The effect of a mobile-liquid saturation on turbulence factors for gas-liquid systems was studied by measuring the turbulence factors for a two-phase f10w system using nitrogen-water and limestone cores. The steady-state, two-phase flow tests were conducted at pressure drops of 200 and 400 psi, both at a back pressure of 400 psig.
It was observed that increasing the liquid saturation from 40 to 70 pH cent pore volume could result in as much as an eight-fold increase in turbulence factor. The increase in turbulence factor, together with the decrease in effective gas permeability around the well bore, could result in a substantial reduction in gas-n-ell productivity. It was also determined that the turbulence factors for a two-phase flow system can be approximated by using a turbulence factor – permeability correlation obtained with dry cores, provided that the correlation is established experimentally for the rock type in question.
GAS FLOW IN THE REGION OF THE WELL BORE is generally in the turbulent-flow regime, The pressure drop resulting from turbulent flow is greater than that predicted by the Darcy equation. Forchheimer(1) was first to add an additional term to the Darcy equation to account for this increased pressure drop, and his equation is as follows:
For an isothermal system, assuming that the gas viscosity and the compressibility factor are independent of pressure for small pressure changes, a plot of the left-hand side of Equation (2) versus W/Aµ results in a straight line. The slope and intercept of the straight line give the turbulence factor and the reciprocal of the gas permeability, respectively.
The turbulence effect in a gas well is usually determined by well tests; however, the effect can also be evaluated if the turbulence factors βis known. The only published data on turbulence factors are those of Janicek and Katz(2), who correlated the turbulence factors with rock permeability using porosity as a parameter. The applicability of the Janicek-Katz correlation to limestone cores has been evaluated by Gewers and Nichol(3), who found that the measured turbulence factors were an order of magnitude higher than those given by the Janicek-Katz correlation. As shown by Gewers and Nichol, productivity estimates based on the Janicek-Katz correlation would be optimistic by a factor of two. They also measured the gas turbulence factors for the same cores with immobile liquid satu-rations up to 30 per cent pore volume. The results indicated that the gas turbulence factors decreased to a minimum at a liquid saturation of about 10 per cent pore volume and then increased over the saturation range between 10 and 30 per cent pore volume. The present study is an extension of the work by Gewers and Nichol to include measurement of gas turbulence factors at higher liquid saturations and under two-phase flow conditions. Such information would be useful in making performance estimates for gas condensate reservoirs where there is a possible liquid buildup around the well bore.