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

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.

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Yang Lei ◽  
Shurong Li ◽  
Xiaodong Zhang ◽  
Qiang Zhang ◽  
Lanlei Guo

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.


2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Mingchen Ding ◽  
Yugui Han ◽  
Yefei Wang ◽  
Yigang Liu ◽  
Dexin Liu ◽  
...  

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.


1975 ◽  
Vol 15 (04) ◽  
pp. 338-346 ◽  
Author(s):  
M.T. Szabo

Abstract Numerous polymer floods were performed in unconsolidated sand packs using a C14-tagged, cross-linked, partially hydrolyzed ployacrylamide, and the data are compared with brine-flood performance in the same sands. performance in the same sands. The amount of "polymer oil" was linearly proportional to polymer concentration up to a proportional to polymer concentration up to a limiting value. The upper limit of polymer concentration yielding additional polymer oil was considerably higher for a high-permeability sand than for a low-permeability sand. It is shown that a minimum polymer concentration exists, below which no appreciable polymer oil can be produced in high-permeability sands. The effect of polymer slug size on oil recovery is shown for various polymer concentrations, and the results from these tests are used to determine the optimum slug size and polymer concentration for different sands. The effect of salinity was studied by using brine and tap water during polymer floods under similar conditions. Decreased salinity resulted in improved oil recovery at low, polymer concentrations, but it had little effect at higher polymer concentrations. Polymer injection that was started at an advanced stage of brine flood also improved the oil recovery in single-layered sand packs. Experimental data are presented showing the effect of polymer concentration and salinity on polymer-flood performance in stratified reservoir polymer-flood performance in stratified reservoir models. Polymer concentrations in the produced water were measured by analyzing the radioactivity of effluent samples, and the amounts of retained polymer in the stratified models are given for each polymer in the stratified models are given for each experiment. Introduction In the early 1960's, a new technique using dilute polymer solutions to increase oil recovery was polymer solutions to increase oil recovery was introduced in secondary oil-recovery operations. Since then, this new technique has attained wide-spread commercial application. The success and the complexity of this new technology has induced many authors to investigate many aspects of this flooding technique. Laboratory and field studies, along with numerical simulation of polymer flooding, clearly demonstrated that polymer additives increase oil recovery. polymer additives increase oil recovery. Some of the laboratory results have shown that applying polymers in waterflooding reduces the residual oil saturation through an improvement in microscopic sweep efficiency. Other laboratory studies have shown that applying polymer solutions improves the sweep efficiency in polymer solutions improves the sweep efficiency in heterogeneous systems. Numerical simulation of polymer flooding, and a summary of 56 field applications, clearly showed that polymer injection initiated at an early stage of waterflooding is more efficient than when initiated at an advanced stage. Although much useful information has been presented, the experimental conditions were so presented, the experimental conditions were so variable that difficulties arose in correlating the numerical data. So, despite this good data, a systematic laboratory study of the factors influencing the performance of polymer flooding was still lacking in the literature. The purpose of this study was to investigate the effect of polymer concentration, polymer slug size, salinity in the polymer bank, initial water saturation, and permeability on the performance of polymer floods. The role of oil viscosity did not constitute a subject of this investigation. However, some of the data indicated that the applied polymer resulted in added recovery when displacing more viscous oil. The linear polymer-flood tests were coupled with tests in stratified systems, consisting of the same sand materials used in linear flood tests. Thus, it was possible to differentiate between the role of polymer in mobility control behind the flood front in each layer and its role in mobility control in the entire stratified system through improvement in vertical sweep efficiency. A radioactive, C14-tagged hydrolyzed polyacrylamide was used in all oil-recovery tests. polyacrylamide was used in all oil-recovery tests. SPEJ P. 338


Polymers ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 1046 ◽  
Author(s):  
Saeed Akbari ◽  
Syed Mohammad Mahmood ◽  
Hosein Ghaedi ◽  
Sameer Al-Hajri

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.


