This function was evaluated numerically for the following set of parameters:

　

　

 The above referenced function, ψ is easily evaluated numerically and is shown in FIG. 4 for three different yield stress values of S for gas. For ease of analysis the efficiency function ψ can be analyzed in relation to the ratio of diameter of the pipe to the thickness of the pipe as represented by

　

　

 FIG. 4 shows how the ratio of the mass of the gas per mass of pipe material (defined as the efficiency) varies with the ratio of the diameter to thickness of the pipe. This type of curve is used when choosing the optimum D/t or maximum efficiency ψ as discussed above. As can be seen in FIG. 4, the maximum of ψ occurs at different D/t for different yield stress values; these maxima are tabulated below for materials of different yield stress.

　

　

 The efficiency increases dramatically as S increases and thus it is prudent to choose the material with a high maximum yield stress, such as around 100,000 psi. For this value of the yield stress, the maximum efficiency occurs at a D/t of about 50 and is approximately 0.316 for the gas and 0.265 for the methane. But this still does not indicate the exact pipe selection; however, if D is fixed based on availability, or other considerations, the necessary wall thickness can be determined immediately. Selecting a diameter D=20 in, as an example, the wall thickness should be 0.375 in. This is a standard size and therefore is readily available; for this pipe, D/t=53.3 and the mass of gas/mass of steel is found to be 0.315, which is close to the optimum selection. The weight of this pipe is 78.6 lb/ft; the weight of the pipe with the gas is 102.79 lb/ft. The pressure of the gas at this optimum configuration is 1840 psi. Note that if the 100 ksi material is not available, or if criteria on ultimate strength limits is applicable, other optimum D/t can be selected based on material availability, but the ratio of mg/ms will not be as high as for the 100 ksi material. Although a 20 inch pipe diameter is used here as an example, other sizes such as the 36 inch diameter pipe discussed earlier are also valid.

 While the above example uses the maximum yield stress as the critical factor in choosing a material, it is understood that, when considering the applicable codes and regulations, other material properties and design factors may also be important. For example, as previously discussed, certain regulatory bodies require that the maximum principal stress not exceed 0.33 of the ultimate tensile strength of the material, thereby making the ultimate tensile stress a critical selection factor. In low temperature service, regulatory bodies also require a certain toughness characteristic of the material, as typically determined by a Charpy V-notch impact test, so that low temperature performance of the material becomes important. Also, note that additional stresses might arise due to bending caused by self weight, marine vessel flexure, and thermal stresses, and although these are orthogonal to the hoop stress on which the above calculation is based, these stresses may also become an important design consideration based on the particular application.

 Other design considerations also may be considered when selecting a suitable gas container and storage system. For example, since the operating stress is above 40% of the specified minimum yield stress, according to ASME B31.8 Code, Section 841.11c, the selected material should be subjected to a crack propagation and control analysis assuring adequate ductility in the pipe and/or providing mechanical crack arrestors. Note that the pipe supports can be designed to double as crack arrestors. Additionally, the calculations thus far have been concerned only with the gas and the pipe to contain it; however, these pipes have to be stacked in a structural framework, disposed on the marine vessel, provided with manifolds, pumps, valves, controls etc. for on-loading and off-loading operations, and provided with insulation and refrigeration systems for chilling and maintaining the gas at a reduced temperature. The pipes used as gas containers must also be able to resist the loads created by other gas containers and the additional equipment.

 The preferred embodiment includes a 36 inch diameter pipe and a D/t ratio of 50. Once the diameter and D/t ratio have been selected, then the wall thickness is determined, The compressibility factor for the gas, of course, has been included in the calculation of the ratio. Thus, in the design for a gas with a certain composition at -20°F., the equation of state calculates a preferred pressure for the compressed gas. Knowing that pressure, this provides the best compressibility factor. Thus the pipe is designed for this optimum compressibility factor at -20°F. The equation for pressure and wall thickness is then used knowing the pressure, to calculate the wall thickness for the pipe at a given diameter.

 Thus, the design of the pipe is made for the pressures to be withstood at -20°F. considering the particular composition of the gas. However, there is a relatively fiat area on the curve where the optimum Z factor is obtained. Thus, as shown in FIG. 3, the design pressure can be between about 1,200 and 1,500 psia, for a 0.7 specific gravity gas, without a significant variance in the compressibility factor. This allows flexibility in the composition of gas that can be efficiently transported in the gas storage system of the present invention.

 It is preferred that the gas container design be optimized because of the production and fabrication costs of the storage system, as well as a concern with the weight of the system as a whole. If the gas containers are not designed for the composition of gas at -20°F., the gas containers may be over-designed, and thus be prohibitively expensive, or be under-designed for the pressures desired. The preferred embodiment optimizes the gas container design to achieve the efficiency of the optimum compressibility of the gas. The efficiency is defined as the weight of the gas to the weight of the pipe used in fabricating the gas container. In a preferred embodiment for a 0.7 specific gravity gas, an efficiency of 0.53 can be achieved when using a pipe material having a yield strength of 100,000 psi. Thus, the weight of the contained gas is over one-half the weight of the pipe.

 The optimum wall thickness for a given diameter pipe may or may not coincide with a wall thickness for pipe that is typically available. Thus, a pipe size for the next standard thickness for a pipe at that given diameter is selected. This could lower efficiency a little bit. The alternative, of course, is to have the pipe made to specific specifications to optimize efficiency, i.e, the cost of the pipe for a particular composition of natural gas. It would be cost effective to have the pipe built to specifications if the quantity of pipe needed to supply a fleet of marine vessels was great enough to make the manufacture of special pipe economical.

 Using the equations discussed above, the wall thickness of the pipe can be calculated for storing a gas at established conditions. For storing a 0.6 specific gravity gas at 1825 psia using a 20 inch diameter pipe with an 80,000 psi yield strength, the wall thickness is in the range of 0.43 to 0.44inches and preferably 0.436. For a pipe diameter of 24 inches the wall thickness is in the range of 0.52 to 0.53 and preferably 0.524 inches. For a pipe diameter of 36 inches, the wall thickness is in the range of 0.78 to 0.79 and 45 preferably 0.785 inches.

 For storing a 0.7 specific gravity gas at 1335 psia using a 20 inch diameter pipe with an 80,000 psi yield strength the wall thickness is in the range of 0.32 to 0.33 inches and preferably 0.323. For a pipe diameter of 24 inches the wall thickness is in the range of 0.38 to 0.39 and preferably 0.383 inches. For a pipe diameter of 36 inches, the wall thickness is in the range of 0.58 to 0.59 and preferably 0.581 inches.

 The PB-KBB report, hereby incorporated herein by reference, describes another method of calculating pipe diameters and thickness for storing gases of given specific gravities. For 0.6 specific gravity natural gas with a pipe diameter of 24 inches, the wall thickness for a design factor of 0.5,is in the range of 0.43 to 0.44 inches and preferably 0.438 inches and for a 20 inch pipe diameter, the wall 60 thickness is in the range of 0.37 to 0.38 inches and preferably 0.375 inches, for a pipe material having a yield strength of 100,000 psi. For 36 inch diameter pipe, the wall thickness is in the range of 0.48 to 0.50 inches and preferably 0.486 inches for a gas with a 0.7 specific gravity and is in the range of 0.66 to 0.67 inches and preferably 0.662 inches for a gas with a 0.6 specific gravity, for a pipe material having a yield strength of 100,000 psi.

 The thickness ranges described above do not include any corrosion or erosion allowance that may be desired. This allowance can be added to the required thickness of the storage container to offset the effects of corrosion and erosion and extend the useful life of the storage container