scholarly journals Dynamic Optimization of a Polymer Flooding Process Based on Implicit Discrete Maximum Principle

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yang Lei ◽  
Shurong Li ◽  
Xiaodong Zhang ◽  
Qiang Zhang ◽  
Lanlei Guo
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Oil Recovery ◽  
Polymer Concentration ◽  
Inequality Constraints ◽  
Control Model ◽  
Polymer Flooding ◽  
Discrete Maximum Principle ◽  
Flow Equations ◽  
Injection Strategies

Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and some inequality constraints as polymer concentration and injection amount limitation. The optimal control model is discretized by full implicit finite-difference method. To cope with the discrete optimal control problem (OCP), the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s discrete maximum principle. A modified gradient method with new adjoint construction is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.

scholarly journals Optimal Control of Polymer Flooding Based on Maximum Principle

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Yang Lei ◽  
Shurong Li ◽  
Xiaodong Zhang ◽  
Qiang Zhang ◽  
Lanlei Guo
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Oil Recovery ◽  
Polymer Concentration ◽  
Inequality Constraint ◽  
Polymer Flooding ◽  
Polymer Injection ◽  
Flow Equations ◽  
Optimal Injection ◽  
Injection Strategies

Polymer flooding is one of the most important technologies for enhanced oil recovery (EOR). In this paper, an optimal control model of distributed parameter systems (DPSs) for polymer injection strategies is established, which involves the performance index as maximum of the profit, the governing equations as the fluid flow equations of polymer flooding, and the inequality constraint as the polymer concentration limitation. To cope with the optimal control problem (OCP) of this DPS, the necessary conditions for optimality are obtained through application of the calculus of variations and Pontryagin’s weak maximum principle. A gradient method is proposed for the computation of optimal injection strategies. The numerical results of an example illustrate the effectiveness of the proposed method.

A weak maximum principle for optimal control problems with mixed constraints under a constant rank condition

2020 ◽  
Vol 37 (3) ◽  
pp. 1021-1047
Author(s):  
Roberto Andreani ◽  
Valeriano Antunes de Oliveira ◽  
Jamielli Tomaz Pereira ◽  
Geraldo Nunes Silva
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Necessary Optimality Conditions ◽  
Inequality Constraints ◽  
Equality Constraints ◽  
Control Problems ◽  
Constant Rank ◽  
Rank Condition ◽  
Weak Maximum Principle

Abstract Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

scholarly journals A New Empirical Model for Viscosity of Sulfonated Polyacrylamide Polymers

Polymers ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1046 ◽  
Author(s):  
Saeed Akbari ◽  
Syed Mohammad Mahmood ◽  
Hosein Ghaedi ◽  
Sameer Al-Hajri
Keyword(s):  
Polymer Solution ◽  
Oil Recovery ◽  
Empirical Model ◽  
Linear Regression Analysis ◽  
Polymer Concentration ◽  
Polymer Flooding ◽  
Solution Viscosity ◽  
Operational Variables ◽  
Reservoir Conditions ◽  
Sulfonated Polyacrylamide

Copolymers of acrylamide with the sodium salt of 2-acrylamido-2-methylpropane sulfonic acid—known as sulfonated polyacrylamide polymers—had been shown to produce very promising results in the enhancement of oil recovery, particularly in polymer flooding. The aim of this work is to develop an empirical model through the use of a design of experiments (DOE) approach for bulk viscosity of these copolymers as a function of polymer characteristics (i.e., sulfonation degree and molecular weight), oil reservoir conditions (i.e., temperature, formation brine salinity and hardness) and field operational variables (i.e., polymer concentration, shear rate and aging time). The data required for the non-linear regression analysis were generated from 120 planned experimental runs, which had used the Box-Behnken construct from the typical Response Surface Methodology (RSM) design. The data were collected during rheological experiments and the model that was constructed had been proven to be acceptable with the Adjusted R-Squared value of 0.9624. Apart from showing the polymer concentration as being the most important factor in the determination of polymer solution viscosity, the evaluation of the model terms as well as the Sobol sensitivity analysis had also shown a considerable interaction between the process parameters. As such, the proposed viscosity model can be suitably applied to the optimization of the polymer solution properties for the polymer flooding process and the prediction of the rheological data required for polymer flood simulators.

