Silent prayer is mentioned in Scripture.
1Sa 16:7 And Jehovah saith unto Samuel, `Look not unto his appearance, and unto the height of his stature, for I have rejected him; for it is not as man seeth--for man looketh at the eyes, and Jehovah looketh at the heart.'
1Sa 1:12 And it came to pass, as she continued praying before the LORD, that Eli marked her mouth.
1Sa 1:13 Now Hannah, she spake in her heart; only her lips moved, but her voice was not heard: therefore Eli thought she had been drunken.
1Sa 1:14 And Eli said unto her, How long wilt thou be drunken? put away thy wine from thee.
1Sa 1:15 And Hannah answered and said, No, my lord, I am a woman of a sorrowful spirit: I have drunk neither wine nor strong drink, but have poured out my soul before the LORD.
1Sa 1:16 Count not thine handmaid for a daughter of Belial: for out of the abundance of my complaint and grief have I spoken hitherto.
1Sa 1:17 Then Eli answered and said, Go in peace: and the God of Israel grant thee thy petition that thou hast asked of him.
Rom 8:26 Likewise the Spirit also helpeth our infirmities: for we know not what we should pray for as we ought: but the Spirit itself maketh intercession for us with groanings which cannot be uttered.
Rom 8:27 And he that searcheth the hearts knoweth what is the mind of the Spirit, because he maketh intercession for the saints according to the will of God.
So there is Silent prayer, sometimes we don't even know it, that's how silent it is.