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In this article, we consider the non-linear Choquard equation − Δ u + V ( ∣ x ∣ ) u = ∫ R 3 ∣ u ( y ) ∣ 2 ∣ x − y ∣ d y u in R 3 , -\Delta u+V\left(| x| )u=\left(\mathop{\int }\limits_{{{\mathbb{R}}}^{3}}\frac{| u(y){| }^{2}}{| x-y| }{\rm{d}}y\right)u\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em}\hspace{0.33em}{{\mathbb{R}}}^{3}, where V ( r ) V\left(r) is a positive bounded function. Under some proper assumptions on V ( r ) V\left(r) , we are able to establish the existence of infinitely many non-radial solutions.

In refineries, some hydrogen-rich streams contain considerable light hydrocarbons that are important raw materials for the chemical industry. Integrating hydrogen networks with light hydrocarbon recovery can enhance the reuse of both hydrogen and light hydrocarbons. This work proposes an automated method for targeting hydrogen networks with light hydrocarbon recovery. A pinch-based algebraic method is improved to determine the minimum fresh hydrogen consumption and hydrogen sources fed into the light hydrocarbon recovery unit automatically. Rigorous process simulation is conducted to determine the mass and energy balances of the light hydrocarbon recovery process. The targeting procedures are developed through combination of the improved pinch method and rigorous process simulation. This hybrid method is realized by coupling the Matlab and Aspen HYSYS platforms. A refinery hydrogen network is analyzed to illustrate application of the proposed method. The integration of hydrogen networks with light hydrocarbon recovery further reduces fresh hydrogen requirement by 463.0 Nm3·h-1 and recovers liquefied petroleum gas and gasoline of 1711.5 kg·h-1 and 643 kg·h-1, respectively. A payback period of 9.2 months indicates that investment in light hydrocarbon recovery is economically attractive.

In this paper, we consider the following modified quasilinear problem:−Δu−κuΔu2=λa(x)u−α+b(x)uβinΩ,u>0inΩ,u=0on∂Ω,$$\begin{array}{} \left\{\begin{array}{c}\, -{\it\Delta} u-\kappa u{\it\Delta} u^2 = \lambda a(x)u^{-\alpha}+b(x)u^\beta \, \, in\, {\it\Omega}, \\\!\! u \gt 0 \, \, in\, {\it\Omega}, \, \, \, \, \, \, \, u = 0 \, \, on \, \partial{\it\Omega} , \\ \end{array}\right. \end{array} $$whereΩ⊂ ℝNis a smooth bounded domain,N≥ 3,a,bare two bounded continuous functions,α> 0, 1 <β≤ 22*− 1 andλ> 0 is a bifurcation parameter. We use the framework of analytic bifurcation theory to obtain an analytic global unbounded path of solutions to the problem. Moreover, we get the direction of solution curve at the asmptotic point.

With the increasing supply of sour crude oil and rising demand of low-sulfur fuel oil products, desulfurization becomes important in refineries, leading to notable energy cost for desulfurization solvent regeneration. This paper presents the integration of desulfurization solvent network and develops a systematic targeting and design method in order to improve the overall solvent utilization. First, the desulfurization solvent sink/source and desulfurization solvent network are defined referring to the characteristics of desulfurization units. Next, a novel problem table method is developed to identify the minimum fresh solvent consumption and design the desulfurization solvent network simultaneously. A case study is conducted to provide quantitative insights in designing desulfurization solvent network and saving fresh desulfurization solvent. Such integration reduces the fresh solvent consumption by 25% and has a good practicability.

We establish global multiplicity results of solutions for the singular nonlinear problem 0\quad \text{in}\enspace {\Omega},\enspace u=0\enspace \text{on}\enspace \partial {\Omega},\quad \end{cases}\end{equation*}?> − Δ u − u Δ u 2 = λ a ( x ) u − α + b ( x ) u β in Ω , u > 0 in Ω , u = 0 on ∂ Ω , where Ω ⊂ R N is a smooth bounded domain; N ⩾ 3; a, b are bounded continuous functions, 0 < α < 1 < β ⩽ 22* − 1 and λ > 0 is a real parameter. We first prove a comparison principle to prove the existence of a minimal solution by the method of sub and super solutions and then we also obtain the second solution by critical point theory.

We study the following class of pseudo-relativistic Hartree equations − e 2 Δ + m 2 u + V ( x ) u = e μ − N ( | x | − μ ⁎ F ( u ) ) f ( u ) in R N , where the nonlinearity satisfies general hypotheses of Berestycki-Lions type. By using the method of penalization arguments, we prove the existence of a family of localized positive solutions that concentrate at the local minimum points of the indefinite potential V ( x ) , as e → 0 .