Experimental Investigation of the Heterogeneity Limit for the Application of Polymer Flooding in Reservoirs

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Mingchen Ding ◽  
Yugui Han ◽  
Yefei Wang ◽  
Yigang Liu ◽  
Dexin Liu ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Oil Recovery ◽  
Polymer Concentration ◽  
Experimental Information ◽  
Polymer Flooding ◽  
Polymer Injection ◽  
Low Concentration ◽  
Visual Models ◽  
Combined Use

Abstract It is generally accepted that polymer flooding gets less effective as the heterogeneity of a reservoir increases. However, very little experimental information or evidence has been collated to indicate which levels of heterogeneity correspond to reservoirs that can (and cannot) be efficiently developed using polymer flooding. Therefore, to experimentally determine a heterogeneity limit for the application of polymer flooding to reservoirs, a series of flow tests and oil displacements were conducted using parallel sand packs and visual models possessing different heterogeneities. For low-concentration polymer flooding (1.0 g/l), the limit determined corresponds to permeability contrasts (PCs) of 10.8 and 10.2, according to the parallel and visual tests, respectively. A significant increase in oil recovery can be achieved by polymer injection within these limits. Increasing the polymer concentration to 2.0 g/l increased these limiting PCs to 52.8 and 50.0, respectively. Additionally, within or beyond these limits, the combined use of polymer and gel may be the best.

scholarly journals Artificial Neural Network to Forecast Enhanced Oil Recovery Using Hydrolyzed Polyacrylamide in Sandstone and Carbonate Reservoirs

Polymers ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2606
Author(s):  
Hossein Saberi ◽  
Ehsan Esmaeilnezhad ◽  
Hyoung Jin Choi
Keyword(s):  
Neural Network ◽  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Salt Concentration ◽  
Polymer Concentration ◽  
Fuzzy Neural Networks ◽  
Polymer Flooding ◽  
Statistical Parameters ◽  
Inference System ◽  
Simulation Tools

Polymer flooding is an important enhanced oil recovery (EOR) method with high performance which is acceptable and applicable on a field scale but should first be evaluated through lab-scale experiments or simulation tools. Artificial intelligence techniques are strong simulation tools which can be used to evaluate the performance of polymer flooding operation. In this study, the main parameters of polymer flooding were selected as input parameters of models and collected from the literature, including: polymer concentration, salt concentration, rock type, initial oil saturation, porosity, permeability, pore volume flooding, temperature, API gravity, molecular weight of the polymer, and salinity. After that, multilayer perceptron (MLP), radial basis function, and fuzzy neural networks such as the adaptive neuro-fuzzy inference system were adopted to estimate the output EOR performance. The MLP neural network had a very high ability for prediction, with statistical parameters of R2 = 0.9990 and RMSE = 0.0002. Therefore, the proposed model can significantly help engineers to select the proper EOR methods and API gravity, salinity, permeability, porosity, and salt concentration have the greatest impact on the polymer flooding performance.

scholarly journals Enhanced Oil Recovery by Polymer Flooding: Direct, Low-Cost Visualization in a Hele–Shaw Cell

2019 ◽  
Vol 9 (3) ◽  
pp. 186
Author(s):  
Yukie Tanino ◽  
Amer Syed
Keyword(s):  
Enhanced Oil Recovery ◽  
Oil Recovery ◽  
Polymer Concentration ◽  
Polymer Flooding ◽  
Team Work ◽  
Petroleum Engineering ◽  
Laboratory Model ◽  
Oil Reservoir ◽  
Laboratory Exercise ◽  
Hele Shaw Cell

