (SAR) sensors have been widely used to identify oil spills due to their ability to provide high resolution images during day and night under all weather conditions. In recent years, the use of artificial intelligence (AI) systems, especially convolutional neural networks (CNNs), have led to many important improvements in performing this task. However, most of the previous solutions to this problem have focused on obtaining the best performance under the assumption that there are no constraints on the amount of hardware resources being used. For this reason, the amounts of hardware resources such as memory and power consumption required by previous solutions make them unsuitable for remote embedded systems such as nano and micro-satellites, which usually have very limited hardware capability and very strict limits on power consumption. In this paper, we present a CNN architecture for semantically segmenting SAR images into multiple classes. The proposed CNN is specifically designed to run on remote embedded systems, which have very limited hardware capability and strict limits on power consumption. Even if the performance in terms of results accuracy does not represent a step forward compared with previous solutions, the presented CNN has the important advantage of being able to run on remote embedded systems with limited hardware resources while achieving good performance. The presented CNN is compatible with dedicated hardware accelerators available on the market due to its low memory footprint and small size. It also provides many additional very significant advantages, such as having shorter inference times, requiring shorter training times, and avoiding transmission of irrelevant data. Our goal is to allow embedded low power remote devices such as satellite systems for remote sensing to be able to directly run CNNs on board, so that the amount of data that needs to be transmitted to ground and processed on ground can be substantially reduced, which will be greatly beneficial in significantly reducing the amount of time needed for identification of oil spills from SAR images.