Volume of Fluid Simulations of Multiphase Flow through Fractures: Analysis of Individual Fractures for Application in Reservoir Scale Models

Study of reservoir rock and caprock integrity in geo-sequestration of carbon dioxide

Steady state immiscible oil/water flow experiments were conducted in horizontal smooth-walled fractures. The effects of fracture aperture, injection rate and injection method on the immiscible flow characteristics were investigated. The experimental data were analysed using a porous medium approach and an equivalent homogeneous single-phase method. The pressure gradients predicted by the latter are in good agreement with those measured in the experiments. Contrary to the well-known Romm's relative permeability versus saturation correlation, the experimental data indicated that the sum of the relative permeabilitiesis less than one over a range of saturation, which is attributed to the effect of phase interference on the immiscible flow. The effect of phase interference is more significant in the case of well mixed oil/water flow than otherwise. The results also indicate that the fracture aperture does not have a significant influence on the relative permeabilities of oil and water flow in smooth-walled fractures. Introduction Investigation of fluid flow in porous and fractured media is of practical importance in areas such as the recovery of oil and gas, the isolation and remediation of nuclear and toxic wastes in geological formation, and the exploitation of geothermal energy. In these applications, fluid flow in fractured media is often dominated by the highly permeable pathways provided by rock fractures, either natural or induced. Understanding the mechanics, which govern the multiphase flow in fractures, will certainly help to improve the energy recovery efficiency and optimize the waste isolation and remediation process. It is well known that the flow of multiphase fluids in a porous medium is generally governed by the saturation of the pore space occupied by the percolating fluids. Pores occupied by one phase are not available for the flow of the other, which implies that each phase interferes with the flow of the other. At steady state, only the portion that forms a continuous path contributes to the fluid production, whereas the discontinuous portion is considered to be immobile. The phase interference is attributed to the capillary forces developed at the contact zones of the fluid phases in the pore channels. The smaller the size of the pores, the more significant will be the effect of capillary forces. To quantify the interference between different fluids, relative permeability functions are introduced and defined as: Equation 1 (available in full paper) where ki is the effective permeability to phase i, k is the absolute permeability of the medium, and kri is the relative permeability to phase i. Numerous experimental studies have shown that the relative permeabilities of multiphase flow in porous media are strong functions of phase saturation and phase saturation is governed by capillary forces. It is postulated that phase interference also exists in multiphase flow in fractures. However, the mechanisms governing the phase interference in a fracture is not well understood. The physics of fluid flow in a fracture is different from that in a homogeneous porous medium. Unlike the three-dimensional nature of flow in a porous medium, fluid flow in a fracture occurs in a two-dimensional variable aperture plane.

Conventional models to represent fractured media are often based on the "dual-\nporosity" concept (Warren and Root, 1963). In most simulators, to represent the \nexchange between the fracture and matrix media, we use an approximate pseudo-steady-\nstate mass exchange formulation resulting from an upscaling of the matrix block-\nscale flow (Landereau et al., 2001). This formulation is reasonably predictive for \nsingle-phase flows, but generally inaccurate for multiphase flows. This is mainly \ndue to the impact of non-linearities and the coupling between several physical \nmechanisms, especially capillarity and gravity, that do not yield the same \nhomogenised flow behaviour at the matrix block scale. A numerical approach to \novercome this limitation consists in sub-gridding the matrix blocks (Pruess and \nNarasimhan, 1985), which may be viewed as a mixed model as obtained from \nhomogenization theory (Arbogast et al., 1990). However, this method is still unused \nin practical situations because of its high computational cost. This paper describes \nthe optimisation of this sub-gridding technique in the capillary imbibition case, by \ntaking into account the physical specificities of this mechanism and with a \ncriterion of minimal computational cost. Implemented in a conventional flow \nsimulator, this technique allows the calculation of very reliable exchange terms \nbetween matrix blocks and fractures. \nThe study of the capillary imbibition mechanism on a single matrix block (possibly \nanisotropic) allows one to create an optimised one-dimensional model. This sub-\ngridding methodology has been validated by comparison with reference fine-grid \nsimulations, for various rock-fluid properties and anisotropic flow conditions. The \nreference solutions are reproduced very accurately, including the detailed time \nevolution of the matrix-fracture transfer rates. Since the sub-gridding methodology \nprovides accurate exchange terms, it has been implemented in a conventional flow \nsimulator dedicated to fractured porous media. The sub-gridding methodology improves \nthe calculation of matrix-fracture exchanges driven by capillary forces. Moreover, \nmatrix and fractures unknowns have been decoupled in order to reduce the \ncomputational cost. Therefore, short- and long-term flows of water-drive fractured \nmedia can be reliably predicted. This methodology can be applied to other multiphase \nflow problems solved with an industrial fractured reservoir simulator.\nThe main technical contributions of this work are the development of an optimised \nmethod for sub-gridding matrix blocks, and the implementation of this sub-gridding \nmethodology into a conventional flow simulator dedicated to fractured media.\n\n T. Arbogast, J. Douglas Jr and U. Hornung (1990), Derivation of the double \nporosity model of single phase flow via homogenization theory, SIAM J. Math. Anal,. \n21(4), 823-836.\n P. Landereau, B. Noetinger and M. Quintard (2001), Quasi-steady two-equation \nmodels for diffusive transport in fractured porous media: large-scale properties for \ndensely fractured systems, Advances in Water Resources 24, 863-876\n K. Pruess and T.N. Narasimhan (1985), A practical method for modeling fluid and \nheat flow in fractured porous media, SPE Journal.\n J.E. Warren and P.J. Root (1963), The behavior of naturally fractured reservoirs, \nSPE Journal.

