On SS-supplemented subgroups of some sylow subgroups of finite groups

Let [Formula: see text] be a finite group. A subgroup [Formula: see text] of [Formula: see text] is called to be [Formula: see text]-permutable in [Formula: see text] if [Formula: see text] permutes with all Sylow subgroups of [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is said to be [Formula: see text]-supplemented in [Formula: see text] if there exists a subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is [Formula: see text]-permutable in [Formula: see text]. In this paper, we investigate [Formula: see text]-nilpotency of a finite group. As applications, we give some sufficient and necessary conditions for a finite group belongs to a saturated formation.

SIMULATION OF REFLECTION OF A PLANE ELECTROMAGNETIC WAVE IN A MULTILAYER MEDIUM: OIL-SATURATED FORMATION ENCLOSING A HYDRAULIC FRACTURE

Propagation of a plane electromagnetic wave of the microwave range is simulated to calculate the coefficient of its reflection from a homogeneous layer. A particular case of a multilayer geomediumis considered: an oil-saturated formation enclosing a hydraulic fracture. When justifying the choice of the frequency range, the value of fracture surface irregularity was taken into account. The dependence of the reflection coefficient on frequency for an electrically less dense non-absorbing layer inside a denser non-absorbing substance (a void layer inside a rock) has been calculated.

Evaluation of NaCl and MgCl2 heat exchange fluids in a deep binary geothermal system in a sedimentary halite formation

Halite formations are attractive geothermal reservoirs due to their high heat conductivity, resulting in higher temperatures than other formations at similar depths. However, halite formations are highly reactive with undersaturated water. An understanding of the geochemical reactions that occur within halite-saturated formation waters can inform decision making regarding well construction, prevention of well clogging, formation dissolution, and thermal short-circuiting. Batch reaction and numerical 3-D flow and equilibrium reactive transport modeling were used to characterize the produced NaCl-brine in a well targeting a halite-saturated formation. The potential for inhibition of precipitation and dissolution using an MgCl2-brine and NaCl + MgCl2-brine were also investigated. Within the injection well, heating of an NaCl-brine from 70 to 120 °C caused the solubility of halite to decrease, resulting in the potential dissolution of 0.479 mol kg−1 halite at the formation. Conversely, cooling from 120 to 100 °C in the production well resulted in potential precipitation of 0.196 mol kg−1 halite. Concurrent precipitation of anhydrite is also expected. Introduction of MgCl2 into the heat exchange brine, which has a common Cl− ion, resulted in a decreased potential for dissolution by 0.290 mol kg−1 halite within the formation, as well as decreased precipitation within the production well, compared to the NaCl-brine. The halite solubility was altered by changes in pressure up to 0.045 mol kg−1. This indicates that designing and monitoring the composition of heat exchange fluids in highly saline environments is an important component in geothermal project design.

Evaluation of NaCl and MgCl2 heat exchange fluids in a deep binary geothermal system in a sedimentary halite formation

Halite formations are attractive geothermal reservoirs due to their high heat conductivity, resulting in higher temperatures than other formations at similar depths. However, halite formations are highly reactive with undersaturated water. An understanding of the geochemical reactions that occur within halite-saturated formation waters can inform decision making regarding well construction, prevention of well clogging, formation dissolution, and thermal short-circuiting. Batch reaction and numerical 3-D flow and equilibrium reactive transport modeling were used to characterize the produced NaCl-brine in a well targeting a halite-saturated formation. The potential for inhibition of precipitation and dissolution using an MgCl2-brine and NaCl+MgCl2-brine were also investigated. Within the injection well for an NaCl-brine, with heating from 70 to 120°C, the solubility of halite decreases resulting in the potential dissolution of 0.479 mol kg-1 halite at the formation. Cooling from 120 to 100°C in the production well results in precipitation of 0.196 mol kg-1 halite as well as anhydrite. Introduction of MgCl2, resulting in a common Cl- ion, into the heat exchange brine resulted in a decreased potential for dissolution by 0.290 mol kg-1 halite within the formation, as well as decreased precipitation within the production well, compared to the NaCl-brine. The halite solubility was altered by changes in pressure up to 0.045 mol kg-1. This indicates that designing and monitoring the composition of heat exchange fluids in highly saline environments is an important component in geothermal project design.

