GEOLOGY & GEOLOGICAL EXPLORATION
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Application Limits For Deterministic Geological-And-Reservoir Models
Об ограниченности области эффективного применения детерминированных геолого-гидродинамических моделей
Р.С. Хисамов, д.г.-м.н. (ОАО «Татнефть»),
А.В. Насыбуллин, д.т.н.,
А.В. Лифантьев (ТатНИПИнефть)
Адреса для связи: arslan@tatnipi.ru, vip@tatnipi.ru
Ключевые слова: геолого-гидродинамическая модель, геофизические исследования скважин, коэффициент извлечения нефти (КИН), детальная расчетная сетка, неоднородность пласта.
В данной статье освещены проблемы качества исходных данных для моделирования и полноты учета неоднородности пласта. Показано, что данные параметры, замеряемые на скважинах даже с малым шагом квантования, не гарантируют улучшения точности расчета, что при переносе этих данных на конечно-разностную сетку детерминированными методами происходит занижение неоднородности пласта вне зависимости от метода интерполяции. Доказано, что при увеличении детальности конечно-разностной сетки не происходит увеличение расчетной неоднородности пласта, что подтверждается тремя методами анализа. Выявлено, что с увеличением фактической неоднородности пласта темп ее снижения при переходе к сеточным данным не изменяется.
В соответствии с требованиями регламентов по проектированию разработки нефтяных месторождений принято выполнять проектные документы с использованием геолого-гидродинамических моделей. В статье рассмотрены особенности информационного обеспечения геолого-гидродинамических моделей на основе геофизических исследованиях скважин, бурения скважин-дублеров. Показана зависимость неоднородности параметров в геолого-технологических моделях от детальности сетки по трем методам:
- качественная (визуальная) оценка по графику плотности распределения вероятности;
- количественная оценка энтропии системы;
- количественная оценка по коэффициенту вариации. Кроме того, доказано, что при увеличении детальности конечно-разностной сетки не происходит увеличение расчетной неоднородности пласта.
Выявлено, что с увеличением фактической неоднородности пласта темп ее снижения при переходе к сеточным данным не изменяются. Показано, что распределение проницаемости на рассматриваемом примере имеет фрактальный характер и подчиняется гиперболическому закону. Фрактальное распределение не может быть смоделировано детерминированными методами. Для учета влияния плотности сетки скважин на КИН необходимо применение стохастических моделей.
05'2014
НЕФТЯНОЕ ХОЗЯЙСТВО
R.S. Khisamov
(Tatneft ОАО RF, Almetyevsk), A.V. Nasybullin, A.V. Lifantyev
(TatNIPIneft, RF, Bugulma)
E-mail: arslan@tatnipi.ru, vip@tatnipi.ru
Key words: geological-and-reservoir model, well logging, oil recovery efficiency, fine grid, reservoir heterogeneity.
According to reservoir engineering regulations, design projects should be based on permanently updated geo-logical-and-reservoir models. However, there are some doubts concerning these models, as if they don't take into account the effect of well spacing on oil recovery efficiency, and these doubts enlarge every day. This is due to the fact that most of the models are not based on the actual reservoir heterogeneity, or, to be more exact, they underestimate it. In fact, in a limiting case a homogeneous reservoir model allows developing a whole reservoir with one well. Conventional techniques don't have this drawback. They are based on heterogeneity, so they consider the effect of well spacing on oil recovery.
Why do models underestimate heterogeneity, though they use the same input data? Moreover, these data are often entered with 0.2 m vertical interval, which means that the data are quite numerous and their difference (or non-uniformity) should be high. Simulation engineers usually say that this depends on the grid size and try to build excessively fine-scale models. Typically, these are sector models in which some grid cells can be 2 cm thick. Such models are called "detailed" or "high-quality", meaning that other models are poor and useless. Let's analyze the input data quality and the reasons for heterogeneity loss in a model.
Model dataware
Let's consider geophysical data reliability. The sampling interval is usually 10-20 cm along the wellbore. Are these data reliable? In fact, there can be two types of error.
First, vertical resolution of geophysical tools is approximately 60-80 cm. So, the value recorded at some depth (with 20 cm interval) represents some average value for this interval. In case of a highly compartmentalized heterogeneous reservoir we get the moving average for the targeted interval which will be further distributed between the grid nodes. The value at a certain point is interpreted without regard to this notice. We believe that it is incorrect to infer the parameter value at one point. The invariance interval shall first be identified and the values shall be interpreted for the whole interval like in "manual" interpretation. As for propagation depth in conventional well logging, it is also not very high, about 1 m.