Producing aromatics from coal via methanol is a novel technology, which could mitigate the energy shortage in a petroleum-poor area. However, the selectivity of methanol to aromatics is merely 40–70 wt % due to the byproducts of light hydrocarbons. In this paper, three novel designs are proposed to improve the aromatics yield by directly or indirectly converting light hydrocarbons into aromatics. In addition, cofeeding of coal and natural gas is applied in two of the three designs. On the basis of detailed process modeling and simulation, the process designs are assessed by mass balance, technoeconomic, and life cycle analyses. The results show that the aromatics yield is significantly improved by integrating light hydrocarbon conversion units. The CO₂ emissions and water consumption are notably decreased in the two cofeeding designs. In addition, the net present value of the design integrated with steam reforming of C₂– hydrocarbons and aromatization of C₃₊ hydrocarbons is the highest, about 1.9 times as much as that of the nonintegrated design. The cofeeding design integrated with steam reforming of C₂– hydrocarbons and aromatization of C₃₊ hydrocarbons leads to the lowest global warming potential and abiotic depletion potential, only 46.1 and 71.1% of the nonintegrated design, respectively. It implies that a more complex design shows better environmental performances.

In this paper, we are interested in a coupled Schrodinger system with Stein–Weiss type convolution part. Firstly we study the existence and nonexistence of the solutions by variational methods. Second, by changing the system into an equivalent integral form, we study the symmetry, regularity and asymptotic behaviors of the solutions by moving plane arguments.

Hydrogen is the core source to both refinery and synthetic plant of chemicals. Refinery consumes high purity hydrogen while synthetic plant of chemicals needs syngas consists of hydrogen and carbon oxides. As main hydrogen production technologies, industrial coal gasification and steam methane reforming based pathways generate H2, CO and CO2, which is actually the mixture of hydrogen and carbon oxides. Hence, the gases demand of refinery and synthetic plant of chemicals and their supply from hydrogen production can form hybrid hydrogen networks. On the basis of complementary reuse, this paper firstly proposes integration of hybrid hydrogen network for refinery and synthetic plant of chemicals. Superstructures of individual and hybrid hydrogen networks are employed as problem illustration and corresponding linear programming (LP) mathematical models are formulated. Practical refinery and synthetic plant of chemicals cases are employed to demonstrate its application. Compared with individual networks, the natural gas conservation case can recover 8660.4 Nm3·h-1 hydrogen in purge gas, reduce 1386.6 Nm3·h-1 CO2 emission, equaling to reduction of 278.11 kmol·h-1 natural gas feedstock and 14.8% of total gas production load; the coal conservation case can even waive the total coal consumption and extra 104.1 kmol·h-1 natural gas, recover 8660.4 Nm3·h-1 hydrogen in purge gas, reduce 5255.8 Nm3·h-1 of CO2 emission and decrease 21.2% of the total gas production load. Furthermore, economic evaluation is also placed to account for the economic advantage of hybrid network.

An industrial solvent recovery system in a rubber process consists of four distillation columns to recover solvent and unreacted 1,3-butadiene monomer. After the solvent is changed from raffinate oil to hexanes, it needs to investigate whether the current system can be retrofitted to reduce the number of columns and save energy. This work presents stepwise retrofit of the solvent recovery system by distillation sequence intensification and simulation-based optimization. Based on insights in distillation columns, an evolutionary strategy is introduced to generate intensified distillation sequences from the current distillation system. Next, a simulation-based optimization method considering comprehensive hydraulic evaluation is developed to obtain the best operating parameters of distillation columns. Seven distillation sequence alternatives to the current solvent recovery system are generated. The result indicates that the most compact sequence with two distillation columns can decrease the energy cost by 41.50%, while the preferred solution is a three-column sequence with the least modifications that reduces the energy cost by 33.13%. The proposed method also gives insights in energy saving and identifies bottlenecks to further improve the energy performance.

In this paper we are interested in the existence of semiclassical states for the Choquard type equation − ε 2 Δ u + V ( x ) u = ∫ R N G ( u ( y ) ) | x − y | μ d y g ( u ) in R N , where 0 < μ < N, N ⩾ 3, ɛ is a positive parameter and G is the primitive of g which is of critical growth due to the Hardy–Littlewood–Sobolev inequality. The potential function V(x) is assumed to be nonnegative with V(x) = 0 in some region of R N , which means it is of the critical frequency case. Firstly, we study a Choquard equation with double critical exponents and prove the existence and multiplicity of semiclassical states by the mountain-pass lemma and the genus theory. Secondly, we consider a class of critical Choquard equation without lower perturbation, by establishing a global compactness lemma for the nonlocal Choquard equation, we prove the multiplicity of high energy semiclassical states by the Lusternik–Schnirelman theory.

