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Ye. O. Cherkas (OJSC NK Rosneft-NTC, D. A. Antonenko and P. V. Stavinsky (OJSC NK Rosneft)

Introduction
Drilling of horizontal holes imposes special requirements on the reliability of prediction of reservoir structure and quality within a large radius from the borehole. However, the reservoir prediction tools currently available to geologists suffer, to some extent or another, from measurement errors, which inevitably leads to modeling uncertainty and increases risks associated with drilling of horizontal holes. In view of the high costs involved in horizontal drilling projects and uncertainties inherent in any model, it has become imperative to address this issue. Incorrect description of a reservoir may result in swelling of irrecoverable field development costs. In a typical geological model, four major sources of uncertainty may be identified: (1) data quality and interpretation; (2) structural and stratigraphic models; (3) geological-statistical model and its parameters; and (4) uncertainty related to equiprobable realizations. In an ideal case, uncertainty decreases as the field becomes more developed.
As regards the Vankor field, which is currently under development, the most challenging tasks from the uncertainty standpoint are as follows: (1) reducing risks associated with horizontal drilling; (2) putting together a program for detailed exploration; and (3) refining the drilling program.

This paper proposes a method for analyzing uncertainties inherent in geological models. Modeling based on this method will yield data (in the form of maps) representing the quantitative distribution of uncertainties in determining the presence of a reservoir and its properties, which must be used to evaluate potential drilling risks.

General Information about the Field
The Vankor gas and oil field is located in the Krasnoyarsk Krai. This paper deals with one of five productive reservoirs with about 390 million tonnes of original oil in place. The field was discovered in 1988 and is yet to be put into commercial production. As of this study, there were 27 wells already drilled into the reservoir of interest. The deposit is a layer-uplifted pool, and the reservoir is terrigenous.

The Vankor uplift is an isometric structure extending from the south northward. The predominant depositional environment was shallow-water (barrier-bar complex).

Method
The best criterion for assessing the overall ambiguity determining the accuracy of geological model parameters is the "validity of the oil-in-place estimate". This criterion is dependent upon the basic characteristics of the reservoir and, therefore, may serve as a measure of accuracy in constructing the model. To evaluate the validity of the reserve estimate, one must evaluate the calculation accuracy of every parameter in the calculation formula


where stands for "stock tank oil initially in place", GRV stands for "gross rock volume", N/G stands for "net-to-gross", is porosity, is oil saturation, is oil density, and is the oil shrinkage factor.

To this end, a general procedure was established for handling each parameter, namely:

1. estimating possible variations in the value of each input parameter;
2. defining the RMS deviation;
3. mapping mean values of the parameter, with fixed values assigned to individual wells and taking into account the RMS deviation in the crosshole space;
4. estimating parameter variance; and
5. mapping oil-in-place variance by multiplying out variance maps for all parameters, provided that they are independent (this condition has been introduced to simplify the estimation process).

Uncertainty Calculation Approach
The principle of accounting for uncertainties is as follows: At first, one should estimate the possible error of the measurements determining the RMS deviation. Then, this error is multiplied by a random surface whose spread of values follows a Gaussian curve with mathematical expectation equal to zero and a variance equal to unity. Finally, the result is added to the reference surface:



where is one of the surface realizations, is the reference surface, is a surface or a constant determining the RMS deviation error, and is a random surface of errors with + and - values around zero.

A characteristic feature of the error surface is the fact that errors at well points acquire zero value, to increase gradually as one moves away from the wells. Thus, the RMS deviation depends on data quality and distance to the well. This approach suffers from the drawback that the range of the error variogram is unknown. It cannot be taken as equal to the variogram ranges used in the modeling of a property of interest because of their heterogeneity. Besides, randomly modeled errors may acquire positive as well as negative values because possible scenarios lie on either side of the baseline interpretation. The variogram range is selected by the interpreter based on subjective estimates of the error variance length. If the range is excessive, the final uncertainty map is smoothed out with partial or complete loss of information. If the range is too small, one will end up with a heavily "noisy" picture.

Structural Uncertainty: Presence of Reservoir
One of the burning questions during early phases of field development is whether oil is present in field areas not covered by exploratory drilling. Analysis of uncertainties may give a feel about the degree of uncertainty in identifying the presence of oil. One of the criteria for such analysis is the position of the top of the OWC. Analysis should proceed along the following lines: (1) delineate a surface over the top of a reservoir (average value); (2) introduce an error into the average value; and (3) derive intersection contours for multiple realizations of the top of reservoir and OWC surfaces.



A set of 200 contours of the top of reservoir-OWC intersection contours has been obtained for the Vankor field. The extreme values are shown in Figure 1. It can be seen that uncertainty in the position of the OWC top, which is essentially the sum total of uncertainties in the positions of the top of reservoir and the OWC, may give rise to a serious error in oil-in-place estimates. In the Vankor field, no reservoir was present within the area marked by the solid black line in 23% of cases out of the set of multiple realizations. A well drilled into the questionable target after this work had been completed failed to reveal any presence of oil. Thus, the high likelihood of absence of oil, predicted by modeling, was corroborated by real evidence. In the course of this work, two other areas characterized by great uncertainty as regards presence of oil were identified (marked by broken lines).

