Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode (DTM) are numerically investigated through the three-dimensional, toroidal, nonlinear resistive-MHD code (CLT). We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations, which are similar to those driven by the kink mode. The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations. With a high perpendicular thermal conductivity, the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow. However, with a low perpendicular thermal conductivity, the system tends to exhibit sawtooth-like oscillations. With a sufficiently high or low heating rate, the system exhibits sawtooth-like oscillations, while with an intermediate heating rate, the system quickly evolves into a steady state. At the steady state, there exist the non-axisymmetric magnetic field and strong radial flow, and both are with helicity of m/n=2/1. Like the steady state with m/n=1/1 radial flow, which is beneficial for preventing the Helium ash accumulation in the core, the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady-state operations in future fusion reactors. We also find that the behaviors of the sawtooth-like oscillations are almost independent of Tokamak geometry, which implies that the steady state with saturated m/n=2/1 islands might exist in different Tokamaks.

A Single Equation to Depict Bottomhole Pressure Behavior for a Uniform Flux Hydraulic Fractured Well

Pressure transient analysis for a vertically hydraulically fractured well is evaluated using two different equations, which cater for linear flow at the early stage and radial flow in the later stage. However, there are three different stages that take place for an analysis of pressure transient, namely linear, transition and pseudo-radial flow. The transition flow regime is usually studied by numerical, inclusive methods or approximated analytically, for which no specific equation has been built, using the linear and radial equations. Neither of the approaches are fully analytical. The numerical, inclusive approach results in separate calculations for the different flow regimes because the equation cannot cater for all of the regimes, while the analytical approach results in a difficult inversion process to compute well test-derived properties such as permeability. There are two types of flow patterns in the fracture, which are uniform and non-uniform, called infinite conductivity in a high conductivity fracture. The study was conducted by utilizing an analogous study of linear flow equations. Instead of using the conventional error function, the exponential integral with an infinite number of wells was used. The results obtained from the developed analytical solution matched the numerical results, which proved that the equation was representative of the case. In conclusion, the generated analytical equation can be directly used as a substitute for current methods of analyzing uniform flow in a hydraulically fractured well.

Modeling of Before Closure Zero Slope Pressure Derivative in a Diagnostic Fracture Injection Test DFIT

Recent diagnostic fracture injection test (DFIT) data presented on a Bourdet log-log diagnostic plot showed derivative slope of 0 in the before closure (BC) portion of the DFIT response. Some works qualitatively describe it as radial flow. This behavior has not been quantitatively analyzed, modeled and matched. The present work disagrees with the hypothesis of radial flow and successfully matches the relatively flat trend in the Bourdet derivative with a model dominated by friction dissipation coupled with tip extension. The flat trend in Bourdet derivative occurs shortly after shut-in during the before closure period. Because a flat derivative trend suggests diffusive radial flow, our first approach was to consider the possibility that an open crack at a layer interface stopped the fracture propagation and caused the apparent radial flow behavior observed in falloff data. However, a model that coupled pressure falloff from diffusive flow into a layer interface crack with pressure falloff from closure of a fracture that propagated up to the layer interface failed to reproduce the observed response. Subsequently, we discovered that existing models could match the data without considering the layer interface crack. We found that data processing is very important to what is observed in derivative trends and can mislead the behavior diagnosis. We succeeded to match one field DFIT case showing an obvious early flat trend. The presence and dominance of geomechanics, coupled with diffusive flow, disqualify the description of the flat trend in Bourdet derivative as radial flow. Instead, flow friction coupled with tip extension can completely match the observed behavior. Based on our model, cases with a long flat trend have large magnitude near-wellbore tortuosity friction loss and relatively long tip extension distance. Further, we match the near wellbore tortuosity behavior with rate raised to a power lower than the usually assumed 0.5. The significance of these analyses relates to two key factors. First, large magnitude near wellbore tortuosity friction loss increases the pressure required for fracture propagation during pumping. Second, tip extension is a way to dissipate high pumping pressure when very low formation permeability impedes leakoff. Matching transient behavior subject to the presence of both of these factors requires lowering the near-wellbore tortuosity exponent.