1984 ◽  
Vol 24 (05) ◽  
pp. 545-554 ◽  
Author(s):  
Jeffrey H. Harwell ◽  
Robert S. Schechter ◽  
William H. Wade

Abstract The chromatographic movement of surfactant mixtures through porous media is examined to determine possible injection strategies for minimizing the amount of surfactant required in a tertiary oil recovery chemical flood. The model used does not consider the presence of oil but does account for mixed micelle formation. Expressions are derived that represent the surfactant required to expose an entire reservoir to an "effective oil recovery mixture." This effective mixture may be either one whose overall composition is within prescribed limits of the composition of the injected surfactant solution or it may be a mixture whose overall composition varies but which contains micelles of fixed composition. Mixtures considered contain cosolvents and one, two, or three surfactant components. Initial calculations neglect dispersion, but numerical calculations including dispersion leave the conclusion unchanged; within the limitations of the model, there are optimal strategies for the propagation of surfactant mixtures through porous media. The optimal injection strategy varies, depending on the nature of the surfactant solution injected into the porous medium. Conditions for and the location of the optimum are discussed. Conclusions based on observations about these systems then are extended to cover the injection of surfactant mixtures currently available commercially. Introduction Commercial application of surfactants for EOR now appears feasible. The principle at work in such processes is the lowering of interfacial tension (IFT) between the continuous flowing water and trapped residual oil droplets to allow the oil to be mobilized. Mixtures that effectively lower oil/water IFT are often blends of various surfactant types, isomers of the same surfactant, and/or cosurfactants in an electrolyte solution. The oil recovery efficiency of the injected mixture generally is quite sensitive to changes in mixture composition. Change of composition after injection into the reservoir may occur by one or a combination of mechanisms. For example, the mixture components may partition selectively into the various phases present in the reservoir. The mechanism considered here is the chromatographic separation of the mixture into its components due to preferential adsorption of various components onto reservoir minerals-"the chromatographic problem." The recent reports of the Bell Creek Unit A micellar/polymer pilot showed 20% of the injected surfactant produced before any oil bank with negligible concomitant incremental tertiary oil production. Significantly, the surfactants produced were the lower-molecular-weight species. Though alternative mechanisms for this separation yet may be established, the hypothesis of chromatographic separation of the components in the mobile aqueous phase seems adequate. Not only did this produced surfactant not result in enhanced recovery, but since the injected solution was designed to give ultralow IFT's with the low-molecular-weight components in place, it seems likely that the oil recovery efficiency of the remaining surfactant also may have been impaired. These results emphasize the importance of understanding the mechanisms of surfactant chromatographic movement. One means of combatting the chromatographic problem is to reduce the local adsorption of the mixture components-that is, modify the adsorption isotherms of the constituents. This may be done either by changing the reservoir minerals (e.g., by a caustic flood) or by modifying the structure of the surfactant molecules. A complementary approach is to examine the dynamics of the chromatographic movement of surfactant mixtures to identify injection strategies, if they exist, that minimize the total surfactant requirement. It is this question that is considered here. The analysis considers an oil-free linear system and neglects many of the complex features that are encountered in an actual chemical flood. There are several reasons for ignoring these complicating factors. The coherence solutions apply to the systems considered here; whereas the only solutions that include the presence of oil employ numerical computations. An analytical solution is desirable; however, there is an additional more compelling argument that has been used to justify neglecting the presence of oil. The chromatographic movement of a surfactant/ cosurfactant mixture through an oil-free core should demonstrate the qualitative features of the actual oil recovery process. While multiple flowing phases do arise in an actual flood, the released oil forms a bank ahead of the surfactant slug. SPEJ P. 545^


2008 ◽  
Vol 11 (06) ◽  
pp. 1117-1124 ◽  
Author(s):  
Dongmei Wang ◽  
Randall S. Seright ◽  
Zhenbo Shao ◽  
Jinmei Wang

