Effect of Permeability Stratification in Cycling Operations

A general theory has been developed for the effect of permeabilitystratification on the efficiency of the gas-injection phase of cyclingoperations. It has been applied to three special types of permeabilityvariation; namely, exponential, probability, and linear. In the case of theexponential permeability distribution the effect of areal pattern sweepefficiency was also taken into account. The exponential permeability distribution can be characterized by the ratioof the maximum to minimum permeability, which has been termed thestratification constant. Curves were calculated for the variation in total wetgas recovery and total gas throughflow, to give that recovery to variousabandonment limits of the wet gas content in the produced gas, as a function ofthe stratification constant. The cumulative wet gas recovery decreasesmonotonically as the stratification constant increases and is generally higherat the lower values of the wet gas content abandonment limits. The total gasthroughflow first rises to a maximum as the stratification increases, and thenultimately declines. The effect of the areal sweep pattern efficiency isrelatively minor as compared to that of the stratification constant, except inthe region of low values of the latter where the formation is substantiallyuniform. The probability distribution can be characterized by a "variation"parameter varying from O to I as the formation changes from strict uniformityto extreme variability. The curves of total wet gas recovery and total gasthroughflow to different abandonment limits of wet gas content versus thevariation parameter have the same general characteristics as for theexponential permeability distribution. In the linear permeability distribution the ratio of maximum to minimumpermeability also serves as a stratification constant index defining thedistribution. The curves of total wet gas recovery and gas throughflow to fixedabandonment limits versus the stratification constant are similar to those forthe exponential permeability distribution. However, for the higher values ofthe stratification constant the recoveries and throughflows do notasymptotically fall to 0 as in the latter, but approach constant valuesdetermined by the abandonment limit of wet gas content in the produced gas. Introduction It is becoming generally recognized that one of the most important factorsdetermining the economic feasibility of cycling operations is the arealcontinuity and permeability distribution of the producing formation. While theeffects of areal variations in permeability, porosity, thickness, and wellpattern on the sweep efficiency can be evaluated by electrical model studies, those due to permeability stratification require separate treatment: Severalstudies have been reported on the influence of permeability variations on thewet gas recovery by cycling. In these, however, discontinuous permeabilityvariations either have been assumed explicitly, or the analysis has beencarried through as if they were discontinuous. T.P. 2494