To　improve　the　energy-to-CH4　efficiency　and　enhance　renewable　power　utilization,　we　investigate　direct　Power-to-Methane　at　low　inlet　H-2　content　(25　vol%)　in　solid　oxide　electrolysis　cell　(SOEC).　The　synergy　of　the　pressurized　operation　and　the　electricity　input　effectively　enhances　CH4　yield　by　one-order　of　magnitude　from　2.8%　to　28.7%　and　the　CO2-to-CH4　ratio　from　4.4%　to　39.5%　in　the　H-2-reduced　case,　where　the　ratio　of　H-2　consumption　to　total　energy　consumption　decreases　to　41%　and　the　energy-to-CH4　efficiency　increases　to　53%.　We　develop　a　multiphysics　tubular　SOEC　model　to　understand　the　intrinsic　coupling　between　electrochemistry　and　heterogeneous　catalytic　chemistry.　From　the　perspective　of　performance　enhancement,　geometry　optimization,　and　thermal　design,　inhibiting　CH4　production　in　the　inlet　gas-controlled　zone　and　promoting　CH4　production　synergistically　in　both　the　electrochemistry-controlled　zone　and　the　temperature-controlled　zone　is　the　key　to　improve　the　energy-to-CH4　efficiency.