Structural Uncertainty: Rock Volume
Uncertainty in the position of reservoir boundaries and contact determination contribute the error in the gross rock volume measurement. As regards the structural modeling error, its major source is the ambiguity of structural surfaces in the crosshole space. The error grows with distance from wells and is zero in their immediate vicinity.

The error in determining the position of reservoir boundaries was selected based on the quality of seismic data. For the Vankor field, it was assigned as +-15 m.

Estimation of the spread of OWC values was based on the results of well tests in target sands. The spread of values was defined as the difference between the highest and lowest OWC levels. In the case of the Vankor field, the spread of OWC values was 15 m.

In this case, selection of variogram ranges was based on seismic data pertaining to the reservoir and well spacing.

As a result, maps of potential errors in determination of the top and bottom of the reservoirs as well as OWC were produced. Within the boundaries of the field, the average spread of reservoir top and bottom positions is about 5 to 6 m. Uncertainty in OWC position approaches maximum toward the field boundary and between the two blocks of the Vankor field. The rock volume was calculated as the product of gross thickness within a cell times the cell area. Figure 2 is a map showing possible deviations of the gross rock volume from average values.


Proceeding from the results of analysis of structural uncertainties, one can draw conclusions as to the presence of oil in field areas yet to be covered by exploratory drilling. This information is useful in deciding whether additional exploration of the field is needed. Information about possible variations in reservoir boundaries and OWC levels in the presence of oil is instrumental in decision-making processes as part of the field development strategy, especially when it comes to drilling of horizontal holes.

Uncertainty in Reservoir Properties
Variances of reservoir properties are mapped as follows. The input data include zero-variance points or, in other words, correlation marks by wells. An algorithm using a continuous Gaussian distribution and predetermined variogram parameters provide the basis for constructing error surfaces for a property with a given deviation from the mean. Variogram parameters are assigned based on the depositional environment (barrier-bar features, pronounced lateral consistency of properties) and well spacing. All realizations of error surfaces for a given property are reduced to a single variance map of this property at the assigned level of deviation from the mean.

Net-to-gross Ratio
The primary sources of error in identification of pay zones in wells include the resolution of logs, accuracy of determination of reservoir quality by logging, and error in the use of critical values to identify a reservoir. In order to assess uncertainty in reservoir properties, one must first know the deviation from the mean. It is recommended to select the deviation of the net-to-gross ratio from the mean on a distribution bar chart of the model (tied to log data), because we are dealing essentially with assessment of the uncertainty inherent in the model’s volumetrics. As can be inferred from Figure 3(I) the maximum net-to-gross ratio distribution density in accordance with the model is close to the interval of 15% deviation from the mean. The deviation of the net-to-gross ratio from the mean in the crosshole space is close to 4-5%.

Porosity Ratio
The sources of porosity determination error include measurement techniques, instrument error, and subjective factors. The deviation was selected from porosity distribution based on log data in correlation with core data (Fig. 3(II). It can be seen from Figure 3(II) that the maximum density of porosity values coincides with the 0.18-0.22 interval. This spread of values corresponds to 10% deviation from mean porosity. In the crosshole space, the deviation of porosity values is 0.6%, increasing to 0.8% toward field boundaries. The map indicates areas requiring updated data.

Oil Saturation Factor
The error in determining the oil saturation factor stems from the quality of interpretation of log data, reservoir resistivity determination error, groundwater level, height above groundwater level, capillary curve, etc.

According to the model, the distribution of the oil saturation factor is at its maximum in the 0.4-0.7 interval, which corresponds to 25% deviation from the mean (Fig. 3(III)). In the crosshole space, the deviation of oil saturation from the mean is 4.5%.



Uncertainty in Oil Properties
The oil shrinkage factor and density at the surface were determined as the average of a number of analyzed samples. To take the determination error into account, distribution functions were created with due account for the results of analysis of all oil samples in surface and reservoir conditions. The distributions provided the basis for calculation of oil parameter variances.

Uncertainty in Oil-in-place Estimates
After mapping of variances of each parameter in the oil-in-place estimation formula, variances of oil-in-place estimates are mapped by multiplying out variance maps for all parameters, provided that they are independent.

A map of uncertainties inherent in the density of oil in place is shown in Figure 4. According to the map, the overall uncertainty in field reserves may amount to about 10% of original oil in place.



A set of structural maps and maps of reservoir parameters with whatever errors they contained was used to produce a set of Vankor field reserve density maps, and estimation was made of the probability density and cumulative frequency functions for oil-in-place reserves expressed in tonnes. Over a set of a hundred realizations, the spread of oil-in-place estimates is within +-10% of the mean. According to the diagram of sensitivity of oil reserves to the major estimation parameters, the most tangible impact on uncertainty in oil reserves within the bottom portions of the reservoir is produced by oil saturation, although in most cases it is the gross rock volume. This can be explained by the fact that most of uncertainty is associated with the edges of the field and the space between two of its blocks, where rocks exhibit poorer reservoir properties (see Fig. 3).

Conclusion
The proposed method for assessing the overall uncertainty inherent in oil-in-place estimates makes it possible to plan detailed exploration of the field and to refine the reservoir management plan in order to reduce the combined geological risks and, consequently, increase the profitability of the project.

Labels: drilling risk assessment, Exploration, horizontal well, Label, modeling, oil gas, reservoir, Rosneft, Russia, Vankor field

posted by The Rogtec Team @ 10:50 

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