Methanol aromatization occurs with considerable byproducts of light hydrocarbons, resulting in a low yield of benzene, toluene, and xylene (BTX). This work proposes two novel process designs by int...

This article presents a conceptual design of hybrid separation processes of refinery off-gas on the refinery scale, aiming at the recovery of high-value-added components toward near-zero hydrogen e...

In this paper we are interested in the following critical coupled Hartree system \begin{document}$ \left\{\begin{array}{l} (-\Delta)^{s} \tilde{u}+\lambda_{1}\tilde{u} = \alpha_{1}\int_{\Omega}\frac{|\tilde{u}(z)|^{2_{\mu}^{\ast}} }{|x-z|^{\mu}}dz|\tilde{u}|^{2_{\mu}^{\ast}-2}\tilde{u}\\ \quad +\beta\int_{\Omega}\frac{|\tilde{v}(z)|^{2_{\mu}^{\ast}}} {|x-z|^{\mu}}dz|\tilde{u}|^{2_{\mu}^{\ast}-2}\tilde{u}, \ \ &&\mbox{in} \ \Omega,\\ (-\Delta)^{s} \tilde{v}+\lambda_{2}\tilde{v} = \alpha_{2}\int_{\Omega}\frac{|\tilde{v}(z)|^{2_{\mu}^{\ast}} }{|x-z|^{\mu}}dz|\tilde{v}|^{2_{\mu}^{\ast}-2}\tilde{v}\\ \quad +\beta\int_{\Omega}\frac{|\tilde{u}(z)|^{2_{\mu}^{\ast}}} {|x-z|^{\mu}}dz|\tilde{v}|^{2_{\mu}^{\ast}-2}\tilde{v}, \ \ &&\mbox{in} \ \Omega,\\ \tilde{u} = \tilde{v} = 0, \ \ && \mbox{on} \ \partial \Omega, \end{array} \right. $\end{document} where \begin{document}$ 0 , \begin{document}$ \alpha_{1}, \alpha_{2}>0 $\end{document} , \begin{document}$ \beta\neq0 $\end{document} , \begin{document}$ 4s , \begin{document}$ 2_{\mu}^{\ast} = (2N-\mu)/(N-2s) $\end{document} , \begin{document}$ \Omega\subset\mathbb{R}^N(N\geq3) $\end{document} is a smooth bounded domain, \begin{document}$ -\lambda_{1}(\Omega) with \begin{document}$ \lambda_{1}(\Omega) $\end{document} the first eigenvalue of \begin{document}$ (-\Delta)^{s} $\end{document} under the Dirichlet boundary condition. Assume that the nonlinearity and the coupling terms are both of the upper critical growth due to the Hardy–Littlewood–Sobolev inequality, by applying the Dirichlet-to-Neumann map, we are able to obtain the existence of the ground state solution of the critical coupled Hartree system.

We study a class of gauged nonlinear Schrödinger equations in the plane \begin{document}$ \left\{ \begin{array}{l} -\Delta u+V(|x|) u+\lambda\bigg(\int_{|x|}^\infty \frac{h_u(s)}{s}u^2(s)ds+\frac{h_u^2(|x|)}{|x|^2} \bigg)u\\\qquad \, = K(|x|)f(u)+\mu g(|x|)|u|^{q-2}u, \\ u(x) = u(|x|) \; {\rm{in}}\; \mathbb{R}^2, \\\\ \end{array} \right. $\end{document} where \begin{document}$ h_u(s) = \int_0^s\frac{r}{2}u^2(r)dr $\end{document}, \begin{document}$ \lambda,\mu>0 $\end{document} are constants, \begin{document}$ V(|x|) $\end{document} and \begin{document}$ K(|x|) $\end{document} are continuous functions vanishing at infinity. Assume that \begin{document}$ f $\end{document} is of critical exponential growth and \begin{document}$ g(x) = g(|x|) $\end{document} satisfies some technical assumptions with \begin{document}$ 1\leq q, we obtain the existence of two nontrivial solutions via the Mountain-Pass theorem and Ekeland's variational principle. Moreover, with the help of the genus theory, we prove the existence of infinitely many solutions if \begin{document}$ f $\end{document} in addition is odd.

Feed of hot material from the upstream process is a strategy to improve energy efficiency, but the energy saving contributed by hot feed depends on the characteristics of the feed stream and receiv...

