TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractDarcy's law can not describe fluid flow accurately when the flow rate is high. In most cases in the recovery process, fluid flow is governed by Darcy's law. But when the flow rate is very high, for an instance, near the wellbore, Darcy's law is inadequate to describe fluid flow.In 1901, Forchheimer put forward a classical equation, known as the Forchheimer equation, to make up the deficiency encountered by Darcy's law at high flow rates. He added a non-Darcy term into the Darcy flow equation. The non-Darcy term is the multiplication of the non-Darcy coefficient, fluid density, and the second power of velocity. One of the most important aspects in determining the non-Darcy effect is to estimate the non-Darcy coefficient as accurately as possible.In this paper, theoretical and empirical correlations of the non-Darcy coefficient in one-phase and multi-phase cases in the literature are reviewed. Most researchers have agreed that the non-Darcy effect is not due to turbulence but to inertial effect. The non-Darcy coefficient in wells is usually determined by analysis of multi-rate pressure test results, but such data are not available in many cases. So, people have to use correlations obtained from the literature. This paper summarizes many correlations in the literature, and will provide a good reference for those who are interested in the investigation of the non-Darcy effect in the recovery process.

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BackgroundThe thumb carpometacarpal (CMC) osteoarthritis is very common. Multiple methods are used to treat progressive thumb CMC osteoarthritis, among which trapeziometacarpal arthrodesis and trapezial excision with ligament reconstruction and tendon interposition (LRTI) are the most common. These two surgical treatment methods have received mixed reviews in previous studies in the west patients. This retrospective study studied the effects, advantages, and disadvantages of arthrodesis and arthroplasty for treating thumb carpometacarpal osteoarthritis in Chinese patients.MethodsBetween February 2012 and September 2017, 39 Chinese patients with stage II or III thumb carpometacarpal osteoarthritis underwent surgery (trapeziometacarpal arthrodesis in 22, trapezial excision with ligament reconstruction and tendon interposition in 17). Postoperative objective and subjective evaluations were performed. The objective evaluation involved grip strength, pinch strength, thumb abduction degree (palmar and radial), and Kapandji opposition scores. The subjective evaluation involved visual analog scale (VAS) and Disabilities of the Arm, Shoulder, and Hand (DASH) scores.ResultsIntergroup differences in pinch strength, thumb abduction degrees (palmar and radial), and Kapandji opposition scores were obvious, whereas those in grip strength, VAS score, and DASH score were not.ConclusionIn Chinese patients, both techniques relieved pain and improve grip strength. Arthrodesis displayed better pinch strength, while arthroplasty displayed better motor function. Patients were satisfied with the effects of both techniques.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractDarcy's law governs most flow patterns in petroleum recovery processes. However, when fluid flow velocity is very high, for example, near the wellbore, Darcy's law may be inadequate to simulate the fluid flow.The non-Darcy effect has been incorporated into the Department of Energy (DOE) reservoir simulator MASTER (Miscible Applied Simulation Techniques for Energy Recovery). Based on the simulator BOAST (Black-Oil Applied Simulation Tool), MASTER was developed by DOE mainly to solve gas injection problems. However, only Darcy's flow was considered in these simulators. In this study, Forchheimer's non-Darcy flow equation has been incorporated into the simulator code and an iterative method has been used to solve for pressures.The modeling of non-Darcy flow proved successful and enabled the simulator to match high-velocity gas flow more accurately. Based on a number of non-Darcy flow coefficient equations found in the literature, a general correlation was proposed. The appropriate constants in the proposed correlation were found by running simulations with the modified simulator for the non-Darcy flow experiments.The model has been verified using laboratory high flow data obtained using single-phase nitrogen gas. The data comprised a wide range of flow rates collected using a heterogeneous Berea sandstone wafer. The gas flowed into and out of a hockey puck-shaped wafer via 0.125-in. diameter ports. Thus the flow rate varied within the wafer, simulating near-wellbore flow conditions. It was found that, the differential pressures from simulations were in good agreements with their counterparts from experiments.