Subnormality and residuals for saturated formations: A generalization of Schenkman’s theorem

Let 𝐺 be a finite group, and let 𝔉 be a hereditary saturated formation. We denote by Z F ⁢ ( G ) \mathbf{Z}_{\mathfrak{F}}(G) the product of all normal subgroups 𝑁 of 𝐺 such that every chief factor H / K H/K of 𝐺 below 𝑁 is 𝔉-central in 𝐺, that is, ( H / K ) ⋊ ( G / C G ⁢ ( H / K ) ) ∈ F (H/K)\rtimes(G/\mathbf{C}_{G}(H/K))\in\mathfrak{F} . A subgroup A ⩽ G A\leqslant G is said to be 𝔉-subnormal in the sense of Kegel, or 𝐾-𝔉-subnormal in 𝐺, if there is a subgroup chain A = A 0 ⩽ A 1 ⩽ ⋯ ⩽ A n = G A=A_{0}\leqslant A_{1}\leqslant\cdots\leqslant A_{n}=G such that either A i - 1 ⁢ ⊴ ⁢ A i A_{i-1}\trianglelefteq A_{i} or A i / ( A i - 1 ) A i ∈ F A_{i}/(A_{i-1})_{A_{i}}\in\mathfrak{F} for all i = 1 , … , n i=1,\ldots,n . In this paper, we prove the following generalization of Schenkman’s theorem on the centraliser of the nilpotent residual of a subnormal subgroup: Let 𝔉 be a hereditary saturated formation containing all nilpotent groups, and let 𝑆 be a 𝐾-𝔉-subnormal subgroup of 𝐺. If Z F ⁢ ( E ) = 1 \mathbf{Z}_{\mathfrak{F}}(E)=1 for every subgroup 𝐸 of 𝐺 such that S ⩽ E S\leqslant E , then C G ⁢ ( D ) ⩽ D \mathbf{C}_{G}(D)\leqslant D , where D = S F D=S^{\mathfrak{F}} is the 𝔉-residual of 𝑆.

Evaluation of NaCl and MgCl2 heat exchange fluids in a deep binary geothermal system in a sedimentary halite formation

Halite formations are attractive geothermal reservoirs due to their high heat conductivity, resulting in higher temperatures than other formations at similar depths. However, halite formations are highly reactive with undersaturated water. An understanding of the geochemical reactions that occur within halite-saturated formation waters can inform decision making regarding well construction, prevention of well clogging, formation dissolution, and thermal short-circuiting. Batch reaction and numerical 3-D flow and equilibrium reactive transport modeling were used to characterize the produced NaCl-brine in a well targeting a halite-saturated formation. The potential for inhibition of precipitation and dissolution using an MgCl 2 -brine and NaCl+MgCl 2 -brine were also investigated. Within the injection well, with heating from 70 to 120°C, the solubility of halite decreases resulting in the potential dissolution of 0.479 mol kg -1 at the formation. Cooling from 120 to 100°C in the production well results in precipitation of 0.196 mol kg -1 halite as well as anhydrite, brucite, carnallite, goergeyite, gypsum, halite, kieserite and polyhalite. Introduction of MgCl 2 , resulting in a common Cl - ion, into the heat exchange brine resulted in a decreased potential for dissolution by 0.290 mol kg -1 as the heat exchange fluid entered the formation and within the formation itself, as well as decreased precipitation within the production well, compared to the NaCl-brine. The halite solubility was altered by changes in pressure up to 0.045 mol kg -1 . This indicates that designing and monitoring the composition of heat exchange fluids in highly saline environments is an important component in geothermal project design.

Active seismic monitoring of CO2-saturated brine injection into a fault (CS-D experiment in the Mont Terri Rock Laboratory)

<p>Confirming the permanent containment is a key challenge for the storage of CO<sub>2 </sub>in deep underground reservoirs. Faults in the cap rock of such reservoirs are potential flow paths for the CO<sub>2</sub> to escape. Our decametre-scale experiment at the Mont Terri Rock Laboratory aims to better understand mechanisms of CO<sub>2</sub> leakage trough a fault, and to test strategies to monitor the propagation of CO<sub>2</sub>-saturated water through faults.</p><p>Two boreholes were drilled through the main fault in Mont Terri with packer-intervals dedicated to fluid-injection and hydraulic/geochemical monitoring. Another five boreholes in the close surrounding were equipped with various instruments for geotechnical and geophysical observations. During the first phase of the experiment, the hydraulic response of the fault was characterized with injections of formation water in a step-up mode at pressures up to 6.0 MPa. The second phase, which was still on-going at the time of the abstract submission, consists of a long-term (several months) injection of CO<sub>2</sub>-saturated formation water at a constant head of 4.5 MPa, which is below the fault opening pressure. All injection activities were monitored with active seismic measurements, along with a comprehensive set of hydraulic-, mechanical-, geochemical- and other geophysical surveys. We will present the active seismic imaging results from the step-up injection test and compare them with the other surveys. Additionally, preliminary results will be shown acquired during the long-term injection of CO<sub>2</sub>-saturated formation water into the fault.</p>