Boundedness character of a max-type system of difference equations of second order

The boundedness character of positive solutions of the next max-type system of difference equations $$x_{n+1}=\max\left\{A,\frac{y_n^p}{x_{n-1}^q}\right\},\quad y_{n+1}=\max\left\{A,\frac{x_n^p}{y_{n-1}^q}\right\},\quad n\in\mathbb{N}_0,$$ with $\min\{A, p, q\}>0$, is characterized

On a higher-order system of difference equations

Here we study the following system of difference equations xn = f −1 cnf(xn−2k) ∏k an + bn i=1 g(y) n−(2i−1))f(xn−2i) yn = g −1 γng(yn−2k) ∏k αn + βn i=1 f(x) n−(2i−1))g(yn−2i) n ∈ N0, where f and g are increasing real functions such that f(0) = g(0) = 0, and coefficients an, bn, cn, αn, βn, γn, n ∈ N0, and initial values x−i, y−i, i ∈ {1, 2,..., 2k} are real numbers. We show that the system is solvable in closed form, and study asymptotic behavior of its solutions

Time-Dependent Physicochemical Changes of Carbonate Surfaces from SmartWater (Diluted Seawater) Flooding Processes for Improved Oil Recovery.

Over the past few decades, field- and laboratory-scale studies have shown enhancements in oil recovery when reservoirs, which contain high-salinity formation water (FW), are waterflooded with modified-salinity salt water (widely referred to as the low-salinity, dilution, or SmartWater effect for improved oil recovery). In this study, we investigated the time dependence of the physicochemical processes that occur during diluted seawater (i.e., SmartWater) waterflooding processes of specific relevance to carbonate oil reservoirs. We measured the changes to oil/water/rock wettability, surface roughness, and surface chemical composition during SmartWater flooding using 10-fold-diluted seawater under mimicked oil reservoir conditions with calcite and carbonate reservoir rocks. Distinct effects due to SmartWater flooding were observed and found to occur on two different timescales: (1) a rapid (<15 min) increase in the colloidal electrostatic double-layer repulsion between the rock and oil across the SmartWater, leading to a decreased oil/water/rock adhesion energy and thus increased water wetness and (2) slower (>12 h to complete) physicochemical changes of the calcite and carbonate reservoir rock surfaces, including surface roughening via the dissolution of rock and the reprecipitation of dissolved carbonate species after exchanging key ions (Ca2+, Mg2+, CO32-, and SO42- in carbonates) with those in the flooding SmartWater. Our experiments using crude oil from a carbonate reservoir reveal that these reservoir rock surfaces are covered with organic-ionic preadsorbed films (ad-layers), which the SmartWater removes (detaches) as flakes. Removal of the organic-ionic ad-layers by SmartWater flooding enhances oil release from the surfaces, which was found to be critical to increasing the water wetness and significantly improving oil removal from carbonates. Additionally, the increase in water wetness is further enhanced by roughening of the rock surfaces, which decreases the effective contact (interaction) area between the oil and rock interfaces. Furthermore, we found that the rate of these slower physicochemical changes to the carbonate rock surfaces increases with increasing temperature (at least up to an experimental temperature of 75 °C). Our results suggest that the effectiveness of improved oil recovery from SmartWater flooding depends strongly on the formation of the organic-ionic ad-layers. In oil reservoirs where the ad-layer is fully developed and robust, injecting SmartWater would lead to significant removal of the ad-layer and improved oil recovery

Crystal structure of 1,1-dimethyl-3-(2-phenylethyl)urea, C11H16N2O

Abstract C11H16N2O, orthorhombic, Pbca (no. 61), a = 10.7388(6) Å, b = 9.8449(5) Å, c = 21.1259(14) Å, V = 2233.5(2) Å3, Z = 8, R gt (F) = 0.0582, wR ref (F 2) = 0.1795, T = 293 K.</jats:p