Lattice Boltzmann simulation of solute transport in a single rough fracture

Steady state two-phase (oil-water) flow experiments were conducted in horizontal smooth parallel-plate fractures. The effect of fracture aperture, oil viscosity, injection rate, and injection method on the multiphase flow characteristics were investigated. The experiment data were analyzed using a porous medium approach and an equivalent homogeneous single phase method. The pressure gradients predicted by the latter are consistent with the measured pressure gradients in all the experiments. Contrary to the well-known Romm's relative permeability versus saturation relationship, the experimental data showed that the sum of the relative permeability's is less than one, which is due to the effect of phase interference on the oil-water flow. The effect of phase interference is more significant in the case of well mixed oil water flow than otherwise. The results also indicate that fracture aperture and oil viscosity do not have an significant impact on the relative permeability's of the oil and water in smooth parallel-plate fractures. INTRODUCTION Investigation of fluid flow in porous and fractured media is of practical importance in areas such as the recovery of oil and gas, the isolation and remediation of nuclear and toxic wastes in geological formation, and the exploitation of geothermal energy. In these applications, fluid flow in fractured media is often dominated by the highly permeable pathways provided by rock fractures and joints understanding the mechanics which govern the multiphase flow in fractures will certainly help to improve the energy recovery efficiency and optimize the waste isolation and remediation process. It is well known that the flow of multiphase fluids in a porous medium is generally governed by the saturation of the pore space occupied by the percolating fluids. Pores occupied by one phase are not available for the flow of the other, that is, each phase interferes with the flow of the other. This interference is controlled primarily by the action of capillary forces developed at the contact zones of the fluid phases in the pore canals. The smaller the size of the pores the more significant will be the effect of capillary forces. To quantify the interference between different fluids, relative permeability functions are introduced and defined as, Equation(1) (available in full paper) where k1 is the effective permeability to phase i, k is the absolute permeability of the medium, and kn is the relative permeability to phase i. Numerous experimental studies have shown that the relative permeabilities are strong functions of phase saturation. Similarly, it is expected that phase interference will affect multiphase flow in fractures. The physics of fluid flow in a fracture is different from that in a homogeneous porous medium. Unlike the three dimensional nature of flow in a porous medium, fluid flow in a fracture occurs in a two-dimensional variable aperture plane, and the rate and flow pattern are controlled by the geometry of the fracture and the effective stress change applied on the fracture. One simple approach to study fluid flow in a fracture is to treat the flow as if it were between two smooth parallel plates.

