A gate valve comprises a valve body having an internal working fluid passage and an internal gate chamber extending transverse to the working fluid passage. In addition, the gate valve comprises a gate disposed in the internal gate chamber and movable within the gate chamber between a closed position obstructing fluid flow through the working fluid passage and an open position allowing fluid flow through the working fluid passage. Further, the gate valve comprises an internal sealing arrangement coaxially disposed in the working fluid passage and extending between the valve body and the gate to form a barrier between the internal working fluid passage and the gate chamber. The internal sealing arrangement includes a frustoconical metal sealing surface adapted to sealingly engage an opposed mating frustoconical metal sealing surface on the valve body to form a first tapered metal-to-metal seal between the sealing arrangement and the valve body.