Combining spin-lattice relaxation time measurements and signal intensity measurements vs temperature of water confined in mesoporous molecular sieves (MCM-41 materials) gives information regarding the activation enthalpy of bound water and the width of the log-normal distribution of correlation times of the water molecules. Three different water "phases" are observed which have significantly different relaxation strength. The overall spin-lattice relaxation rate is shown to be strongly dependent on the number of silanol protons. "Analytical" formulas for the average spin-lattice relaxation rates are derived.