The successful exploration and development of unconventional shale gas reservoirs was possible with advances in hydraulic fracturing and horizontal drilling. Hydraulic fracture treatments open these natural fractures and create a fracture network in gas shales. However, the fracture propagation is not fully understood as of now. A critical review of hydraulic fracture propagation in shale gas formations is presented in this paper. Effects of pertinent factors on hydraulic fracture propagation are described and discussed. The factors are classified into three categories: well completion, fracture treatment, and formation properties. Well completion factors include casing roughness, perforation friction, tortuosity, fracture reorientation, and horizontal wells. Fracture treatment parameters include fluid property change, friction due to proppant, variable injection rate, multi-phase flow, proppant transport, and multi-stage treatment. Formation properties include rock toughness, temperature and pore pressure expansion, stress anisotropy, natural fractures, Young’s modulus, and formation permeability. This review gives engineers and researchers a better understanding of fracture propagation in shale gas reservoirs. Keywords: Hydraulic fracturing, fracture propagation, shale gas reservoirs, net pressure

Numerical investigation for simultaneous growth of hydraulic fractures in multiple horizontal wells

In this paper, we present a mathematical model and analysis for a microbeam fixed at one end and coupled to a microplate at its other end under the effect of capillary, shock and electrostatic forces. The model considers the microbeam as a flexible structure, the plate as a rigid body. First, we subject the system to capillary force via a drop of fluid which is trapped underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microbeam-microplate system. We then subject the system to shock loads for both case (capillary and electrostatic forces). The Galerkin procedure is used to derive a set of nonlinear ordinary-differential equations that describe the microsystem dynamics. We investigate the influence of the fluid volume ratio and the applied DC voltage on the microbeam response. We find that the effect of capillary force has much more dominant role compared to shock and electrostatic forces.

The purpose of this study is to evaluate the effects of capillary forces and adsorption on the distribution of a hydrocarbon mixture in an oil-gas-condensate reservoir. These effects consist in the precipitation of the liquid phase in thin pores and on the internal surface of the reservoir rock. To estimate the amount of the dispersed liquid condensate, analytical methods based on the generalization of the Kelvin equation and on the potential theory of adsorption have been developed. Sample calculations show significant role of adsorption, especially, in the neighborhood of the critical point of a mixture. Introduction Characterization and development of a petroleum reservoir can be highly affected by the fact that the behavior of hydrocarbon fluids in the reservoir differs from that in the PVT experiments. Such a difference is caused by the action of capillary forces and adsorption. The capillary forces can lead to precipitation of dispersed liquid phase containing valuable intermediate and heavy hydrocarbons and to its entrapment in macro- and mesopores. Due to the phenomenon of adsorption, significant amount of the reservoir fluid can be "caught" by the internal surface of the porous matrix and by the micropores. The effect of capillary forces on reserves distribution was extensively studied. Especial attention was paid to the coupled effect of gravity and capillary forces. In thick low permeable oil-gas-condensate reservoirs, the capillary forces lead to spreading the gas-oil contact into the transition zone. Such zone can be as thick as hundred meters, however the pressure in it is still close to the dew point. The condensate saturation in this zone may non-monotonously vary with depth, due to reservoir heterogeneity. Recent studies show that the mutual action of the capillary forces and thermal gradient breaks the equilibrium state in the transition zone, which results in formation of the diffusion fluxes. The internal surface of many reservoir rocks is quite large (up to 107 m2/m3) and completely wetting which shows its high capability to accumulate adsorbate. However the adsorption of hydrocarbons in gas-condensate reservoirs has not attained considerable attention, at least, compared to the effects of capillary forces. Only nitrogen adsorption as a method of determining the internal surface (in couple with capillary pressure data), adsorption in specific conditions of Devonian shale formations, and adsorption of asphaltenes have been studied. Any study of the surface effects in reservoir conditions must take into account the following peculiarities of reservoir thermodynamics:Bulk phases (vapor and liquid condensate) are highly non-ideal, multicomponent mixtures;The reservoir mixture shows retrograde behavior, condensation occurs when the pressure decreases;The effects of capillary forces and adsorption are especially significant in the neighborhood of a dew point (or, geometrically, close to the gas-oil contact). These peculiarities plague studies of the capillary effects, making it impossible to apply usual tools (such like the classical Kelvin equation) without their thorough modification. Additionally, the capillary pressure behaves as a singular small parameter in the governing system of equations for capillary equilibrium, which results in some difficulties and instabilities in numerical and analytical methods for solution of this system. An application of the existing adsorption theories to reservoir conditions is even more difficult, since, to the best of our knowledge, the great majority of these theories describes adsorption from a one-component ideal fluid, or from a dilute solution. Only few concepts are related to the mixture adsorption (the most well-known of them being IAS and RAS theories). However, the adsorbed mixture is still supposed to be far from the dew point. Extrapolation of the existing schemes onto the neighborhood of the dew point is a non-trivial problem because, when this neighborhood is approached, the properties of the adsorbed mixture must be continuously transformed to the properties of the bulk liquid condensate, at least in the case when the last one is completely welling. P. 441

