Incipient Yielding and Solids Production for Perforated Casing Completions

1986 ◽  
Vol 108 (4) ◽  
pp. 321-325 ◽  
Author(s):  
E. P. Fahrenthold ◽  
J. B. Cheatham
Keyword(s):  
Lower Bounds ◽  
Cylindrical Cavity ◽  
Spherical Cavity ◽  
Yield Condition ◽  
Rock Properties ◽  
Upper And Lower Bounds ◽  
Weak Rock ◽  
Rock Formations ◽  
In Situ Conditions

Production rate limits for perforated casing completions in weak rock formations are estimated for a material obeying a quadratic yield condition. Plastic stresses around a spherical cavity are calculated to determine the well pressure value which precipitates solids production. Elastic solutions for a cylindrical cavity are utilized to place upper and lower bounds on the well pressure value which initiates yielding around a perforated casing. The separate analyses define consistent critical well pressure values for initial yield and solids production as a function of rock properties and in-situ conditions.

Load-Carrying Capacities of Simply Supported Rectangular Plates

1963 ◽  
Vol 30 (4) ◽  
pp. 617-621 ◽  
Author(s):  
H. E. Shull ◽  
L. W. Hu
Keyword(s):  
Lower Bounds ◽  
Yield Condition ◽  
Radial Symmetry ◽  
Upper And Lower Bounds ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Load Carrying ◽  
Uniformly Distributed Loads

The upper and lower bounds on the load-carrying capacities of simply supported rectangular plates with uniformly distributed loads are obtained. The usefulness of Tresca’s yield condition in a problem lacking radial symmetry is demonstrated.

Prediction research of deformation modulus of weak rock zone under in-situ conditions

2011 ◽  
Vol 8 (2) ◽  
pp. 345-353 ◽  
Author(s):  
Yong Zhang ◽  
JiangDa He ◽  
Yufeng Wei ◽  
Dexin Nie
Keyword(s):  
Deformation Modulus ◽  
Weak Rock ◽  
In Situ Conditions

Experimental investigations on the temperature and strain-rate dependence of failure and friction criteria for a porous sandstone

2020 ◽  
Author(s):  
Benedikt Ahrens ◽  
Mandy Duda ◽  
Erik H. Saenger
Keyword(s):  
Elastic Properties ◽  
Rate Dependence ◽  
Rock Properties ◽  
Experimental Investigations ◽  
Ultrasound Wave ◽  
Triaxial Deformation ◽  
Temperature Conditions ◽  
In Situ Conditions ◽  
Porous Sandstone

<p>Understanding the deformation-related thermomechanical state of reservoir rocks under in-situ conditions is essential for modelling the stress distribution and stability of subsurface structures, for example associated with aftershock activity and induced seismicity. Commonly, reservoir modelling approaches make use of the generalized friction criterion according to Byerlee, which distinguishes between depths below and above approximately 6 km. However, numerous studies have shown that thermomechanical rock properties under elevated pressure and temperature conditions differ significantly from those at the surface and among rock types. The significant influence of the geothermal gradient on elastic and inelastic rock properties has already been demonstrated for temperature variations as low as 150 °C. Studies on the effect of in-situ stress and temperature conditions on post-failure behaviour and frictional properties are completely lacking.</p><p>In our experimental study we determined the thermomechanical properties of porous Ruhr sandstone samples during conventional triaxial deformation tests to derive stress- and temperature-dependent failure and friction criteria. Effective confining pressures and temperatures applied in the tests cover the range of in-situ conditions equivalent to depths up to three kilometres. Simultaneously, ultrasonic P- and S-wave measurements were performed to determine properties of ultrasound wave propagation (i.e. dynamic elastic properties) as a function of in-situ conditions. Triaxial deformation experiments were conducted at various strain rates to investigate the deformation-rate dependence of the failure and friction criteria and the correlation between dynamic and static elastic properties.</p>

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

scholarly journals Rock Surface Fungi in Deep Continental Biosphere—Exploration of Microbial Community Formation with Subsurface In Situ Biofilm Trap

2020 ◽  
Vol 9 (1) ◽  
pp. 64
Author(s):  
Maija Nuppunen-Puputti ◽  
Riikka Kietäväinen ◽  
Lotta Purkamo ◽  
Pauliina Rajala ◽  
Merja Itävaara ◽  
...  
Keyword(s):  
Significant Proportion ◽  
Debaryomyces Hansenii ◽  
Fungal Communities ◽  
Fungal Colonization ◽  
Rock Surface ◽  
Mica Schist ◽  
Deep Subsurface ◽  
Bacterial Phyla ◽  
In Situ Conditions

Fungi have an important role in nutrient cycling in most ecosystems on Earth, yet their ecology and functionality in deep continental subsurface remain unknown. Here, we report the first observations of active fungal colonization of mica schist in the deep continental biosphere and the ability of deep subsurface fungi to attach to rock surfaces under in situ conditions in groundwater at 500 and 967 m depth in Precambrian bedrock. We present an in situ subsurface biofilm trap, designed to reveal sessile microbial communities on rock surface in deep continental groundwater, using Outokumpu Deep Drill Hole, in eastern Finland, as a test site. The observed fungal phyla in Outokumpu subsurface were Basidiomycota, Ascomycota, and Mortierellomycota. In addition, significant proportion of the community represented unclassified Fungi. Sessile fungal communities on mica schist surfaces differed from the planktic fungal communities. The main bacterial phyla were Firmicutes, Proteobacteria, and Actinobacteriota. Biofilm formation on rock surfaces is a slow process and our results indicate that fungal and bacterial communities dominate the early surface attachment process, when pristine mineral surfaces are exposed to deep subsurface ecosystems. Various fungi showed statistically significant cross-kingdom correlation with both thiosulfate and sulfate reducing bacteria, e.g., SRB2 with fungi Debaryomyces hansenii.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema

Algorithms ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 164
Author(s):  
Tobias Rupp ◽  
Stefan Funke
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Real World ◽  
Road Network ◽  
Upper And Lower Bounds ◽  
Bounded Degree ◽  
Shortest Path Routing ◽  
Graph Classes ◽  
Speed Up ◽  
To Come

We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds.

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