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УДК 550.832
ВЫСОКОПРОИЗВОДИТЕЛЬНОЕ КАРТИРОВАНИЕ ОБЛАСТЕЙ НЕОПРЕДЕЛЕННОСТИ ПАРАМЕТРОВ В ЗАДАЧАХ ГЕОНАВИГАЦИИ
Михаил Владимирович Свиридов
Новосибирский технологический центр компании «Бейкер Хьюз», 630090, Россия, г. Новосибирск, ул. Академика Кутателадзе, 4а, научный сотрудник, тел. (383)332-94-43 (доб. 147), e-mail: Mikhail. Sviridov@bakerhughes.com
Антон Павлович Мосин
Новосибирский технологический центр компании «Бейкер Хьюз», 630090, Россия, г. Новосибирск, ул. Академика Кутателадзе, 4а, научный сотрудник, тел. (383)332-94-43 (доб. 141), e-mail: Anton.Mosin@bakerhughes.com
Юрий Евгеньевич Антонов
Новосибирский технологический центр компании «Бейкер Хьюз», 630090, Россия, г. Новосибирск, ул. Академика Кутателадзе, 4а, кандидат технических наук, научный сотрудник, тел. (383)332-94-43 (доб. 140), e-mail: Yuriy.Antonov@bakerhughes.com
В работе представлен краткий обзор существующих подходов для картирования областей неопределенности параметров. Предложен новый метод картирования областей неопределенности параметров применительно к задачам геонавигации. Для подтверждения работоспособности предложенного метода приведены результаты тестовых расчетов.
Ключевые слова: область неопределенности параметров, геонавигация, глубинный прибор электромагнитного каротажа с азимутальной чувствительностью измерений, инверсия данных электромагнитного каротажа.
HIGH-PERFORMANCE MAPPING OF PARAMETER UNCERTAINTY REGION IN RESERVOIR NAVIGATION APPLICATIONS
Mikhail V. Sviridov
Novosibirsk Technology Center «Baker Hughes», 630090, Russia, Novosibirsk, 4a Kutateladze St., Scientist, tel. (383)332-94-43 (ext. 147), e-mail: Mikhail.Sviridov@bakerhughes.com
Anton P. Mosin
Novosibirsk Technology Center «Baker Hughes», 630090, Russia, Novosibirsk, 4a Kutateladze St., Scientist, tel. (383)332-94-43 (ext. 141), e-mail: Anton.Mosin@bakerhughes.com
Yuriy E. Antonov
Novosibirsk Technology Center «Baker Hughes», 630090, Russia, Novosibirsk, 4a Kutateladze St., Ph. D., Scientist, tel. (383)332-94-43 (ext. 140), e-mail: Yuriy.Antonov@bakerhughes.com
The paper provides a brief overview of existing approaches to mapping of parameter uncertainty region. New method of parameter uncertainty region mapping is proposed for reservoir navigation applications. The results of test computations are presented to confirm the efficiency of the proposed method.
Key words: parameter uncertainty region, reservoir navigation, deep-azimuthal resistivity tool, resistivity data inversion.
Modern exploration resistivity tools utilized in the oil industry for reservoir navigation and formation evaluation purposes provide a large range of measurements. This data is subsequently used for resolving parameters of the surrounding formation through sophisticated multi-parametric inversion techniques. The question of inversion results accuracy is very important because in some unfavorable cases poor quality of formation parameter resolution can lead to the erroneous perception of reservoir structure.
The accuracy of inversion results can be evaluated by means of the uncertainty analysis algorithms. The purpose of these algorithms is to map uncertainty region in parameter domain and then estimate the uncertainty ranges for each formation parameter. For example, if the range is narrow, an appropriate formation parameter can be reliably recovered. On the contrary, a wide range means that the inversion cannot accurately resolve the value of the appropriate parameter.
Another application of uncertainty analysis algorithms is investigation of exploration tool capabilities in known formation.
Following items should be specified as an input for uncertainty analysis algorithms:
- configuration of exploration tool (set of measurements that tool is able to provide for the processing)
- noise model (value of measurement noise and its distribution law) for each measurement composing tool configuration
- formation model (maybe a priori known or recovered from tool measurements through inversion)
There are several basic approaches to perform uncertainty analysis and map parameter uncertainty region [1]:
- Construction of linear approximation and mapping of parameter uncertainty region as an equivalency ellipsoid in the parameter domain. This approach is highperformance even in case of high dimensionality of parameter domain, but in some cases linear approximation can be inaccurate, so real uncertainty region cannot be represented as an ellipsoid. Another disadvantage of this approach enables mapping of only local uncertainty region
- Full scanning in the parameter domain with some specified step size (sufficiently small) for each parameter, and check if scanning point belongs to parameter uncertainty region or not. This approach enables mapping of both local and global parameter uncertainty region and ensures reliable results, but it is very time-consuming in case of high dimensionality of parameter domain because a lot of points should be examined.
- Variations of the Monte-Carlo method that generates random points over parameter domain, and check the scanning point belonging to parameter uncertainty region. This approach is able to map both local and global parameter uncertainty region, but requires a lot of computational time in case of high dimensionality of parameter domain because not all examined points belong to uncertainty region. Nevertheless, reliable result is guaranteed in case of large number of random points generated.
