Piecewise continuous control of groundwater remediation

• US 5,813,798 A
• Filed: 03/28/1997
• Issued: 09/29/1998
• Est. Priority Date: 03/28/1997
• Status: Expired due to Term

• Current Assignee: Greg Whiffen
• Original Assignee: Greg Whiffen
• Inventors: Whiffen, Greg
• Primary Examiner(s): Graysay, Tamara L.
• Assistant Examiner(s): LEE, JONG SUK
• Application Number:
  US08/829,915
• Time in Patent Office: 550 Days
• Field of Search: 405/52, 405/128, 405/129, 210/141, 210/143, 210/170, 210/747, 364/578, 364/804, 395/500, 588/249, 588/250, 588/260, 588/261
• US Class Current: 405/52
• CPC Class Codes: B09C 1/00 Reclamation of contaminated soil
• CPC Class Codes: B09C 1/002 involving in-situ ground water treatment
• CPC Class Codes: E03B 3/06 from underground consolidating foundation soil by draining, e.g. by lowering the water level E02D3/00; subsoil filtering E21B43/02

Abstract

A piecewise continuous-time dynamic control method and apparatus for optimizing re-mediation of groundwater is disclosed. The piece-wise continuous control process is used to generate efficient designs for remediation systems based on differentiable groundwater models. The remediation strategies generated are characterized by piece-wise continuous functions of time which dictate the operation of remediation devices. The piece-wise continuous functions may change discontinuously at the end of each management period, or, optionally, a finite number of times during each management period. The duration and number of management periods covering a groundwater cleanup may be selected by the user of the invention to maximize the contamination removal efficiency and reflect the mechanical limitations of the specific remediation devices chosen. The continuous-time property of piece-wise continuous control requires simpler (usually sparse) derivatives of a groundwater model than the derivatives required by static and discrete-time control of groundwater remediation.

Claims

1. A method for remediating a contaminated groundwater site comprising the steps:

(a) determining contaminated groundwater site characterization information;

(b) generating a model of said contaminated groundwater site from said characterization information;

(c) designing a remediation system for said model by;

(c1) defining at least one management period; and

(c2) utilizing a control capable of continuously changing and allowing for discontinuity within each management period; and

(d) implementing said remediation system to remediate said contaminated groundwater site.

2. The method of claim 1, wherein the step of determining the site characterization information includes:

identifying contaminants and location of said contaminants at said contaminated groundwater site; and

determining physical properties of said contaminated groundwater site including at least one of size, depth, topography, volume, materials, hydraulic conductivity, porosity, dispersivity, retardation, biological reactivity, hydraulic head, and recharge rates.

3. The method of claim 1, wherein the step of generating the model further comprises:

selecting a model having a plurality of nodes, cells, or elements;

implementing into said model, state variables including hydraulic heads and contamination concentrations at each of said nodes, sells, or elements; and

implementing into said model remediation system, design variables including, at least one of, location of remediation devices, operational rate of remediation devices, outflow concentrations of nutrients or surfactants from remediation devices.

4. The method of claim 3, wherein the steps of selecting the model of said groundwater site comprises:

selecting one or more models from the group consisting of;

finite element models, finite difference models, finite volume models, spectral method models, boundary element models, transform models, neural network models, and analytic models.

5. The method of claim 1, further comprises:

specifying design objectives, and specifying design constraints for insertion into piecewise continuous control.

6. The method of claim 5, wherein the step of specifying the design objectives further comprises:

specifying objective function having at least one of the following design objectives;

cost, clean-up time, contamination level, number of cleanup devices, and minimum flow rate from cleanup devices.

7. The method of claim 5, wherein the step of specifying the design constraints further comprises:

specifying at least one of;

a pumping rate range for extraction wells;

a pumping rate range for injection wells;

a hydraulic capture zone; and

a cleanup level at the end of remediation.