Single-phase and multi-phase fluid flow through an artificially induced, CT-scanned fracture

Objective To map OTA/AO type B and type C distal radial fractures according to three-dimensional (3D) CT scan data, and to describe the morphological distribution of fracture lines. Methods A total of 468 cases of distal radius fractures admitted to the Affiliated Hospital of Chengdu University from January 2016 to March 2019 were analyzed and AO classification were performed. AO type B and type C fractures meet the inclusion criteria and then CT data were 3D reconstructed, and morphological description were performed on the fracture lines of each joint surface, including fracture shape angle, fracture area and fracture ratio. At the same time, the articular surface fracture model was superimposed on the standard model, then fracture line and fracture area distribution map were drawn to create the fracture map of intra-articular distal radial fractures. Result Intra-articular fractures of the distal radius were 209 cases, accounting for 44.7% (209/468) of the distal radius fractures, among which 67 cases of AO type B fracture. In type B fractures, average fracture height were 20.30±11.26 mm, average fracture width were 12.24±6.83 mm, average fracture area were 189.61±101.84 mm2, average angle were 57.23°±14.95°, and average area ratio of fracture (fracture zone area/joint surface area ratio) were 32.42%±10.24%. 142 cases were OA type C fracture, the average fracture height were 24.43±11.37 mm, average fracture width were 20.38±7.59 mm, average fracture area were 425.26±314.31 mm2, average angle were 51.26°±13.17°, and average area ratio of fracture were 73.81%±26.29%. According to fracture map formed by main fracture lines, five different fracture areas were identified: ① 63 cases in central area; ② 25 cases in Lister's nodule area; ③ 59 cases in scaphoid area; ④ 36 cases in lumbar fossa area; ⑤ 26 cases in lower iliac area. Main fracture lines were concentrated in the area on the dorsal side of the central area and the scaphoid area. The fracture lines of type B fracture mainly concentrated in scaphoid region, which accounted for 29.85% (20/67), and dorsal side and central area accounted for 26.87% (18/67). The fracture lines of type C fracture accounted for 27.46% (39/142) in scaphoid area and 31.69% (45/142) in central area. The fracture line of type C fracture increased in the lumbar fossa region (17.61%, 25/142) and the lower ulnar region (12.68%, 18/142) compared with type B fracture (28.69%). Compared with the type B fracture, the overall distribution of the fracture line of the type C fracture is more central. Conclusion The map of intra-articular fracture of distal radius was drawn and morphological distribution of fracture lines were quantified. Fracture-prone site and shape of fracture line were visually recognized. At the same time, description of articular surface fracture line and fracture area of type B and type C fractures of OA classification were improved, which may help with new classification and diagnosis. Key words: Radius fractures; Intra-articular fractures; Imaging, three-dimensional; Maps

