Identification of Well-Test Models by Use of Higher-Order Neural Networks

Abstract

In a well test, the central objective is to "prove" the fonnation in terms of a sustainable economic flow rate. This objective is related to the characterization of the reservoir and the estimation of its parameters, like permeability and skin, by knowledge of only the input and output signals, such as pressure and flow rate, and, in certain cases, other reservoir characteristics, such as the drainage area and the distance to faults.Interpretation efforts, therefore, can be performed in two phases: (l) the identification of "reasonable" theoretical reservoir models representing the field data, and (2) the estimation of pertinent parameters of the selected theoretical reservoir model. The second phase is well established in the literature, whereas many problems are associated with model selection, such as uncertain data, incomplete data, and the ambiguity of the models (i.e., more than one model might be representing the field data).One can identify the theoretical models based on similarities of the curvature of both the type curves (from both simple analytical models and complex numerical models) and the field data. The whole process can be conceived as a pattern-recognition task. In this paper, we present an approach by which it is possible to identify an appropriate welltest model in a consistent and objective manner, thereby reducing some of the problems associated with the task. The approach is based on the application of higher-order neural networks (HONN's).Conventional neural networks are used in general for both optimization and classification tasks. For classification purposes, these networks will find appropriate mappings to any set of patterns with dependence on both spatial and temporal positions. That is, such networks find it extremely difficult and often impossible to deal with patterns invariant to some transformation groups, such as scaling, translation, and rotation. Well-test models are inherently translation invariant with respect to the field data and are also scale invariant. Thus, we propose the use of HONN's, by which we can encode the invariant properties of patterns into the architecture of the network, thereby constraining some of its weights (parameters). Constructing such networks enables us to identify well-test models in an automated and robust manner. Moreover, these networks are both pattern and training-rule independent. Additionally, the training time for such networks is extremely fast compared to conventional neural networks.Our system has been used to identify various models, such as naturally fractured reservoir, homogeneous reservoir, multilayer reservoir, dual porosity, commingled, and fractured wells. We performed all implementation using VISUAL C++ 1.0 and Microsoft Foundation Classes 2.

Automated Classification of Well Test Responses in Naturally Fractured Reservoirs Using Unsupervised Machine Learning

“…It is important to note that this study is fundamentally different to previous applications of Artificial Intelligence in the field of Pressure Transient Analysis (e.g., Al-Kaabi and Lee, 1990;Allain and Horne, 1990;Deng et al, 2000;Ershaghi et al, 1993;Kumoluyi et al, 1995;Sinha and Panda, 1996;Sung et al, 1995). These previous studies mostly focused on the automatic identification of analytical models for Pressure Transient Analysis to assist the well test interpretation, assuming that appropriate analytical models to represent real reservoirs exist.…”

Artificial Neural Network (ANN) to estimate reservoir parameters in Naturally Fractured Reservoirs using well test data

“…Although the pressure derivative data are typically used in the normalized form as input to the ANN, it has been found that normalizing poses the following problems (Kumoluyi et al, 1995;Deng and Chen, 2000):…”

The Artificial Neural Network Method of Well-Test Interpretation Model Identification and Parameter Estimation

“…Using the actual well test curve to train ANN is not the appropriate approach because the training sample aggregate is too large, which made it difficult to train ANN successfully. The theory pressure derivative curves were selected as the training samples in the literatures [1][2][3][4][5][6] , and the input vector of ANN was the data point series selected from the theory pressure derivative curve. Before inputting to ANN, the vectors must be normalized.…”

“…That is because the traditional normalization of data points can't efficiently unit the input vectors of actual tested curve to the same model area as its training samples. Some researchers have noticed this problem and proposed different methods 5,6 to uniform the tested curve and the training samples, but they are not the most efficient approaches. It has been demonstrated in this study that using data point series as input vectors to train ANN is not the appropriate approaches.…”