An Integrated Approach of Numerical Well Test for Well Intersecting Fractures Based on FMI Image

Fluid flow is strongly affected by fractures in unconventional reservoirs. It is essential to deeply understand the flow characteristics with fractures for improving the production and efficiency of unconventional reservoir exploitation. The purpose of this work is to develop an accurate numerical model to evaluate the transient-pressure response for well intersecting fractures. The meshes generated from Fullbore Formation Micro-Imager (FMI) images ensure an efficient numerical description of the geometries for fractures and interlayers. The numerical simulation is implemented by an inhouse finite element method-based code and benchmarked with drill stem test (DST) data. The results show that three flow regimes appear in the reservoir with fractures within the test period: wellbore afterflow, pseudolinear flow, and radial flow. In contrast, only the wellbore afterflow and radial flow appear for the wells without fractures. The results also reveal that fractures dominate the flow near the wellbore. Verification and application of the model show the practicability of the integrated approach for investigating the transient-pressure behaviors in the unconventional reservoir.

Simultaneous Enzymatic Cellulose Hydrolysis and Product Separation in a Radial-Flow Membrane Bioreactor

Hydrolysis is the heart of the lignocellulose-to-bioethanol conversion process. Using enzymes to catalyze the hydrolysis represents a more environmentally friendly pathway compared to other techniques. However, for the process to be economically feasible, solving the product inhibition problem and enhancing enzyme reusability are essential. Prior research demonstrated that a flat-sheet membrane bioreactor (MBR), using an inverted dead-end filtration system, could achieve 86.7% glucose yield from purified cellulose in 6 h. In this study, the effectiveness of flat-sheet versus radial-flow MBR designs was assessed using real, complex lignocellulose biomass, namely date seeds (DSs). The tubular radial-flow MBR used here had more than a 10-fold higher membrane surface area than the flat-sheet MBR design. With simultaneous product separation using the flat-sheet inverted dead-end filtration MBR, a glucose yield of 10.8% from pretreated DSs was achieved within 8 h of reaction, which was three times higher than the yield without product separation, which was only 3.5% within the same time and under the same conditions. The superiority of the tubular radial-flow MBR to hydrolyze pretreated DSs was confirmed with a glucose yield of 60% within 8 h. The promising results obtained by the novel tubular MBR could pave the way for an economic lignocellulose-to-bioethanol process.

Estimation of the value of leaks through a through defect of the pipeline when using in-pipe repair elements

The loss of hydrocarbons when using in-pipe repair elements is determined by the nature of the fluid flow in the gap between the pipe and the repair sleeve. An accurate analytical calculation of the flow parameters for a real sleeve, taking into account its length, the asymmetry of the defect and other design features, is very difficult. In this article, the problem of accurate calculation of the radial flow of a viscous incompressible fluid in a thin layer between two annular plates simulating a circular region with a center coincide with a pipeline defect is solved. The area consists of two circles formed by the pipeline wall with a through defect and the surface of the internal repair element. The results obtained will allow us for accurate calculations in the area adjacent to the defect of the pipe and approximate calculations for the whole repair element.

