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Multi-stage stochastic programs (MSP) pose some of the more challenging optimization problems. Because such models can become rather intractable in general, it is important to design algorithms that can provide approximations which, in the long run, yield solutions that are arbitrarily close to an optimum. In this paper, we propose a statistically motivated sequential sampling method that is applicable to multi-stage stochastic linear programs, and we refer to it as the multistage stochastic decomposition (MSD) algorithm. As with earlier SD methods for twostage stochastic linear programs, this approach preserves one of the most attractive features of SD: asymptotic convergence of the solutions can be proven (with probability one) without any iteration requiring more than a small sample-size. This data-driven approach also allows us to sequentially update value function approximations, and the computations themselves can be organized in a manner that decomposes the scenario generation (stochastic) process from the optimization computations. As a by-product of this study, we also show that SD algorithms are essentially approximate dynamic programming algorithms for SP. Our asymptotic analysis also reveals conceptual connections between multiple SP algorithms.

In the recent years, Mn4+‐doped phosphors for indoor plant cultivation have received extensive concern owing to the far‐red emission that can match well with the absorption spectra of plant pigments. Whereas, many Mn4+‐doped phosphors still face some challenges such as poor light efficiency and low thermal stability. It is an effective way to resolve these problems via cation vacancies engineering. Herein, the Ca14−xAl10Zn6−yO35: Mn4+ phosphors are successfully synthesized by combustion method. The luminescence intensity of Ca14−xAl10Zn6−yO35: Mn4+ phosphor is enhanced through engineering Ca2+ and Zn2+ vacancies according to the charge compensation mechanism. The optimal content of each Ca2+ and Zn2+ vacancy is equal to be 0.3. Furthermore, the defect formation is accompanied with lattice distortion, which plays a vital role in driving the excited phonon traps to reduce the energy loss by non‐radiation transitions. Therefore, the thermal stability of Ca14−xAl10Zn6−yO35: Mn4+ phosphor is also improved via engineering cation vacancies. In addition, the Ca14−xAl10Zn6−yO35: Mn4+ phosphors can be effectively excited by blue light and it exhibits far‐red emission due to the Mn4+ spin‐forbidden 2E → 4A2 transition. The results suggest that the Ca14−xAl10Zn6−yO35: Mn4+ phosphors can have a tremendous potential in indoor plant cultivation.

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Clay swelling affects not only reservoir quality but also many aspects of drilling operations in conventional oil production and in enhanced oil recovery. The focus of this paper is to characterize the swelling behaviour of smectites in direct contact with reservoir solutions. Two types of clay swelling are identified: crystalline swelling and osmotic swelling. Osmotic swelling is the major cause for permeability reduction due to smectites in hydrocarbon reservoirs. An X-ray diffraction cell was developed and used to quantify the swelling sensitivity of the smectites. In this method, a claywater mixture is X-rayed so that the effeCt of solution composition on clay swelling can be determined directly. Smectite swelling is very sensitive to the composition of fluids with which it contacts. The magnitude of swelling was found to be inversely proportional to ionic strength and depends on the dominant cation in system. New data collected for mixed electrolyte solutions shows that smectite swelling is not linear but a complex function of both ionic strength and cation ratios. The experimental data obtained allow us to construct a set of swelling diagrams for montmorillonite and other swelling clays. These swelling diagrams can be used to evaluate the effect of swelling clays on reservoir quality. Introduction Clay swelling has been long recognized as one of the major causes for formation damage in hydrocarbon reservoirs. In conventional hydrocarbon production, most of the clay related problems occur in the near well region, and are associated with well operations (drilling, completion, workover, etc.). Krueger(l) has provided an excellent review on this subject. In enhanced oil recovery (EOR), the potential for formation damage to occur is in many instances much greater because incompatible injection fluids often cause clay swelling or fines migration and thus impair the formation permeability. Even formations which do not contain smectite can have smectite-related formation damage because smectite clays can be synthesized through mineral/fluid reactions during thermal recovery(2,3). The formation of smectite was responsible for the reduction in porosity, permeability, and oil recovery rate at the Great Plain Pilot Project, Cold Lake(4). It was also partly responsible for the low steam sweep at the Ipiatik Heavy Oil Pilot, Cold Lake(5). Coreflood experiments have been used to characterize the effect of clay swelling on reservoir quality(6,7,8,9). In the coreflood experiments, a decrease in permeability (or an increase in injection pressure) is used as a measure of formation damage. However, a fair amount of core, which is not always available, is required to run coreflood experiments. In addition, coreflood experiments can be expensive. In this paper, we will introduce a relatively simple X-ray diffraction (XRD) method to quantify the clay swelling. This method requires a small amount of sample and offers an alternate tool to coreflood experiments in characterizing the effect of clay swelling on reservoir quality. Theoretical Basis of the XRD Method Swelling clays include two groups of layer silicate: smectites and vermiculites.