Rediscovering Non-Darcy Flow Effect In Gas Reservoir

Abstract

The paper demonstrates and explains the importance of global inclusion (i.e. throughout the reservoir) of Non-Darcy (N-D) flow component for better prediction of well performance in gas reservoirs with bottom water drive by using a numerical simulator. Traditionally, Non-Darcy flow effect in gas reservoirs has been attributed only to high gas flow rates, and considered locally around the wellbore. Consequently, most numerical simulators have the N-D component assigned to the well rather than distributed throughout the reservoir. Also, the common judgment is that the effect is insignificant at gas rates lower than 10 MMscf/d, so it would not affect gas recovery in the low-rate wells. In this project, we used an analytical model, field data, and a numerical simulator with global and local N-D component to study sensitivity of final recovery and gas rate to N-D flow for a variety of reservoir properties. The results show that disregarding the N-D flow globally leads to overestimation of cumulative gas recovery by up to 42.2 percent. Moreover, this overestimated recovery is the same when N-D is ignored, or assigned locally to the wellbore. It is also shown that N-D effect is significant at low production rates. Shown is the range of reservoir properties where gas wells producing only 9.8 MMscf/D would have total pressure draw-down comprising 70% contribution of N-D flow effect. Introduction Traditionally, the Non-Darcy (N-D) flow effect in a gas reservoir has been associated only with high gas flow rates. Moreover, all petroleum engineering's publications claim that this phenomenon occurs only near the wellbore and is negligible far away from the wellbore. As a result, the N-D flow has not been considered in gas wells producing at rates below 10 MMscf/d, or it has been assigned only to the wellbore skin area. Aditional pressure drop generated by the N-D flow is associated with inertial effects of the fluid flow in porous media.1 Forchheimer2 presented a flow equation including the N-D flow effect as,Equation 1 Where dp/dL=flowing pressure gradient; v=fluid velocity; µ=fluid viscosity; k=formation permeability; ?v2=inertia flow term; and ß= inertia coefficient.2 In deriving an analytical model for ß many authors considered permeability, porosity, and tortuosity the most important factors controlling ß.3–6 Empirical correlations7–12 supported the analytical models, and included rock type as another important factor. Also, liquid saturation was found another important factor. ß increases with water (immobile) saturation.13,14 Experimental studies provided data needed for inclusion of liquid saturation in the equation for inertia coefficient.15–16 Frederic and Graves17 presented three empirical correlations for a wide range of permeability. In the actual wells, (can be calculated from the multi-flow rate tests using Houper's procedure. The objective of this study is to identify the effect of N-D in gas well flowing at low rates, and to qualify the effect of N-D on the cumulative gas recovery. Non-Darcy Flow Effect in Low-Rate Gas Wells Table-1 shows data used to evaluate the effect of N-D on the well's flowing pressure using the analytical model of the N-D flow effect described in Appendix-A. Three different permeability values were used for the study, 1, 10, and 100 md. Three porosity values were used, 1, 10, and 20%. Five values of gas rates were included in the analysis, 0.1, 1, 10, 100, and 1000 MMscf/D. Using equations 4 and 5 a and b were calculated. F was calculated with equation 8. Figures 1 to 3 show F versus gas rates.

Coupled 3-D numerical simulation of proppant distribution and hydraulic fracturing performance optimization in Marcellus shale reservoirs

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Semianalytical Model for Reservoirs With Forchheimer's Non-Darcy Flow

“…On the basis of the above analyses, it is understandable that models based on Darcy flow can misinterpret the pressure distribution in the reservoir with global non-Darcy flow and can cause errors in determining the infill-well locations. Armenta and Wojtanowicz (2003) showed that disregarding global non-Darcy flow may overestimate gas recovery by up to 42.2% for waterdrive gas reservoirs. The results would be similar whether non-Darcy flow in the reservoir were ignored or were represented by the non-Darcy skin factor.…”

Coupled 3-d numerical simulation of proppant transport and fluid flow in hydraulic fracturing

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