Abstract: A seal system is disclosed for sealing a housing and rotatable shaft against leakage of high vapor-pressure liquids. The method of sealing contemplates phase change of the liquefied hydrocarbon fluid across a first module. The gas so formed is contained by a second seal module which operates as a dry running gas seal. The seal system has plural, axially spaced spiral-groove seal modules mounted between the shaft and housing. Each seal module has a primary ring affixed to the housing and a mating ring affixed for rotation with the shaft and the modules define an intermediate cavity. The rings have opposed, radially extending faces, one of which has a plurality of downstream pumping spiral grooves extending from one circumference. The grooves of the grooved ring of the upstream module are of a depth not to exceed about 100 micro-inches. In a preferred form, the depth of the grooves of the upstream module do not exceed 50 micro-inches.