A hydraulic fracture stimulation conducted during 1983-84 in nonmarine, deltaic. Mesaverde strata at 7,100 ft [2164 m] was cored in a deviated well in 1990. The observed fracture consists of two fracture intervals, both containing multiple fracture strands (30 and 8, respectively), abundant gel residue on the fracture surfaces, and many other complexities.3.7 x 10 6 psi [25 GPa] and a Poisson's ratio of 0.22. Few natural fractures 42 ,43 were found in the vertical core taken from the paludal interval (numerous fractures were found in the deviated SHCT core), but nearly all natural fractures found at MWX trended nearly east/west, indicating a highly anisotropic permeability system.Stress tests throughout the paludal interval yielded relatively high stress contrasts between the sandstones and the nonreservoir lithologies. 41 ,44 The azimuth of the maximum horizontal stress was found to be about 65° north of west at this depth. 44Zones 3 and 4 were perforated with two 14-g jet shots per foot from 7,120 to 7,144 ft [2170 to 2177 m] in Zone 3 and from 7,076 to 7, 100ft [2157 to 2164 m] in Zone 4. The 96 perforations were then broken down and balled out with 60 bbl [9.5 m 3 ] of 2 % KCI water.Extensive well testing in paludal Zones 3 and 4 gave an effective reservoir permeability of 36 Itd. 40 ,45,46 No interference was observed between wells during a 7-day drawdown at 200 to 250 Mcf/D [5565 to 7080 m 3 /d] or during a 7-day buildup. Calibration Injections. A step-ratelflowback test and a pumpin/flowback test 40 ,41 conducted in the two sandstones yielded a closure stress of 5,900 psi [40.7 MPa]. Each injection was about 120 bbl [19 m 3 ] of 2 % KCI, with the peak pressure reaching 600 psi [4.1 MPa] above closure. These pump tests were conducted in Dec. 1983. Immediately after the flowback tests, two minifractures 40 ,41 were pumped into Zones 3 and 4 to determine fracture parameters and to observe growth behavior in these lenticular sands. In Minifracture 1, 15,000 gal [57 m 3 ] of 30-lbm [14-kg] linear gel was pumped at 10 bbl/min [1.6 m3/min]. In Minifracture 2, 30,000 gal [114 m 3 ] of 60-lbm [27-kg] linear gel was pumped at 10 bbl/min [1.6 m 3 /min].

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Summary To determine the effect of water-soluble polyacrylamide polymer adsorption and flow behavior on oil recovery, relative permeability and mobility were determined from flow experiments at various polymer concentrations. A selective reduction of the relative permeability to water with respect to the relative permeability to oil was observed for both Berea and reservoir sandstone cores. Adsorbed polymer layer increases water wettability. Relative permeability reduction could be attributed to both wettability change and pore-size restriction due to the adsorbed polymer layer. An empirical model was proposed to correlate the relative permeability reduction and the amount of polymer adsorption. Depletion-layer effect results in a reduced polymer viscosity in porous media with respect to bulk solutions. Modification of the existing shear-rate model allows for accurate prediction of this effect. The integration of the new models in UTCHEM provides a more accurate tool for engineering design of polymer applications. Introduction Water-soluble polyacrylamide polymers have been used to reduce water production in oil wells and for mobility control in injection wells for decades.1 One of the attractive properties of polyacrylamides is their ability to reduce the relative permeability to water more than the relative permeability to oil in porous media. From the published field tests on well treatments by polymer adsorption in the 1970's and 1980's,1,2 only a few jobs were considered to be economically successful. Results could not be interpreted due to the lack of detailed information. At present, the importance of laboratory research and simulation study are emphasized for successful field design. The selective permeability reduction by polymer adsorption was traditionally termed as "permeability reduction" or "residual resistance factor," which is equivalent to the endpoint relative permeability. Previous laboratory results1 indicated that the maximum reduction of the endpoint relative permeability to water caused by polymer adsorption can be as high as a factor of 10, while the reduction of the endpoint relative permeability to oil is less than 2. If crosslinking or swelling agents are applied, the maximum reduction of the relative permeability to water could be more than two orders of magnitude. The mechanisms of this selective reduction have been explored by several researchers.3–5 An understanding of these mechanisms could be obtained from the selective permeability reduction by gels.6 Measurement of the residual resistance alone may provide a qualitative estimation. To model the effect of polymer adsorption, however, a measurement of the relative permeability is necessary, especially when residual saturation and the shape of the relative permeability curves change after polymer adsorption. Modification of the relative permeability by polymer adsorption has been intensively studied recently.3-5,7-10 Ali et al.4 and Barrufet and Ali,5 derived the relative permeability from drainage capillary pressure measured by an ultracentrifuge and showed that the reduction of the relative permeability caused by starch-based polymers is dependent on saturation. The reduction was interpreted as a change in lubrication along the pore walls. Direct measurement of relative permeability after polymer adsorption was also seen in Refs. 3 and 7 through 10. In water-wet porous media, it was found that the residual oil saturation remained almost the same after polymer treatment. At residual oil saturation, the quantity of adsorbed polymer per gram of rock was also found to be almost the same as at 100% water saturation, but the endpoint relative permeability reduction to water was increased