Mergers of binary neutron stars (BNSs) produce kilonovae, powered by decay of r-process heavy nuclei in their ejecta. Searching and finding kilonovae, associated with gravitational wave (GW) detected BNS mergers, is crucial for multimessenger studies of BNS mergers and their astrophysical and cosmological applications. In this paper, we investigate the detectability of kilonovae by several electromagnetic surveys, including SiTian, the Chinese Space Station Telescope (CSST), the Rubin Observatory, Euclid and the Nancy Grace Roman Space Telescope (RST). We consider BNS mergers detected by both the network of the Laser Interferometer Gravitational-Wave Observatory (LIGO), Virgo and KAGRA (LVK), and of the Einstein Telescope and Cosmic Explorer (ET&2CE). We adopt a binary population synthesis model to obtain a mock sample of BNS mergers with known properties, and a phenomenological kilonova model to predict multiband light curve of the kilonova associated with each BNS merger. We predict the detection rate or efficiency of kilonovae by Rubin and SiTian, CSST, Euclid and RST, associated with BNS mergers either detected by LVK operation 5 (O5) or ET&2CE, under either the wide fast deep survey or time of opportunity strategy. We also predict the parameter (total mass, mass ratio, localization area) distributions of BNS systems jointly detected by GW and EM observations. We emphasize that kilonovae associated with massive BNS mergers like GW190425 (with total mass ≳3.3M⊙) can be detected in a significant fraction ≃20%–30% for ET&2CE or ≃30%–40% for LVK O5 by SiTian with a shallow observational depth or other survey telescopes, providing crucial information for kilonova physics and the equation of state of neutron stars.