“Dispensationalism takes its name from the idea that biblical history is best understood in light of a series of dispensations in the Bible.” Various “models” of Dispensational theology identify between three and seven dispensations. They are variously identified as “periods,” “administrations,” or “epochs” of time during which God works in the lives of people in a particular way, especially in terms of what is required for “salvation.”
According to some Dispensational models, the Covenant with Noah (Gen 6:17-18) falls into the “Dispensation of Conscience” (Gen 3:8-8:22), i.e., the period of time from Adam to Noah. But, the “re-affirmation” of the Covenant (Gen 9:9-10) falls into the “Dispensation of Government” (Gen 9:1-11:32), i.e., the period of time between Noah and Abraham. Dispensations are described as “functioning” sequentially—not concurrently.
However, when God “establish(ed)” the Covenant with Noah in Gen 9:9-10, it was not only made with him but “with (all of his) descendants after (him) and with every living creature that was with (him). Obviously, we are all descendants of Noah, therefore the Covenant with Noah is still in force, i.e., is still effective, is still operational—with us! Noah was “saved” in the same way as you or I. “Noah found grace in the eyes of the Lord” (Gen 6:8 [KJV]). In Noah’s day, salvation was made effective by God’s grace—in the same way it is today!
Furthermore, the “sign” of the Covenant is a “rainbow” (Gen 9:13). And, it too, is something that we still see today in the sky after it rains. So, every time we see a rainbow, we are reminded of God’s promise never to destroy the earth again with a flood. It not only testifies to the truthfulness of God’s Word, but to the fact that He is indeed, the “same yesterday, today and forever” (Heb 13:8 [NIV]).