Due to complexity of quantitative estimation of thin reservoir properties by well logging data, all reservoirs less than 1.5 m thick are considered to be complex.
печатается в авторской редакции.
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Conventional well logging tools and techniques enable determining volumetric parameters (net pay thickness, porosity, oil and gas saturation) only in reservoirs with > 1.5 m net thickness. In thin reservoirs (1.5 m > net thickness > 0.5 m) log data enable determining net pay thickness and porosity. Oil and gas saturation can be sometimes determined with zero or very low penetration depth (Dlogging < dweU). In thin single layers (0.5 m > net thickness > 0.2 m) we can only determine net thickness, while quantitative estimation of other parameters is impossible [1].
Second, logging data are not direct measures of geological and geophysical characteristics of a reservoir. They are the result of inversion which doesn't have a unique solution. Reservoir characteristics are defined through interpretation by regression equations, obtained from core analysis data. These equations usually have a low correlation factor. Direct measures are the results of core analysis but they are quite few. So, even though average data reliability is quite evident, it is still very low in terms of specific wells or intervals. Human errors are also possible. All the above factors show that tendency to model refining with inadequate and single-point data can result in error increase.
But this fact is usually ignored, and it is believed that the more refined the model, the better. Simulation becomes a time consuming and complicated process. It has been noticed that when simulation engineers start operating more powerful computers, they don't reduce simulation time but try to refine the model. The project due date is repeatedly postponed and the result is none the better than using a simple model, or even worse. What is the reason? We can make the following comparison. The larger is the number of degrees of freedom with high uncertainties, the more unstable is the system. However, it is often impossible to over-persuade simulation engineers.
Here is a quotation from a monograph by A. Kh. Mirzadjan-zade, M.M. Khasanov and R.N. Bakhtizin: "Along with the external constraints, deterministic models have also internal problems - lack of reliable data on reservoir geology and poor accuracy of field data. Thus, accuracy of geological and geophysical data is so poor that 3D geological and, particularly, reservoir simulation models using seismic data and permeabil-
ities defined by well logs are nothing else but an obvious fraud (permeability error from logs is 100%). Under these circumstances the integrated 1D or 2D models will be more rigorous because the errors are mutually corrected during the integration process" [2].
We'd like to add that production and injection data can often be distorted for various reasons.
Let's analyze spatial variability (or match percentage) of such parameters as "types of rock" and "reservoir/non-reservoir" for the Romashkinskoye oil field (see the Table). We'll analyze offset wells spaced 50 m and 100 m from each other (i.e., they are located in one grid cell, so they should have the same parameters).
The Table shows that "types of rock" match is only about 54-55%. Does it make sense to interpolate data with such low reliability in a fine grid?
So, we only have well data. As for interwell space, the uncertainty of geological data here is very high due to impossibility of direct measures of geological and geophysical properties between the wells.
Reasons for heterogeneity loss in a model
Let's analyze reservoir parameters heterogeneity vs. grid size by three methods.
1. Qualitative (or visual) evaluationfrom probability density diagram.
Let's analyze the field developed by 4130 wells. Fig.1 shows permeability distribution density curve based on input data for various grid sizes (from 10 to 200 m) generated by deterministic method. Permeability distribution doesn't depend on interpolation technique, except for piecewise methods. Fig. 2 shows that when input data are entered into the grid we observe permeable heterogeneity decrease. At the same time, we don't observe heterogeneity increase when we refine the grid. Number of medium permeability reservoirs grows due to the extremes averaging.
One of 10 "golden" rules for simulation engineers stated by Aziz [3] says: "Be careful in the process of averaging to avoid losing essential information when averaging the extremes. Never average out extremes".
Areas Formations Well spacing up to 50 m Well spacing up to 100 m
'types of rock" Teservoir/non-reservoir" 'types of rock" Teservoir/non-reservoir"
Abdrakhmanovskaya D1 53.3 78.9 53.5 77.2
Aznakaevskaya D1 52.6 73.7 52.9 71.8
Alkeevskaya D0, D1 81.3 93.8 57.8 80.3
Almetyevskaya D0, D1 50.9 75.0 50.5 75.6
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