In this paper, we study the existence and concentration of ground state solution for the Choquard equation $$\begin{aligned} \left\{ \begin{array}{ll} \begin{aligned} &{}-\Delta u+V(x)u=\left( \int _{{\mathbb {R}}^N}\frac{A(\epsilon y)|u(y)|^p}{|x-y|^\mu }\mathrm{d}y\right) A(\epsilon x)|u|^{p-2}u~~\text {in}~{\mathbb {R}}^{N},\\ &{}u\in H^1({\mathbb {R}}^N), \end{aligned} \end{array} \right. \end{aligned}$$where $$N\ge 2$$, $$0

Distillation is important to chemical processes but it is energy intensive, and its optimization is of great significance to energy savings and emissions reduction. Varying the operating pressures of distillation columns could assist heat integration of distillation columns into the overall process, thereby reducing energy consumption. However, influences of varying column pressures on the energy profiles of the overall process have not been systematically analyzed in previous studies. This paper presents an insightful analysis of heat integration of distillation into the overall process considering the change of operating pressure. Firstly, effects of changing the operating pressure of a distillation column on its own utility requirements and the related process streams are studied. Next, such effects are graphically represented and incorporated into the grand composite curve (GCC). The change tendencies of the GCC, pinch temperature, and total utility consumption are analyzed and presented. On this basis, rules to identify the best operating pressure that minimize the overall energy consumption are proposed. A continuous reforming unit in a petrochemical enterprise is quantitatively analyzed to verify the obtained rules. The result indicates that the hot utility of the overall process can be reduced by 758 kW when the column pressure is lowered by 260 kPa.

Hydrogen consumption in oil refineries increases sharply because of more and more heavy and sour crude oil processing, which also makes hydrogen sulfide a considerable contaminant in off-gases of hydrotreaters. This work presents a simulation-based optimization model for synthesis of hydrogen networks with H2S removal. Aspen HYSYS is employed for rigorous process and thermodynamic modeling of the H2S removal unit. The proposed model is solved using the genetic algorithm combined with the linprog and fmincon solvers in the Matlab platform. The optimal hydrogen sources and the recirculated absorbent fed into the H2S removal unit as well as the optimal design of the hydrogen network can be determined simultaneously. A case study is performed to illustrate the application and effectiveness of the proposed model. The result shows that the introduction of H2S removal can decrease the fresh hydrogen consumption by 43% and the total annualized cost by 17%.

This work presents a comparative energy and techno-economic analysis for producing aromatics from methanol and pentane. A novel process design is presented and detailed process simulation models are developed based on five different methanol to pentane mole ratios. On this basis, we obtain the mass and energy balances and conduct energy and techno-economic analyses for the five cases. The results show that co-feeding of methanol and pentane enhance the performance for aromatics production. The case with methanol to pentane ratio of 1:1 results in the highest net present value, which is 1.17–3.66 times of the other four cases. Sensitivity analyses are also performed to investigate the influences of price deviations on the economic performances. The results indicate that co-feeding of methanol-pentane with a mole ratio of 1:1 is more economically attractive when the methanol price ranges from −18% to 8% or the pentane price ranges from −10% to 18%.

In this paper we are interested in the following nonlocal nonhomogeneous elliptic equation in R 2 , − Δ u + V ( x ) u = ( 1 | x | μ ⁎ F ( u ) | x | β ) f ( u ) | x | β + e h ( x ) in R 2 , where V is a positive continuous potential, 0 μ 2 , β ≥ 0 , 2 β + μ ≤ 2 , e is a small parameter and F ( s ) is the primitive function of f ( s ) . Suppose that the nonlinearity f ( s ) is of critical exponential growth in the sense of Trudinger-Moser inequality, we prove the existence and multiplicity of solutions by variational methods.

In this paper, we consider the nonlinear Choquard equation $$-\Delta u + V(x)u = \left( {\int_{{\open R}^N} {\displaystyle{{G(u)} \over { \vert x-y \vert ^\mu }}} \,{\rm d}y} \right)g(u)\quad {\rm in}\;{\open R}^N, $$ where 0 < μ < N, N ⩾ 3, g(u) is of critical growth due to the Hardy–Littlewood–Sobolev inequality and $G(u)=\int ^u_0g(s)\,{\rm d}s$. Firstly, by assuming that the potential V(x) might be sign-changing, we study the existence of Mountain-Pass solution via a nonlocal version of the second concentration- compactness principle. Secondly, under the conditions introduced by Benci and Cerami , we also study the existence of high energy solution by using a nonlocal version of global compactness lemma.