Il'dar Abdullovich Ibragimov

On the convergence of generalized moments in almost sure central limit theorem

Let {[zeta]k} be the normalized sums corresponding to a sequence of i.i.d. variables with zero mean and unit variance. Define random measures and let G be the normal distribution. We show that for each continuous function h satisfying [integral operator] hdG

Production Optimization of Thin-Oil Rims: Evaluation of a Stochastic Steepest-Ascent Approach

Abstract This paper is concerned with waterflood optimization of oil recovery from thin oil rims of gas-condensate fields. Such fields are notorious for gas and water coning problems, i.e. early gas or water breakthrough in producing wells, causing low recovery efficiency. The optimization method employed in this paper is of a steepest ascent type and may be seen as belonging to the class of stochastic optimization methods, as it involves estimation of the gradient search direction using ensembles of perturbed control strategies. The method is easy to implement and, moreover, it offers a great flexibility, as it is adjoint-free and is not restricted to the use of a specific reservoir simulator. The core of the method, named EnOpt, was recently proposed as an optimizer for the closed-loop reservoir production optimization, that is, the joint data assimilation and hydrocarbon production exercise. In this paper, the usefulness and performance of the optimization scheme are tested on a synthetic model of a homogeneous oil rim reservoir equipped with a horizontal producer and a horizontal injector placed on the opposite sides of the field. The reservoir geology is assumed known. The objective to optimize is a net present value (NPV) as a function, over a fixed production time-horizon, of the injected and produced fluid flow-rates weighted by corresponding economical factors and discount rates. Two different types of the control variables and corresponding constraints on their allowable values are considered. In both cases, the injection bottom-hole pressure is kept constant, and the freedom in controlling the fluid flow consisted in controlling the producers bottom-hole pressure and the total liquid rate, respectively, at pre-specified time-instances. Simulation results confirm the potential of the optimization scheme.