We propose a method for high-performance mapping of parameter uncertainty region in reservoir navigation applications. This method can be referred to response surface [1] approaches and consists of two steps. First, tool responses are simulated for specified formation model according to the actual tool configuration. Second, a high-performance inversion [2] of the simulated responses is carried out using the random set of model parameters as an expected value. Inversion assumes that measurements were contaminated with a preset level of noise according to the noise model. In the case of good quality inversion results, the set of recovered parameters represents some point inside of uncertainty parameter region. These two steps should be repeated many times to generate some statistics and eventually map the parameter uncertainty region. Then uncertainty ranges for each model parameter can be estimated through the analysis of this statistics.
This method has a good performance due to the capability of inversion algorithm to eliminate the redundant examination of parameter domain points located at a great distance away from the parameter uncertainty region. Moreover, usually there is high percentage of successful inversions that lead to points inside of uncertainty parameter region.
Let us illustrate the efficiency of proposed method with a very simple example reconstructing the conditions of the Russian West-Siberian fields (Fig. 1). This region is characterized by the low resistivity contrast between shale, oil- and water-bearing layers, which complicates reservoir properties evaluation and reservoir navigation process [3]. Imagine the deep-azimuthal resistivity tool [4, 5] is moving up (relative dip is 91°) in an oil-bearing layer with a resistivity of 10 Ohm m to the shale layer interface located above. The resistivity of the shale layer is 5 Ohmm. Let us assume that tool performs measurements each 50 cm and consider 3-m interval of borehole trajectory where the start point of interval is 1 m away from the boundary.
Fig. 1. Resistivity model reconstructing the conditions of West-Siberian fields
Let us specify the size of model parameter domain: both layer resistivities belong to the interval [0.1, 100] Ohmm, distance to boundary can vary in the interval [-5, 5] m, and the range for relative dip angle is [50, 130] deg.
Let us investigate three scenarios based on different combinations of measurements of deep-azimuthal resistivity tool. In the first scenario we simulate the process of reservoir navigation based on only conventional co-axial measurements (without azimuthal sensitivity) of deep-azimuthal resistivity tool. For the second scenario we enlarged the set of conventional co-axial measurements by low-frequency cross-component signal with azimuthal sensitivity. Measurement configuration for the third scenario includes conventional co-axial measurements and both low- and high-frequency cross-component signals with azimuthal sensitivity.
Assuming that the tool measurements can be contaminated with 2 % relative noise and an absolute noise dependent on signal type (0.01 dB for all attenuation signals, 0.1 degree for all phase difference signals and 10 nV for cross-component signals), we map the parameter uncertainty region for each scenario and present it in Fig. 2-4 below. Moreover, we compare our results with parameter uncertainty ranges estimated through another approach [6] based on the linear approximation of task.
■5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0
Distance to boundary, m Distance to boundary, m
Fig. 2. Projection of parameter uncertainty region for the first scenario (tool configuration contains only conventional co-axial measurements without azimuthal sensitivity). The left picture is a plot of layer resistivities against distance to boundary. Black and grey points represent the resistivity of top and bottom layers
respectively. The right picture is a graph of tool relative angle versus distance to boundary. Value of true model parameters is shown with a triangle. Uncertainty range estimated from linear approximation of task is shown as rectangle for each parameter. Extremely broad parameter uncertainty region for this scenario means that model parameters cannot be resolved without a priori data involvement
Considered scenarios show that parameter uncertainty region is characterized by complex shape and can be mapped by proposed method. Parameter uncertainty region can be locally bordered using the estimates of parameter uncertainty ranges computed through the linear approximation of task, but not globally. Third scenario shows that the use of high-frequency cross-component signal of deep-azimuthal resistivity tool enables the accurate resolution of model parameters even in case of formation with low resistivity contrast.
Fig. 3. Projection of parameter uncertainty region for the second scenario (tool configuration includes conventional co-axial measurements and low-frequency cross-component measurement with azimuthal sensitivity). The left picture is a plot of layer resistivities against distance to boundary. Black and grey points represent the resistivity of top and bottom layers respectively. The right picture is a graph of tool relative angle versus distance to boundary. Value of true model parameters is shown with a triangle. Uncertainty range estimated from linear approximation of task is shown as rectangle for each parameter. Wide parameter uncertainty region denotes that model parameters cannot be reliably recovered without the use of a priori knowledge about the reservoir structure
Fig. 4. Projection of parameter uncertainty region for the third scenario (tool configuration includes conventional co-axial measurements and both low- and high-frequency cross-component measurements with azimuthal sensitivity). The left picture is a plot of layer resistivities against distance to boundary. Black and grey points represent the resistivity of top and bottom layers respectively. The right picture is a graph of tool relative angle versus distance to boundary. Value of true model parameters is shown with a triangle. Uncertainty range estimated from linear approximation of task is shown as rectangle for each parameter. Narrow parameter uncertainty region indicates that all model parameters
can be accurately resolved
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© М. В. Свиридов, А. П. Мосин, Ю. Е. Антонов, 2017
