## Filter Test Expert System

#1684

Development of Expert System on Pumping Test Interpretation

**Tech Area / Field**

- ENV-MRA/Modelling and Risk Assessment/Environment

**Status****3** Approved without Funding

**Registration date****19.10.1999**

**Leading Institute**

VNIIEF, Russia, N. Novgorod reg., Sarov

**Supporting institutes**

- Kazan State University / Scientific Research Institute of Mathematics and Mechanics, Russia, Tatarstan, Kazan

**Project summary**

**Conventional cycle of interpreting a pumping test**

Drawbacks: there are few experts, their resolutions are subjective, the essential part of data (knowledge) is used incompletely.

**The proposed approach**

Advantages of the proposed approach:

· a single integral medium for developing interpretation versions, for carrying out computations and studying their results;

· a possibility of using “opinions” given out by many experts which are available in an expert knowledge database;

· a possibility of using extension of knowledge of the expert himself in a more complete manner;

· the approach will allow to use the collected data more completely without increase in staff of personnel maintaining and processing field data results.

An important condition for successful application of computer technologies [1, 2] for practical solution of environmental problems in hydrogeology [3-17] is a proper preparation of initial data that would adequately represent specific situation on site. One of the most important and often the only source of such information are data on results of water pumping from prospecting wells, represented as tracer diagrams. Meanwhile direct use of such information is difficult, since variation of dynamic level decrease in the course of pumping is a result of interaction between a large complex of perse factors and the phenomena.

In this case some factors (pumping volume, well diameter, flow factor, etc.) are continuous values. Other factors (water yield regime or scheme in single strata, their arrangement order) are discrete. This results a change of shape of level sinking tracer diagram, or, more exactly, change of character of this diagram’s behavior.

One of the most difficult problems is to “decompose” the shape of a tracer diagram into components, i.e. to determine of a single strata’s water yield regime judging by changes in character of the tracer diagram’s behavior, which is stipulated by the necessity to formalize the notion of “the character of plot’s behavior” that is somewhat uncertain. Such decomposition is required in order to create a theoretical and/or computational model corresponding to each element of decomposition.

An important practical point is to provide a hydrogeological specialist in future with an opportunity to promptly create, on the basis of such decomposition, a computer model that would describe pollution flow and transport in the area of a specific well and to conduct the calculations oriented for analysis whether the model created agrees with experimental data. This stipulates the need for typification of flow regimes and creation of computer means to maintain databases for both representative schemes and corresponding parametric sets of analytical and numerical models, as well as means to create computer programs on their basis and their adequacy assessment. While the problem of compiling in a computation programs with available modules can be solved with the traditional computer technology methods, to evaluate parameters for such models basing upon test data is a challenge that is not easy to formalize.

In simple cases, i.e. presence of only two strata with known characteristics, an expert can formulate rules that sound like “rectilinear-to-curvilinear diagram transition point corresponds to a change the stratum flow regime”. In the case of several strata present with non-synchronously change regimes, the diagram behavior being also distorted by various random values (is noised), to specify the points of regime fluctuating presents a challenge even for experts.

In fact, in our case we deal with a challenge to identify only resultant (indirect and therefore blurred) characteristics of the phenomenon known and strong noise present. Traditional mathematical methods appear to be rather unstable under these conditions, and result of their application is highly dependent on input signal errors.

On the other hand, in order to solve such uncertain problems, methods based on self-organizing, space-and-time decomposition and fuzzy logic have been used of late.

The so-called artificial neural networks are important among such methods. While mathematical basis of first neural network models developed before 90s was, in fact, similar to ordinary non-linear regression and other well-known methods, in 90s a number of models appeared whose application permits to qualitatively improve results.

In particular, such models permit, for instance, a Fourier series expansion for periodic time-series in a self-organizing mode. For more complex non-periodic time-series, neural networks permit to perform a more complex decomposition resulting in an analogue of wavelet-expansion. Instead of expanding an amplitude-frequency space by Fourier expansion for periodic functions, wavelets permit local expansions of arbitrary functions into amplitude-scale components, thus performing decomposition of phenomena with different scales and different times. Since neural networks enable such decomposition as invariant with respect to scale variation and shifting, this permits decomposition specifically for the pumping curve and allows to interpreting this expansion in terms of finding flow test (FT) schemes.

Such decomposition may be ambiguous, so training of the neural network with data interpreted by an expert permits it to “absorb” the expert’s knowledge not as strict rules which an expert may be unable to formulate, but as a change of memory status (weights) of the neural network itself.

Since a neural network is very complex (the amount of memory is high), it can master even experts’ contradictory assessments and while analyzing a new diagram it can “recall” those associated with the shape of the diagram being analyzed. After that the neural network, taking into account association strength (excitation degree in relevant neurons of the neural network), outputs a probability (reliability) assessment for a certain regime or/for a combination of regimes.

Probability assessments for different decomposition versions obtained with trained neural networks will be used as an input data for an expert system (ES). Based upon fuzzy logic, it will output a final list of possible parameter values with their evaluation of there reliability taking into consideration all information available on test results (both quantitative and qualitative) and on geological and hydrogeological structure of a water-bearing system.

The Project efforts will include the following tasks:

· study of general situation at the market of expert system;

· analysis of peculiarities of fluid flow towards a well under extremely complicated hydrogeological conditions;

· overview of fuzzy logic methods and elaboration of criteria ensuring ES creation;

· review of neural programming capabilities for development of self-organizingadaptive algorithms (self-organizing algorithms);

· listing major representative schemes (typification of flow tests conditions);

· listing major complicating factors common for all schemes and specific for single schemes (prioritized in term of significance);

· development of analytical solvers;

· development of a module for numerical transition from originals to images (for schemes with no analytical solution);

· development of a code to model the fluid flow towards a well in axially-symmetric lamellar formulation;

· development of a potentiality for graphical representation of results as a set of standard tracer diagrams;

· development of methods for robust study of experimental conditions (by a-priori information and curve shapes);

· development of tools for ranking possible typical schemes (according to probability of their agreement with testing conditions) and in terms of possible complicating factors (using selected representative schemes taking into consideration real experimental situation);

· development of principles to estimate probable ranges values of parameters and complicating factors, as well as their possible variation;

· creation of algorithms for plotting computational curves with probable values of parameters and factors in coordinates and within ranges corresponding to test curves;

· creation of algorithms for interactive and automated comparison of experimental and calculated curves, the latter being varied according to the need within the specified parameter and factor variation ranges;

· development of methods for separation of representative (in particular, asymptotic) sections of experimental tracer diagrams (range fixing) for further quantitative analysis.

The Project study will result into advanced theoretical developments that describe flow phenomena, being used to solve vital environmental and industrial problems. A state-of-the-art tool for FT interpretation and optimization will be created. Scientists previously engaged in nuclear weapons design will be involved in solution of urgent problems in the field of ground water experimental studies.

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