8. The method of claim 5, wherein the step of designing the remediation system further comprises the steps of:

(c1) incorporating the constraints into an objective function;

(c2) providing an initial arbitrary remediation system design and set parameters;

(c3) integrating a linear system of differential equations, thereby establishing a design update law;

(c4) simulating the updated designs; and

(c5) testing each of the updated designs for a satisfactory improvement in the objective function.

9. The method of claim 8, wherein the step of testing further comprises:

testing the updated designs for convergence to an optimal design if satisfactory improvement exists.

10. The method of claim 8, further comprising the step of:

repeating the steps (c3) through (c5) of the piece-wise continuous control process using an improved design if an optimal design is not determined.

11. The method of claim 1, wherein the step of designing the remediation system further comprises:

designing a remediation system containing at least one device selected from;

an extraction well, an injection well, an observation well, a slurry well, an infiltration cap, a soil vapor extractor, an air sparger, a bioventor, and a water treatment plant.

12. The method of claim 1, wherein the step of designing a remediation system using a piece-wise continuous control comprises:

designing a remediation system containing at least one device to stimulate a biodegradation of contamination in said contaminated groundwater site.

13. The method of claim 1, wherein the step of designing the remediation system further comprises the step of implementing at least one of the following modifications:

super-time-stepping, quasi Newton approximation, Hessian shifting, Sequential Approximation Linear Quadratic Regulator, (SALQR) approximation, integration, implicit-time integration, iterative equation solvers, bang-bang optimization, non-convex objective functions, sparse operations, and/or multi-grid methods.

14. A method for remediating a contaminated groundwater site, comprising:

(a) characterizing the groundwater site and creating a model thereof;

(b) applying piece-wise continuous control to said model to obtain a remediation system design; and

(c) implementing said remediation system design.

15. The method of claim 14, wherein the step of applying the piece-wise continuous control comprises the following steps:

(b1) formulating a design problem as a plurality of piece-wise continuous control equations;

(b2) initializing program parameters and providing an initial arbitrary design;

(b3) integrating the piece-wise continuous control equations and establishing a design update law;

(b4) simulating the updated designs; and

(b5) testing each of updated designs for a satisfactory improvement.

16. The method of claim 15, further comprising the step of testing the updated designs for convergence to an optimal design if a satisfactory improvement exists.

17. The method of claim 16, further comprising the step of repeating steps (b3) through (b5) of the piece-wise continuous control process using an improved design if the optimal design is not determined initially.

18. The method of claim 14, wherein the step of creating a model comprises estimating a future behavior of the contamination in the groundwater site.

19. The method of claim 14, wherein the step of obtaining the remediation system design comprises using continuous time management periods.

20. The method of claim 19, wherein the step of using the continuous time management periods comprises using a design within the management period that is at least in part static.

21. The method of claim 19, wherein the step of using the continuous time management periods comprises using a design within the management period that varies over time.

22. The method of claim 14, wherein the step of obtaining the remediation system design comprises obtaining an optimal design.

23. A method for remediating a contaminated groundwater site comprising the step of:

(a) determining contaminated groundwater site characterization information;

(b) generating a model of said contaminated groundwater site from said characterization information;

(c) designing a remediation system with controls for said model using a continuous time approach having discontinuities with management periods; and

(d) implementing said remediation system to remediate said contaminated groundwater site.

24. The method of claim 23, further comprising the step of using piecewise continuous control.

25. A method of remediating a contaminated groundwater site comprising the steps of:

(a) determining contaminated groundwater site characterization information;

(b) generating a model of said contaminated groundwater site from said characterization information;

(c) designing a remediation system for said model by formulating an optimization method with a continuous time accumulation of a design objective, generalized to include a discontinuous control, and an end period design objective, which are functions of the discontinuous control and a state defining the discontinuous control as at least one of a smooth, non-smooth, discrete, continuous, or discontinuous function of time;

defining time as a continuous process allowing said discontinuous control to be discontinuous and non-smooth; and

(d) implementing said remediation system to remediate said contaminated groundwater site.

26. The method of claim 25, further comprising the step of using piecewise continuous control.