in the presence of residual oil. Based on a capillary bundle model, a correlation of the relative permeability curves with polymer-layer thickness was proposed by Zaitoun and Kohler.3 However, the relationship of the polymer-layer thickness with the quantity of adsorbed polymer is still unknown, and further modification of the capillary bundle model may also be needed to model complex pore matrices. On the other hand, as polymer propagates through porous media, polymer solution will be diluted in the propagation front due to dispersion and adsorption, and the dilution could extend to the entire slug if the slug size is too small. So far, few researchers have related the variations of the relative permeability curves as a function of polymer concentration or the quantity of adsorbed polymer. Therefore, one of the objectives in the present study is to measure and correlate relative permeability curves as a function of polymer adsorption. Polymer solution mobility was also studied as a function of polymer concentration. Effective viscosity at low shear rate in porous media is lower than that in bulk solution at the same shear rate. The dependence of the depletion-layer effect on polymer concentration as well as porous media will be examined in this paper. Finally, the numerical models of relative permeability and mobility as a function of polymer concentration developed in this study will be incorporated in UTCHEM. Several cases will be studied to compare incremental oil recovery predicted by these new models with that predicted by previous descriptions of polymer behavior in porous media. A simplified layered reservoir model will be used for comparative simulation runs. Polymer flooding and near-wellbore polymer treatments will also be simulated. Results from these simulations should provide guidelines for future field strategies. Experiment Porous Media. Both strongly water-wet and mildly oil-wet cores were chosen to study the influence of wettability on polymer adsorption, two-phase relative permeability, and polymer solution mobility. The mildly oil-wet medium is a Warden reservoir sandstone core from Santa Fe field, Stephens County, Oklahoma. Two strongly water-wet media are Berea sandstone cores with different permeabilities. Table 1 summarizes the petrophysical properties of these sandstone samples. Fluids. Synthetic brines were prepared to represent reservoir brine (produced water) composition and makeup water (injection water) composition used in the Warden reservoir. Produced water has a total dissolved solid (TDS) of 31,300 ppm which contains 29 g/L NaCl, 0.94 g/L CaCl2, 0.77 g/L MgCl2, 0.11 g/L KCl, and 1.1 g/L NaHCO3, and injection water has a TDS of 1,490 ppm which contains 0.343 g/L CaCl2, 0.252 g/L MgCl2, 0.176 g/L Na2SO4, and 0.72 g/L NaHCO3

Summary The objective of this work was to identify and quantify important parameters affecting gas production through propped fractures under a non- Darcy gas flow regime. The gas flow capacity of a simulated propped fracture was studied systematically to determine the effects of partial saturation. gel damage, and stress conditions. The flow-capacity response of the 20/40-mesh sand tested throughout this project was affected significantly by variations in the effective gas porosity of the proppant pack. Permeability- and non-Darcy flow characteristics were correlated to effective gas porosity. Partial saturation was found to be a key parameter influencing the permeability and non-Darcy gas flow behavior of a proppant pack. Partially saturated fractures may result from incomplete removal of fracturing fluid, mobility of formation waters. or production of condensates. The partial saturation of the proppant pack, in effect, changes the open porosity available for gas flow, which adversely affects gas permeability and non-Darcy flow parameters. The results from this investigation demonstrate that non-Darcy gas flow behavior through propped fractures in which a saturation phase is present cannot be estimated from results using dry-proppant-pack tests. Introduction The generated equation for linear flow through porous media can be represented by the Forchheimer equation as (1) where -, =pressure gradient, =fluid viscosity, =fluid density, =fluid velocity, =permeability of the porous medium, and =coefficient of inertial resistance or the non-Darcy flow factor. For low fluid velocities, the second term in Eq. 1 becomes negligible, and the equation reduces to Darcy's law. As the velocity of the fluid increases, however, the contribution of the second term to the pressure gradient becomes increasingly significant, especially for low-viscosity fluids. Because gas densities vary with pressure, an integrated form of Eq. 1 that accounts for density variations is generally used to describe the flow of gas through a medium in which the change in gas pressure with flow distance is significant. For example, Dranchuk and Kolada provided a generalized integrated form of Eq. 1 that accounts for Klinkenberg effects at low gas velocities and for variations in gas density with pressure. For characterizing gas flow through proppant packs in the laboratory, however, we can use Eq. 1 while avoiding errors resulting from density and Klinkenberg effects if tests are conducted isothermally and if the mean gas pressure within a proppant pack is maintained at a constant moderate pressure. such as 100 psig [0.69 MPa], throughout each test. A plot of - (L v) vs. pv/ from test data recorded under controlled conditions yields a straight line in which the slope equals the 0 factor and the intercept equals 1/k. Greenberg and Weger found 0 to be independent of pressure for pressures up to 2.000 psi [13.8 MPa] in porous metal. Cooke investigated propped hydraulic fractures and found no appreciable difference in 0 owing to the nature of the test fluid. either brine. gas, or oil. He found that log 0 was inversely proportional to log k for gas flow