A pragmatic approach for optimizing gas lift operations

The oil flow rate in a single vertical well undergoing gas lift operations is complicated by three factors: (1) The flow is driven by gas injection, in addition to the fluid flow potential gradient applied along the well, (2) the well is interfaced with a porous and permeable reservoir contributing with a fluid feed, and (3) the wellbore geometry may consist of concentric pipes of varying diameters and lengths, rather than a single-diameter pipe. Dimensional analysis is applied to this complex, highly nonlinear production problem, in order to develop empirical models for predicting the optimal gas injection rate and the maximum oil production rate that may be produced from continuous gas lift operations. Two pairs of coupled dimensionless groups are revealed. The first pair consists of a dimensionless pressure drop ( π 1 ) adjusted to the complex wellbore geometry, and a dimensionless ratio of kinetic to viscous forces ( π 2 ) which accounts for the porous medium feed. A constructed database for 388 vertical wells producing by continuous gas lift operations has been used to validate the dimensionless groups. A power-law relation is revealed between the dimensionless groups π 1 and π 2 , allowing to construct an analytical model for predicting the maximum oil production rate that corresponds to the optimal gas injection rate. The second pair consists of two groups denoted χ 1 and χ 2 . The group χ 1 is a dimensionless pressure drop with adjustment being augmented to account for the temperature effects on gas flow. Similar to π 2 , the dimensionless group χ 2 is a ratio of kinetic to viscous forces, adjusted to account for the porous medium feed. However, χ 2 is a function of the injection rate, instead of the oil production rate. Likewise, a power-law relation is revealed between χ 1 and χ 2 , allowing to construct an analytical model for predicting the optimal gas injection rate. All power-law relations yield high correlation coefficients when the validation data are segregated according to a discrete productivity index. The analytical models developed by applying dimensional analysis appear to capture the physical controls of gas lift operations. Intuitively, the optimal gas injection rate depends on the pressure gradient along the pipe, the wellbore geometry, the temperature conditions at the bottom of the well and in the stock-tank, the oil density, and on the productivity index. Similarly, the maximum oil production rate, corresponding to the optimal gas injection rate, depends on the pressure gradient along the pipe, the wellbore geometry, the oil density, the productivity index which is implicitly affected by the oil permeability, and viscosity. Unlike multivariate nonlinear regression analysis, the application of dimensional analysis for deriving the analytical models, presented in this study, does not require a presumed functional relationship. In retrospect, dimensional analysis evades the guessing process associated with nonlinear regression analysis.