Summary This paper describes the design procedures that led to favorable incremental oil production and reduced water production during 12 years of successful polymer flooding in the Daqing oil field. Special emphasis is placed on some new design factors that were found to be important on the basis of extensive experience with polymer flooding. These factors include (1) recognizing when profile modification is needed before polymer injection and when zone isolation is of value during polymer injection, (2) establishing the optimum polymer formulations and injection rates, and (3) time-dependent variation of the molecular weight of the polymer used in the injected slugs. For some Daqing wells, oil recovery can be enhanced by 2 to 4% of original oil in place (OOIP) with profile modification before polymer injection. For some Daqing wells with significant permeability differential between layers and no crossflow, injecting polymer solutions separately into different layers improved flow profiles, reservoir sweep efficiency, and injection rates, and it reduced the water cut in production wells. Experience over time revealed that larger polymer-bank sizes are preferred. Bank sizes grew from 240-380 mg/L·PV during the initial pilots to 640 to 700 mg/L·PV in the most recent large-scale industrial sites [pore volume (PV)]. Economics and injectivity behavior can favor changing the polymer molecular weight and polymer concentration during the course of injecting the polymer slug. Polymers with molecular weights from 12 to 35 million Daltons were designed and supplied to meet the requirements for different reservoir geological conditions. The optimum polymer-injection volume varied around 0.7 PV, depending on the water cut in the different flooding units. The average polymer concentration was designed approximately 1000 mg/L, but for an individual injection station, it could be 2000 mg/L or more. At Daqing, the injection rates should be less than 0.14-0.20 PV/year, depending on well spacing. Introduction Many elements have long been recognized as important during the design of a polymer flood (Li and Niu 2002; Jewett and Schurz 1970; Sorbie 1991; Vela et al. 1976; Taber et al. 1997; Maitin 1992; Koning et al. 1988; Wang et al. 1995; Wang and Qian 2002; Wang et al. 2008). This paper spells out some of those elements, using examples from the Daqing oil field. The Daqing oil field is located in northeast China and is a large river-delta/lacustrine-facies, multilayer, heterogeneous sandstone in an inland basin. The reservoir is buried at a depth of approximately 1000 m, with a temperature of 45°C. The main formation under polymer flood (i.e., the Saertu formation) has a net thickness ranging from from 2.3 to 11.6 m with an average of 6.1 m. The average air permeability is 1.1 µm2, and the Dykstra-Parsons permeability coefficient averages 0.7. Oil viscosity at reservoir temperature averages approximately 9 mPa·s, and the total salinity of the formation water varies from 3000 to 7000 mg/L. The field was discovered in 1959, and a waterflood was initiated in 1960. The world's largest polymer flood was implemented at Daqing, beginning in December 1995. By 2007, 22.3% of total production from the Daqing oil field was attributed to polymer flooding. Polymer flooding should boost the ultimate recovery for the field to more than 50% OOIP--10 to 12% OOIP more than from waterflooding. At the end of 2007, oil production from polymer flooding at the Daqing oil field was more than 11.6 million m3 (73 million bbl) per year (sustained for 6 years). The polymers used at Daqing are high-molecular-weight partially hydrolyzed polyacrylamides (HPAMs). During design of a polymer flood, critical reservoir factors that traditionally receive consideration are the reservoir lithology, stratigraphy, important heterogeneities (such as fractures), distribution of remaining oil, well pattern, and well distance. Critical polymer properties include cost-effectiveness (e.g., cost per unit of viscosity), resistance to degradation (mechanical or shear, oxidative, thermal, microbial), tolerance of reservoir salinity and hardness, retention by rock, inaccessible pore volume, permeability dependence of performance, rheology, and compatibility with other chemicals that might be used. Issues long recognized as important for polymer-bank design include bank size (volume), polymer concentration and salinity (affecting bank viscosity and mobility), and whether (and how) to grade polymer concentrations in the chase water. This paper describes the design procedures that led to favorable incremental oil production and reduced water production during 12 years of successful polymer flooding in the Daqing oil field.


Polymers ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2606
Author(s):  
Hossein Saberi ◽  
Ehsan Esmaeilnezhad ◽  
Hyoung Jin Choi

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.


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