Class 1 hydrate deposits are characterized by a hydrate-bearing layer underlain by a two-phase zone involving mobile gas. Two kinds of deposits are investigated. The first involves water and hydrate in the hydrate zone (Class 1W), while the second involves gas and hydrate (Class 1G). We introduce new models to describe the effect of the presence of hydrates on the wettability properties of porous media. We determine that large volumes of gas can be readily produced at high rates for long times from Class 1 gas hydrate accumulations by means of depressurization-induced dissociation using conventional technology. Dissociation in Class 1W deposits proceeds in distinct stages, while it is continuous in Class 1G deposits. To avoid blockage caused by hydrate formation in the vicinity of the well, wellbore heating is a necessity in production from Class 1 hydrates. Class 1W hydrates are shown to contribute up to 65% of the production rate and up to 45% of the cumulative volume of produced gas; the corresponding number for Class 1G hydrates is 75% and 54%. Production from both Class 1W and Class 1G deposits leads to the emergence of a second dissociation front (in addition to the original ascending hydrate interface) that forms at the top of the hydrate interval and advances downward. In both kinds of deposits, capillary pressure effects lead to hydrate lensing, i.e., the emergence of distinct banded structures of alternating high-low hydrate saturation, which form channels and shells and have a significant effect on production.