through stressed sandpacks at irreducible water saturation conditions. Cooke described the fits to his data b), an equation of the form (2) where the constants b and a varied with sand size. Cooke observed that some of his data suggested a slight reduction in inertial resistance with oil or gas flowing at irreducible water saturation compared with brine flow alone, although scatter in the data prevented a clear determination of such an effect. Gewers and Nichols measured, for cores with immobile liquid saturations of up to 30% PV. Their results indicated that gas permeabilities were decreased by immobile partial saturations when compared with dry permeabilities. They found that 3 decreased as saturation increased from 0 to 10% and then increased as saturation increased from 10 to 30 %. They described the decrease in 0 values for low immobile partial saturations as a pore-streamlining effect. Gewers and Nichol found that 0 for carbonate cores containing a partial immobile saturation of up to 30% could be estimated with the correlation of dry-core a vs. k if the effective permeability under saturated conditions was known. For sand proppant packs containing partial saturations, Evans and Evans found that 0 values increased with increasing saturation, whether mobile or immobile, and that the correlations for dry proppants were insufficient for predicting the 0 values of partially saturated proppant packs. Geertsma correlated a wide range of 3, permeability, and porosity data from his work and from the literature. For dry porous media, Geertsma found a general fit to the data by (3) In addition, he hypothesized that, for situations in which an immobile saturation phase is present, (4) where k=gas permeability at 100% gas saturation, SL=saturation-phase fraction, and kr=relative permeability under saturation conditions. Eqs. 3 and 4 are dimensionally correct. Noman et al. used several relationships of 3, k, and 0 to fit data derived from core plugs and reservoir production. They found that the best correlation of their experimental and well test data was obtained by relating beta to () -0.5. The units of ()) -0.5 and 0 are dimensionally equivalent-i. e., cm -which facilitates data comparison. The results from our investigation are correlated with the relation-ships proposed by Cooke, Geertsma, and Noman et al. Experimental Procedures Sandpacks were tested in a 10-in.2 [64.5-CM2] linear-flow conductivity cell at closure stresses from 1.000 to 10,000 psi [6.9 to 69 MPa]. The design of the conductivity cell used in this investigation evolved from the cell Cooke developed that has been widely accepted for proppant conductivity testing. 10–19 Accordingly, the cell has metal walls and makes no provision for leakoff or filtercake effects on test results. Fig. 1 is a schematic of the test system. Throughout the proppant testing program, N, gas was used as the flowing medium to simulate gas production through a propped fracture. The gas pressure was maintained at 100 psig [0.69 MPa] in the center of each test proppant pack to ensure that proper gas density and viscosity values were used in calculations. Gas flow rates through proppant packs were maintained sufficiently high to impose non-Darcy flow conditions. Tests were conducted at room temperature. SPEPE P. 417^

To determine the effect of water-soluble polyacrylamide polymer adsorption and flow behavior on oil recovery, both steady-state and unsteady-state flow experiments were performed on Berea sandstone and reservoir cores. Berea sandstone core is strongly water-wet while the reservoir core is mildly oil-wet. Relative permeability curves and polymer adsorption measurements were made at residual oil saturation and 100% water saturation for increasing polymer concentrations. Mobility measurements were made at different polymer concentrations and shear rates. A selective reduction of the relative permeability to water with respect to the relative permeability to oil was observed for both Berea and reservoir sandstone cores. The reduction of the relative permeability to water in the presence of oil phase is more than that at 100% water saturation. As polymer concentration increases, polymer adsorption, irreducible water saturation and relative permeability reduction increase. Residual oil saturation remains almost the same. Wettability is beneficial to water-soluble polymer adsorption. In reservoir core, relative permeability reduction could be attributed to both wettability change and pore-size restriction. Polymer adsorption isotherm follows Langmuir's law. Relative permeability reduction as a function of polymer adsorption exhibits an "S-type" curve. It increases exponentially as polymer adsorption increases and eventually approaches a constant. An empirical model was proposed to correlate this characteristics. As predicted by the depletion layer and viscoelasticity theories, flow behavior of polymer solution in porous media is found to be significantly different from that in bulk solutions. A modification was made to the existing shear rate model based on mobility measurements, showing that the depletion layer effect is in direct proportion to polymer concentration, and is more significant in the reservoir core than in Berea core. New models were incorporated in UTCHEM, a chemical flood simulator developed by the University of Texas. These models can provide more accurate prediction of the combined effects of relative permeability reduction and viscosity over existing models. Case studies show that the long-lasting relative permeability reduction by polymer adsorption is likely to maximize the benefits of polymer solution in polymer flooding. Increased understanding through simulation may lead to improved field profile modification and near wellbore treatments. The effects of cross-flow and the degree of relative permeability reduction are two critical factors to determine polymer placement strategies and success. P. 293