A. Garg, Department of Materials Science and Mineral Engineering, University of California, Berkeley, A.R. Kovscek and M. Nikravesh, Earth Sciences Division, Lawrence Berkeley National Laboratory, L. M. Castanier, Department of Petroleum Engineering, Stanford University, and T. W. Patzek, Department of Materials Science and Mineral Engineering, University of California, Berkeley and Earth Sciences Division, Lawrence Berkeley National Laboratory Abstract We present an integrated approach to imaging the progress of air displacement by spontaneous imbibition of oil into sandstone. We combine Computerized Tomography (CT) scanning and neural network image processing. The main aspects of our approach are I) visualization of the distribution of oil and air saturation by CT, II) interpretation of CT scans using neural networks, and III) reconstruction of 3-D images of oil saturation from the CT scans with a neural network model. The neural networks developed here construct 3-D images of fluid distribution at any time and/or location within the core. One neural network model interpolates between the CT images for a given position at different time levels and extrapolates beyond the interval of time during which the images were collected. Likewise, the network interpolates spatially between images at a given time. After interpolation and extrapolation, other network models have been developed to reconstruct the three-dimensional distribution of oil in the core. Excellent agreement between the actual images and the neural network predictions is found. Introduction An increasing global demand for energy and simultaneous depletion of conventional hydrocarbon reserves impose a formidable challenge for efficient recovery from nonconventional rock systems, such as naturally fractured reservoirs. Fractured petroleum reservoirs provide over 20 % of the world oil reserves. Examples of prolific fractured reservoirs are: the Monterey Shales in California (estimated tens of billions of barrels of oil-in-place); the California Diatomites (estimated fifteen billion barrels of oil-in-place); the West Texas Carbonates; the North Sea Chalks; and the Asmari Limestones in Iran. Hydrocarbon recovery from naturally fractured reservoirs is not yet fully understood. This is mainly due to the lack of a complete understanding of multiphase flow through fractured porous media. Two- or three-phase flow in a fractured reservoir depends on the combined nonlinear effects of hydraulic connectivity and physicochemical properties of fractures, relative permeabilities to multiphase flow in the fractures, rock-matrix nature, matrix block size, capillary forces and fracture closure stress. The nonlinear interplay of all these factors determines the ultimate hydrocarbon recovery from fractured reservoirs. In contrast, most of the published data have been produced in controlled experiments that have focused on one or more of the above factors considered in isolation. These data are then upscaled in numerical simulators to model the coupled nonlinear behavior of fractured reservoirs. As a result, current numerical simulation models of fractured reservoirs lack firm predictive capability and must be tuned for each field case with the available data. Thus, it might be helpful to undertake a systematic experimental and theoretical study of joint effects of all the factors governing multiphase fluid flow in a fractured porous rock. Of course, such a study is beyond the scope of this paper. Nevertheless, we have undertaken a study to evaluate the influence of four major factors on hydrocarbon recovery. These are: fracture configuration, rock-matrix block size, wettability characteristics of the rock, and fluid flow rates. This paper reports our progress on a scoping study of spontaneous imbibition of a hydrocarbon (kerosene) into a single air-filled block of rock matrix (Berea sandstone). P. 695

