Stochastic Modeling of a Fracture Network in a Hydraulically Fractured Shale-Gas Reservoir

The fundamental behavior of fluid production from shale/ultra-low permeability reservoirs that are produced under a constant wellbore pressure remains difficult to quantify, which is believed to be (at least in part) due to the complexity of the hydraulic fracture patterns created during the well stimulation process. This work introduces a novel approach to model the hydraulic fractures in a shale reservoir using a stochastic method called random-walk. We see this approach as a beginning step that could be used to capture a part of the "complexity" of a fracture that has been generated by a hydraulic fracturing treatment and that such "complex" fracture processes may be observed in the Microseismic measurements. To assess the random-walk fracture concept, we performed numerical simulation of the patterns generated using a given random-walk fracture pattern. Using a total of 83 pattern cases, sensitivity analyses were performed on these fracture patterns; where the tortuosity, the extent (length), the tendency to split, and the number of branching stages were the factors considered. The rate performance of the "random-walk" fracture cases were compared to the standard model of a (single) planar hydraulic fracture. In addition to the mass rate performance, the created pressure distribution was analyzed in "time slices" (or "snapshots) to qualitatively assess each complex-pattern during early production times (before the onset of the pseudosteady-state flow regime). Our results were used to create a correlation between fracture performance, in terms of cumulative recovery, and the fracture volume and "complexity." In addition, an empirical correlation between the number of stages of bifurcation (splitting) of the fracture pattern and the value of the mass rate β-derivative for early production times was then established. Finally, as we were limited to a small-scale case due to the intensive gridding required, the feasibility and the advantages of a full-scale reservoir and well model are discussed

Cross-layer distributed power control: A repeated games formulation to improve the sum energy-efficiency

The main objective of this work is to improve the energy-efficiency (EE) of a multiple access channel (MAC) system, through power control, in a distributed manner. In contrast with many existing works on energy-efficient power control, which ignore the possible presence of a queue at the transmitter, we consider a new generalized cross-layer EE metric. This approach is relevant when the transmitters have a non-zero energy cost even when the radiated power is zero and takes into account the presence of a finite packet buffer and packet arrival at the transmitter. As the Nash equilibrium (NE) is an energy-inefficient solution, the present work aims at overcoming this deficit by improving the global energy-efficiency. Indeed, as the considered system has multiple agencies each with their own interest, the performance metric reflecting the individual interest of each decision maker is the global energy-efficiency defined then as the sum over individual energy-efficiencies. Repeated games (RG) are investigated through the study of two dynamic games (finite RG and discounted RG), whose equilibrium is defined when introducing a new operating point (OP), Pareto-dominating the NE and relying only on individual channel state information (CSI). Accordingly, closed-form expressions of the minimum number of stages of the game for finite RG (FRG) and the maximum discount factor of the discounted RG (DRG) were established. The cross-layer model in the RG formulation leads to achieving a shorter minimum number of stages in the FRG even for higher number of users. In addition, the social welfare (sum of utilities) in the DRG decreases slightly with the cross-layer model when the number of users increases while it is reduced considerably with the Goodman model. Finally, we show that in real systems with random packet arrivals, the cross-layer power control algorithm outperforms the Goodman algorithm.Comment: 36 pages, single column draft forma

Microstructure and properties of welds between 5754 Al alloys and AZ31 Mg alloys using a Yb:YAG laser

The authors wish to thank Mr. Henri ANDRZEJEWSKI for his technical assistance in laser experiments. The authors wish to place their sincere thanks to Professor Philippe BOURNOT and Dr. Eric VALERIO for helpful discussions.Dissimilar laser beam welding between A5754 Al alloy and AZ31 Mg alloy with the plate thickness of 2 mm was investigated. Complex flow pattern characterized by a large volume of intermetallic compounds Al12Mg17 and Al3Mg2 is formed in the fusion zone. Microhardness measurement of the dissimilar welds presents an uneven distribution due to the complicated microstructure of the weld, and the maximum value of microhardness in the fusion zone is much higher than of the base materials

ab initio X-ray structure determination of NaAl(SO4)2

The sodium aluminium disulphate NaAl(SO4)2 has been obtained after calcinations at 300 °C of NaAl(SO4)2.12H2O alum. The structure of this compound has been refined from powder       X-ray diffraction data using the Rietveld method. This compound crystallises in trigonal system       P 3 2 1 with the following parameters: a = 4.749(12) Ã…, c = 8.314 (4) Ã… (Z = 1).  The final refinement led to RF = 6.3 %, RB = 4.12 %. In the proposed model the sulfate ions is in disorder between two nonequivalent crystallographic sites with probabilities p1/p2= 0.30/70. The atomic arrangement of NaAl(SO4)2 is characterised by two different alternating layers parallel to (001): the first layer is composed of corner-linked AlO6 octhahedra and SO4 tetrahedra, the second layer is built from monovalent Na+ .Â

Structural, Thermal behaviour and Vibrational study of a new Cesium- Ammonium Dihydrogen Phosphate Arsenate: Cs0.55(NH4)0.45H2(PO4)0.39(AsO4)0.61

Mixed crystals Cs0.55(NH4)0.45H2(PO4)0.39(AsO4)0.61 (CADPA) of the two antiferroelectric NH4H2PO4 (ADP) and NH4H2AsO4 (ADA) and of the two ferroelectric CsH2PO4 (CDP) and CsH2AsO4 (CDA) have been prepared by slow evaporation from aqueous solution at room temperature. The structural properties of the crystal were characterized by X-ray single analysis (performed at room temperature), which revealed that (CADPA) crystallizes in space group I42d with lattice parameters: a = 7.6473(1) Å, c = 7.6803(1) Å and Z = 4. The title compound is isostructural with the tetragonal phases of (ADP) and (ADA). This structure is characterized by two kinds of disorder: a statical or dynamical disorder of the acidic proton in the O–H…O hydrogen bond and another one which is connected with a reorientational motion of NH4+ ions. Broader peaks in the IR spectrum confirm a structural disorder in this material. Thermal analysis of the (CADPA) were characterized by differential scanning calorimetry (DSC), showed that the title compound undergo two phase transitions at T = 204 K and T = 407 K