The goal of this work is to develop a compositional model for WAG injection in a medium-viscosity oil, low-temperature reservoir like Schrader Bluff Pool in the Milne Point Unit, Alaska. Compositional simulation of WAG displacement with CO2-NGL and Prudhoe Bay gas-NGL mixtures shows that three-hydrocarbon phases form in situ because of low temperature. A four-phase relative permeability formulation has been developed by considering the mixed-wettability of the formation and the saturation paths. The simulation results are compared with the laboratory experimental results from the literature. The sensitivity of the laboratory-scale oil recovery to relative permeability, pressure and solvent composition is studied. The sensitivity of oil recovery in a 2D quarter five-spot pattern to relative permeability, WAG ratio, slug size is also studied. CO2 - NGL mixture is a very effective solvent for this reservoir. The minimum miscibility enrichment is more sensitive to pressure for Prudhoe Bay gas - NGL mixtures than in the case of CO2 - NGL mixtures. The oil production rate is sensitive to relative permeability formulation. Oil recovery is faster at lower WAG ratio and higher slug size. Introduction There is a large (> 10 billion barrels) deposit of viscous oil at Schrader Bluff Pool in the Milne Point Unit, Alaska1. Due to high oil viscosity and poorly consolidated sand, primary production is low. However, the viscosity of oil is not high enough for application of steam flood. Fortunately, there are plenty of gases (hydrocarbon and CO2) in North Slope in the absence of any gas pipeline. Gas floods have been considered in the past. Experimental study carried out by Khataniar et al.2 showed that combination of 85% CO2–15% natural gas liquids (NGL) or 60% Prudhoe Bay gas (PBG)–40% NGL developed miscibility with the oil. Mohanty et al.3 have conducted slim tube experiments and simulation studies on the injection of solvents of C1-C4 with varied compositions into the crude. They found that three-hydrocarbon phases coexisted in the reservoir (totaling four phases if we include water) and that high oil recovery was possible in the presence of three-hydrocarbon-phases because of lower oil viscosity and miscible displacement of oil by the second liquid phase after some amount of solvent condensed into the crude. Modeling flow of four fluid phases (water, oil, gas, and the second non-aqueous liquid) is important to the water-alternating-gas (WAG) floods. However, four-phase systems cover a large number of saturation paths. The relation between phase saturation and pressure is also delicate. It is prohibitively expensive if not impossible to experimentally measure relative permeabilities for a four-phase system. Experimental data are not collected regularly for three-phase systems for a similar reason. Pore-scale mechanistic models4–7 have been developed for three-phase flow, but lack of pore-scale structure and wettability data makes them impractical. Instead, empirical models are often used which estimate three-phase relative permeabilities from experimental two-phase relative permeabilities: water-oil and oil-gas. Two empirical models proposed by Stone8,9 are widely used in the oil industry even though comparisons with experiments10–12 have shown many inconsistencies. Baker10 has proposed a simple three-phase model based on saturation-weighted interpolation of two-phase relative permeabilities. These models are primarily for water-wet media and do not take trapping of non-wetting phases into account. Jerauld13 has developed a three-phase relative permeability model for Prudhoe Bay reservoir, which accounts for mixed-wettability, trapping, capillary number effects, and compositional consistency. Blunt14 has used the saturation-weighting technique10,15 and proposed a new model that accounts for trapping and oil layer flow at low saturations. Guler et al.16 are the first to suggest a four-phase relative permeabilities based on the Baker model10 for three-phase flow. This model lumps oil and second phase saturations into one pseudo phase, which reduces the four-phase system to a three-phase system. It applies the Baker model to get the lumped relative permeability of the pseudo phase and then distributes it to the oil and the second liquid phase in proportion to their flowing saturations. This model presumes the medium to be water-wet and it does not account for gas phase hysteresis.