Background Accounting for 6% of all fractures, clavicle fractures are common in clinic with the middle 1/3 fracture as the most common type. The options for treatment include conservative and surgical strategies. The effect of conservative treatment via manipulative reduction is often unsatisfactory (especially for comminuted fractures) . For the middle 1/3 clavicle fractures, the displacement of proximal end caused by the upward and posterior tractions of sternocleidomastoid muscle may result in instability and nonunion of fracture. These risk factors increase the chance of redisplacement, which restrict early activity and affect joint function simultaneously. With in-depth study of the injury and therapeutic effect of clavicle fractures and patients' improved expectation for life quality, more patients require surgical treatment. Those with comminuted and shortened fractures are often treated with plate fixation. The surgical treatment reduces complications including nonunion, shoulder deformity, pain, functional impairment and neurovascular injury, et al., and greatly improves the clinical therapeutic effect of clavicular fracture. However, the excessive dissection of surrounding tissue required by conventional plate fixation increases the chance of nonunion. Moreover, the large incision on skin not only leads to the formation of large scar but also causes supraclavicular nerve damage and numbness in the corresponding area. The minimally invasive percutaneous plate osteosynthesis (MIPPO) technique can nicely solve some of the common drawbacks of traditional surgery. Methord Ⅰ. General information: From January 2012 to December 2014, 86 patients (52 males and 34 females) with mid-shaft clavicle fractures were treated in the first affiliated hospital of dalian medical university. The age ranged from 14 to 70 years old with an average of 40 years. All cases were closed fractures, which included 48 cases of traffic accident and 38 cases of fall injury. 36 cases were affected by left side, and 50 cases were affect by right side. Among the patients, there were 14 cases of combined rib fractures and 3 cases of scapular fractures (minor fractures) . The time from injury to admission ranged from 1 to 10 days with an average of 5 days. The operation indications: fractures of total displacement, comminuted fractures and clavicle shortening of over 2 cm. Locking compression plate was used in all patients who were randomly divided into Conventional ORIF group (Group A, 41 cases) and MIPPO group (group B, 45 cases) based on the different placements of internal fixators. Ⅱ.Inclusive and exclusive criteria: Inclusive criteria: (1) Unilateral displaced mid-shaft clavicle fractures of adult (Robison type II) ; (2) Combined rib or scapular fractures without the affection of shoulder function assessment. Exclusive criteria: (1) Open fractures; (2) Combination of other severe fractures that affect shoulder function assessment; (3) Combined brachial plexus injury or other disease that affects upper extremity function; (4) Pathological fractures; (5) Patients who are lost for follow-up. Ⅲ. Surgical methods: (1) Conventional ORIF group (group A) : After general anesthesia, the patient was placed in semi-sitting position (beach chair position) . The fracture ends and acromion were both marked. The incision was made along the surface of clavicle and was extended toward acromion. The soft tissue was separated and exposed to reveal periosteum and fracture fragments with particular attention to comminuted or displaced disc-shaped fractures. Comminuted fractures were treated with lag screw for fixation. The fracture fragments were converted into 3-part or 2-part fractures. Finally, anatomical locking compression plate was used for fixation with 3 screws on each side. (2) MIPPO technique group (group B) : After general anesthesia, the patient was placed in semi-sitting position (beach chair position) . The situation of fracture was confirmed, and the fracture ends and acromion were both marked to design minimally invasive incisions on the distal and proximal clavicle. 2-3 cm arc incisions were made from the center of fracture toward both sides along the longitudinal axis of clavicle. The skin, subcutaneous tissue and deep fascia were cut open, and the subperiosteum was slightly dissected for fracture reduction. The periosteum at fracture ends was preserved to the greatest extent, and the hematoma was removed to expose the fracture ends. Crossing clavicle downward from superomedial to inferolateral, the supraclavicular nerve should be identified and protected during operation. The fractures were reduced by manipulation or percutaneous poking with Kirschner wire under fluoroscopy. With satisfactory linear and positional alignments, the small fragments were fixed with lag screw. If necessary, Kirschner wire should be adopted for temporarily fixation and maintenance of the position of clavicle. A subcutaneous tunnel was established along the incision edge, through which the appropriate anatomical locking compression plate was selected and inserted towards the distal end of clavicle. With the position of distal incision determined, A 1-2 cm of distal incision was made. Then, the plate was removed and inserted again through the distal incision to the proximal end. With the position of proximal incision determined, a 1-2 cm proximal incision was made as well. As the plate was fully inserted, both the proximal and distal ends were checked to make sure their attachment with clavicle. The plate position was properly adjusted as needed, and 3 screws were placed through each of the two small incisions. The reduction was further observed under fluoroscopy.Ⅳ. Postoperative treatment: Postoperative antibiotic was given to prevent infection within 24 hours. After adequate drainage, the stiches were taken out 7-10 days later. The affected arm was suspended for 2 weeks with triangular bandage, and passive training was initiated on the 2nd postoperative day. Passive should joint exercise was carried out within 2 weeks, and no-weight bearing active exercise started 2 weeks later. The callus was observed during regular reexamination, and normal activities were gradually restored based on the growth.Ⅴ. Outcome Measurements: (1) Surgical situations and postoperative follow-up scores: the operative time and hospital stay of both groups were recorded, and the wound healing was observed as well. After discharge, the patients were required to be followed up every two weeks till fracture healing. The condition of affected limb was observed under fluoroscopy, and the patients were followed up every 3 months after fracture healing. The criteria of fracture healing include continuous callus formation and the disappearance of fracture line revealed by radiographic examination, no tenderness in the clinical examination of fracture ends, and pain free in active movement and weight-bearing activities. The shoulder joint functions including pain, anatomical location and activity were assessed by Neer score. The criteria of Neer score: 90-100 points as excellent; 80-89 points as good; 70-79 points as moderate; less than 70 points as poor. (2) Complication rate and patients’ subjective satisfaction: the common postoperative complications were compared using statistics, including infection, delayed union, hypertrophic scar, supraclavicular nerve damage, et al., and in the meanwhile, the subjective satisfaction (satisfaction or dissatisfaction) with the operation of patients was asked as well. Ⅵ. Statistical analysis: The SPSS 23.0 software was used for data processing. According to the data distribution characteristics, the enumeration data were analyzed using the t test and the measurement data were analyzed using the χ2 test. A P value <0.05 was regarded as statistically significant. Results (1) Comparison of surgical situations and postoperative follow-up scores: The surgical situations were compared between the two groups, including operation time (min) , hospital stay (d) , fracture healing time (w) and Neer score. The operation time (approximately 1 hour) , the hospital stays (5-7 days) and the fracture healing time (11-14 weeks) were the same for both groups. Also, the Neer scores for both groups were excellent without significant statistical difference (P>0.05) . The patients' shoulder joint functions including abduction, internal rotation and external rotation were all well performed. (2) Comparison of complication rate and patients’ subjective satisfaction: Both groups have no infection or delayed union occurred, and the comparison was not statistically significant. However, there were differences in the comparison of hypertrophic scar, supraclavicular nerve damage and subjective satisfaction. There were 12 cases of hypertrophic scar in group A and 0 case in group B, and the comparison had statistical significance (χ2 =15.307, P<0.001) . There were 20 cases of numbness in the dominated region of supraclavicular nerve in group A and only 4 cases in group B, and the comparison had statistical significance (χ2 16.969, P<0.001) . There were 26 cases of subjective incision satisfaction in group A and 39 cases in group B, and the comparison had statistical significance (χ2 =6.285, P<0.012) . Conclusion MIPPO technique has been used for the treatment of mid-shaft clavicle fractures. The surgical incision is small, and the internal fixation is reliable. These not only embody the advantage of plate fixation but also minimize the complications of hypertrophic scar and supraclavicular nerve injury. Thus, it provides good conditions for early functional exercise and is worth of clinical application. Key words: Mid-shaft clavicle fracture; Minimal invasion; Reduction; Internal fixation