The Pressure Buildup Well Test Analysis considering Stress Sensitivity Effect for Deepwater Composite Gas Reservoir with High Temperature and Pressure

Some deepwater gas reservoirs with high temperature and pressure have obvious stress sensitivity effect resulting in difficulty in well test interpretations. The influence of stress sensitivity effect on the pressure drawdown well test is discussed in many papers. However, the influence on the pressure buildup well test is barely discussed. For practices in oilfields, the quality of pressure data from the drawdown stage of well test is poor due to the influence of production fluctuation. Thus, the pressure data from the buildup stage is used for well test interpretations in most cases. In order to analyze the influence of stress sensitivity effect on the pressure buildup well test, this paper establishes a composite gas reservoir pressure buildup well test model considering the stress sensitivity effect and the hysteresis effect. Numerical solutions to both pressure drawdown and buildup well test models are obtained by the numerical differentiation method. The numerical solutions are verified by comparing with analytical solutions and the homogeneous gas reservoir well test solution. Then, the differences between pressure drawdown and buildup well test curves considering the stress sensitivity effect are compared. The parameter sensitivity analysis is conducted. Compared with the conventional well test curve, the pressure derivative curve of pressure drawdown well test considering the stress sensitivity effect deviates upward from the 0.5 horizontal line at the inner zone radial flow stage, while it deviates upward from the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. However, for the pressure buildup well test curve considering the stress sensitivity effect, the pressure derivative curve gradually descends to the 0.5 horizontal line at the inner zone radial flow stage, while it descends to the M/2 (mobility ratio/2) horizontal line at the outer zone radial flow stage. The pressure derivative curve of pressure buildup well test considering the hysteresis effect is higher than the curve without considering the hysteresis effect, because the permeability cannot be recovered to its original value in the buildup stage after considering the hysteresis effect. Meanwhile, skin factor and mobility ratio have different effects on pressure drawdown and buildup well test curves. Based on the model, a well test interpretation case from a deepwater gas reservoir with high temperature and pressure is studied. The result indicates that the accuracy of the interpretation is improved after considering the stress sensitivity effect, and the skin factor will be exaggerated without considering the stress sensitivity effect.

Evaluation of transmissivity in a fractured aquifer—the Nyanzari wellfield, Burundi

Due to population growth, the city of Gitega in the central part of Burundi is lacking drinking water. Therefore, the national urban water supply company decided to expand the Nyanzari wellfield by drilling additional wells.Two additional wells were drilled to 80 m (F7.2) and 85 m (F8bis) depths. Step tests followed by 72-hours aquifer tests were performed in each well. Results indicate bilinear flow followed by linear flow and radial flow in F7.2. No reaction was observed in observation wells. Fracture-matrix transmissivity was estimated at 3 · 10−4 m2/s. In the case of F8bis, linear flow in an infinite flow fracture followed by radial flow was visible. Reaction was measured in observation wells. Transmissivity was estimated at 3.3 · 10−3 m2/s.Both wells lie no more than 300 m apart, but no evidence of interference between them was depicted during the tests. It appears that two independent fracture systems prevail in the wellfield.

Influence of Culture Period on Osteoblast Differentiation of Tissue-Engineered Bone Constructed by Apatite-Fiber Scaffolds Using Radial-Flow Bioreactor

With the limitation of autografts, the development of alternative treatments for bone diseases to alleviate autograft-related complications is highly demanded. In this study, a tissue-engineered bone was formed by culturing rat bone marrow cells (RBMCs) onto porous apatite-fiber scaffolds (AFSs) with three-dimensional (3D) interconnected pores using a radial-flow bioreactor (RFB). Using the optimized flow rate, the effect of different culturing periods on the development of tissue-engineered bone was investigated. The 3D cell culture using RFB was performed for 0, 1 or 2 weeks in a standard medium followed by 0, 1 or 2 weeks in a differentiation medium. Osteoblast differentiation in the tissue-engineered bone was examined by alkaline phosphatase (ALP) and osteocalcin (OC) assays. Furthermore, the tissue-engineered bone was histologically examined by hematoxylin and eosin and alizarin red S stains. We found that the ALP activity and OC content of calcified cells tended to increase with the culture period, and the differentiation of tissue-engineered bone could be controlled by varying the culture period. In addition, the employment of RFB and AFSs provided a favorable 3D environment for cell growth and differentiation. Overall, these results provide valuable insights into the design of tissue-engineered bone for clinical applications.