We designed a hands-on laboratory exercise to demonstrate why injecting an aqueous polymer solution into an oil reservoir (commonly known as “polymer flooding”) enhances oil production. Students are split into three groups of two to three. Each group is assigned to a packed Hele–Shaw cell pre-saturated with oil, our laboratory model of an oil reservoir, and is given an aqueous solution of known polymer concentration to inject into the model reservoir to “push” the oil out. At selected intervals, students record the oil produced, take photos of the cell using their smartphones, and demarcate the invading polymer front on an acetate sheet. There is ample time for students to observe the experiments of other groups and compare the different flow patterns that arise from different polymer concentrations. Students share their results with other groups at the end of the session, which require effective data presentation and communication. Both the in-session tasks and data sharing require team work. While this experiment was designed for a course on Enhanced Oil Recovery for final year undergraduate and MSc students in petroleum engineering, it can be readily adapted to courses on groundwater hydrology or subsurface transport by selecting different test fluids.

Displacement Efficiency for Low-Salinity Polymer Flooding Including Wettability Alteration

SPE Journal ◽  
2016 ◽  
Vol 22 (02) ◽  
pp. 417-430 ◽  
Author(s):  
Saeid Khorsandi ◽  
Changhe Qiao ◽  
Russell T. Johns
Keyword(s):  
Experimental Data ◽  
Oil Recovery ◽  
Analytical Solutions ◽  
Polymer Concentration ◽  
Polymer Flooding ◽  
Wettability Alteration ◽  
Displacement Efficiency ◽  
Low Salinity ◽  
Low Salinity Water ◽  
Salinity Water

Summary Polymer flooding can significantly improve sweep and delay breakthrough of injected water, thereby increasing oil recovery. Polymer viscosity degrades in reservoirs with high-salinity brines, so it is advantageous to inject low-salinity water as a preflush. Low-salinity waterflooding (LSW) can also improve local-displacement efficiency by changing the wettability of the reservoir rock from oil-wet to more water-wet. The mechanism for wettability alteration for LSW in sandstones is not very well-understood; however, experiments and field studies strongly support that cation-exchange (CE) reactions are the key elements in wettability alteration. The complex coupled effects of CE reactions, polymer properties, and multiphase flow and transport have not been explained to date. This paper presents the first analytical solutions for the coupled synergistic behavior of LSW and polymer flooding considering CE reactions, wettability alteration, adsorption, inaccessible pore volume (IPV), and salinity effects on polymer viscosity. A mechanistic approach that includes the CE of Ca2+, Mg2+, and Na+ is used to model the wettability alteration. The aqueous phase viscosity is a function of polymer and salt concentrations. Then, the coupled multiphase-flow and reactive-transport model is decoupled into three simpler subproblems—the first in which CE reactions are solved, the second in which a variable polymer concentration can be added to the reaction path, and the third in which fractional flows can be mapped onto the fixed cation and polymer-concentration paths. The solutions are used to develop a front-tracking algorithm, which can solve the slug-injection problem of low-salinity water as a preflush followed by polymer. The results are verified with experimental data and PennSim (2013), a general-purpose compositional simulator. The analytical solutions show that decoupling allows for estimation of key modeling parameters from experimental data, without considering the chemical reactions. Recovery can be significantly enhanced by a low-salinity preflush before polymer injection. For the cases studied, the improved oil recovery (IOR) for a chemically tuned low-salinity polymer (LSP) flood can be as much as 10% original oil in place (OOIP) greater than with considering polymer alone. The results show the structure of the solutions, and, in particular, the velocity of multiple shocks that develop. These shocks can interact, changing recovery. For example, poor recoveries obtained in corefloods for small-slug sizes of low salinity are explained by the intersection of shocks without considering mixing. The solutions can also be used to benchmark numerical solutions and for experimental design. We demonstrate the potential of LSP flooding as a less-expensive and more-effective way for performing polymer flooding when the reservoir wettability can be altered with chemically tuned low-salinity brine.

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