Improved sampling for ensemble-based reservoir optimization with and without uncertainty

Abstract

Increasing demand for energy, scarcity of conventional energy resources and lack of infrastructure for alternative
sources of energy demands economical and efficient recovery of hydrocarbons like petroleum and
natural gas from the reservoirs deep inside the earth. This effective hydrocarbon recovery strategy depends
on finding efficient and optimal controls like bottom hole pressure or production and injection rates in wells
during the production phase of oil. Dynamic model-based optimization is an efficient concept of systems
and control to determine these optimal controls (design variables) which maximizes an economic objective
function like Net Present Value or sometimes a volumetric function like cumulative oil production. The
optimization can be gradient based or gradient-free technique. Gradient based reservoir optimization is
performed either by solving a system of adjoint equations or through ensemble based optimization. Recently
ensemble based optimization techniques have gained popularity due to its advantages over adjoint
method like minimal code development, treatment of simulator as black-box. One such method is called
Ensemble Optimization (EnOpt) which has been shown as an effective stochastic gradient based optimization
method. Model based life-cycle production optimization can be performed either deterministically
i.e. where the geological model is considered certain (single model) or for robust cases i.e. where the
geological model is considered uncertain (many equi-probable geological models are used). Reservoir
simulations are computationally expensive and time consuming. EnOpt being an ensemble based optimization
method, the ensemble size, i.e. number of perturbed controls used to evaluate the gradient, becomes
an important constraint for the applicability of the method. Smaller ensemble sizes leads to fewer function
evaluations and thus decreases the computational efficiency and time, however this results in inferior
quality gradients which have been shown to affect the optimization performance. In addition to ensemble
size, the sampling strategy (distribution or type) used to generate the ensemble of controls is extremely
important and has received little attention in the literature. This thesis deals with investigating alternative
effective sampling strategies for creating the ensemble for EnOpt to improve gradient quality and thereby
optimization performance. This thesis aims to evaluate a number of different sampling strategies under the
constraint that ensemble size is smaller than number of control variables being optimized. Three different
sampling strategies (Sobol sampling, Latin Hypercube Sampling and UE(s2) - optimal design) and 3
variants for UE(s2) - optimal design are considered as an alternative to the often used multivariate Gaussian
sampling for EnOpt. The effectiveness of the sampling method is analyzed based on the approximate
gradient quality, objective function value, rate of convergence and robustness of the gradient for cases with
and without model uncertainty. Experiments are performed with all sampling strategies and compared to
results obtained with multivariate Gaussian sampling applied to the Rosenbrock function with high dimension
as well as a reservoir model for both deterministic and robust cases. The results in this thesis show that
UE(s2) - optimal design sampling strategies achieve better objective function values with an improved rate
of convergence when compared to any of the other sampling techniques for both deterministic and robust
cases.

Date of Award	2017
Original language	English
Supervisor	Paul M.J. Van den Hof (Supervisor 1), S. Grammatico (Supervisor 2), M.M. Siraj (Supervisor 2), Olwijn Leeuwenburgh (External coach) & Rahul M. Fonseca (External coach)