Multiphase Non-Darcy Pressure Drop in Hydraulic Fracturing

Abstract

Valhall, an offshore field in Norway, is a black oil reservoir producing mainly through multi-fractured (with proppant) horizontal wells.1 The bottom hole flowing pressure is well below the bubble point and hence the fracture conductivity is significantly constrained by multiphase non-Darcy pressure drop losses. Geertsma in 1974 was the first to propose a multiphase Beta (non-Darcy constant) correlation as a function of permeability, porosity (size) and saturation. Recent testing to measure the non-Darcy pressure drop for multiphase flow in proppant packs was successful in verifying a strong relationship to saturation. Three different types of 16/20 proppants with three different resins and one of 12/18 and 20/40 were tested (total of eleven samples) in a conductivity cell under field conditions (temperature of 195 deg F and 1,500–6,500 psi confining stress), for a proppant loading of 4 Lb/ft2. The proppant was placed in the cell using a 30 lb crosslink borate X-link fluid with 4 ppt (lbs/1000 gal gel) of encapsulated breaker for 24 hours to allow fluid break prior to conducting the flow tests. The Geertsma type equation was used to match the laboratory data. The equation constants (for permeability, porosity and saturation) for each proppant/resin type were derived. The non-Darcy correlations for each proppant were used in a numerical simulator to determine the pressure drop in the fracture and to quantify the effects on production rates. The paper highlights the importance of proppant size for optimizing fracture design for wells producing under multiphase flow. Introduction A study was commissioned by BP Norway to assess the effects of various proppant sizes, resins and types on productivity under field conditions. The study contained three parts as follows:Single phase gas flow laboratory tests were performed under ambient conditions to evaluate the validity of the Forchheimer equation under very high rates.Single and two-phase flow (gas and water) laboratory tests were conducted to measure the Beta factors at field conditions with stresses between 1,000 and 6,500 psi and a temperature of 195 F.The multiphase Beta factors for 20/40, 16/20 and 12/18 proppant were then imported into a numerical model and the production was compared. The study indicated only slight difference between the various 16/20 ceramic proppants. The higher density ceramic resin coated proppant indicated less cumulative production mainly due to its higher density and hence lower fracture width for the same proppant concentration of 4 Lb/ft2. On the other hand, the results for two light weight ceramics with the three-tested resins were close. 12/18 ceramic proppant with a high bonding strength dual coated resin results was also compared to 16/20 and 20/40 proppant with the same resign. The results indicate some 25% and 56% more cumulative production after 400 days for the larger proppant, in comparison to 16/20 and 20/40, respectively. Hence, a substantial upside lies in utilizing 12/18 proppants or larger, particularly in depleted areas where the reservoir pressure is close to the bubble point estimated at 3,350 psi. Background Non-Darcy Equation Henry Darcy initially developed his famous correlation by observing water draining through a sand column. Essentially, he conducted his experiments by placing water on top of a sand column and timing how long it took for the water to trickle through the sand. The fluid velocity was very low and Darcy's studies showed that at these velocities, the pressure drop through a porous media is proportional to the fluid velocity.

Applicability of the Forchheimer Equation for Non-Darcy Flow in Porous Media

“…The effect of non-Darcy flow as one of the most critical factors in reducing the productivity of hydraulically fractured high-rate wells has been documented extensively with examples of field cases (Barree and Conway 2004;Holditch and Morse 1976;Olson et al 2004;Smith et al 2004;Vincent et al 1999). The inertia resistance factor, or the so-called beta factor ␤, a parameter in the Forchheimer equation for quantifying the non-Darcy flow effect, is now routinely measured for proppant packs.…”

A Treatise on Non-Darcy Flow Correlations in Porous Media

“…Olson [19] tested three different types of proppants with three different types of resins in conductivity cell under field conditions to study the effect of multiphase non-Darcy pressure effects in hydraulically fractured horizontal well. They proposed the following correlation (Eq.…”

“…An algorithm and a user-friendly simulator has been presented to determine the beta values for a large input data set [11][12][13][14][15][16][17][18][19][20].…”

The Impact of Gravity Segregation on Multiphase Non-Darcy Flow in Hydraulically Fractured Gas Wells

“…Lolon et al used Frederick and Graves (1992) correlation for multiphase non-Darcy flow which leads to less non-Darcy flow effects compared to Geertsma's (1974) correlation, when the permeability is high (as in a fracture). Previous work by Olson et al (2004) found that laboratory data for multiphase non-Darcy flow can be fit to a Geertsma type equation with good accuracy provided that the water saturation is not too high. Olson et al also found that at high water saturations, running experiments is more difficult, which means that there is a lack of laboratory data to compare to Geertsma's correlation at higher water saturations.…”