Fractured reservoirs are characterised by a large difference in permeability of the fracture and matrix system. Usually, the matrix contains the bulk of the oil while the fractures are the flow paths. These characteristics are challenging for projects aiming at increasing hydrocarbon liquid recovery from gas condensate fields by gas injection. While in fractured oil reservoirs, capillary forces (imbibition) or gravity forces can be utilised to improve oil recovery, for gas injection into gas condensate reservoirs, these forces are less important. The recovery mechanisms were investigated using the properties of a rich gas condensate field in the Middle East. A fine grid sector simulation model was created in which the fractures and matrix were introduced explicitly. Without taking diffusion into account, the injected gas breaks through at the producer very fast. The concentration in the produced gas is closely linked to the effective permeability of the fracture divided by the effective permeability of the matrix. However, taking diffusion into account, the increase in injected gas concentration is much slower. The speed of the increase (for the same pore volume injected) depends on matrix porosity, velocity of the front, fracture spacing and permeability contrast. The molecules of the injected gas are diffusing into the matrix while the components of the reservoir gas are diffusing towards the fracture. The various components have different diffusion coefficients. Dependent on the injection gas, the dew point pressure in the matrix can be reached (despite the reservoir pressure being constant) and condensate drops out. Hence, the condensate recovery depends on the injected gas. The results of the study show that neglecting diffusion in fractured reservoirs can result in errors in the condensate recovery of more than 50 %. In addition, the shape of the condensate recovery curve will be incorrect if diffusion is not accounted for.

Detailed understanding of the couplings between fluid flow and solid deformation in porous media is crucial for the development of novel technologies relating to a wide range of geological and biological processes. A particularly challenging phenomenon that emerges from these couplings is the transition from fluid invasion to fracturing during multiphase flow. Previous studies have shown that this transition is highly sensitive to fluid flow rate, capillarity, and the structural properties of the porous medium. However, a comprehensive characterization of the relevant fluid flow and material failure regimes does not exist. Here, we used our newly developed multiphase Darcy-Brinkman-Biot framework to examine the transition from drainage to material failure during viscously stable multiphase flow in soft porous media in a broad range of flow, wettability, and solid rheology conditions. We demonstrate the existence of three distinct material failure regimes controlled by nondimensional numbers that quantify the balance of viscous, capillary, and structural forces in the porous medium, in agreement with previous experiments and granular simulations. To the best of our knowledge, this study is the first to effectively decouple the effects of viscous and capillary forces on fracturing mechanics. Last, we examine the effects of consolidation or compaction on said dimensional numbers and the system's propensity to fracture.