History matching workflow

The history matching process applied in this study uses the main methodological steps proposed in previous studies (e.g. Almeida et al., 2014; Maschio et al., 2015; Avansi et al., 2016). These processes are also part of a closed-loop reservoir development and management process proposed by Schiozer et al. (2015). A common feature in these studies is that they were applied to synthetic datasets (Beta model, UNISIM-I-H benchmark case).

The general HM methodology complies fifteen steps as shown in Figure 2.12.

However, the methodology proposed in this study is focused in the step 1 (geological modeling workflow) and 11 (new characterization), providing an extension to the methodological steps presented in previous studies, improving the geological consistency of our models and, consequently, of the history matching process and further production forecasts (Figure 3.3).

Figure 3.3. History matching workflow used in this work (Almeida et al., 2014; Maschio et al., 2015;

Avansi et al., 2016). The methodology proposed in this work is an extension of the steps 1 and 11 proposed in previous history matching studies.

During the step 1 the model is built including uncertainties in the most relevant attributes. The attributes with spatial variation (geostatistical models) are generated and evaluated during the geological modeling workflow (Figure 3.2). The other attributes (e.g. kr curves, oil-water contact (OWC) and gas-oil contact (GOC), rock compressibility, faults transmissibility) are treated according to their particularities and discretized in levels of uncertainty with different probabilities of occurrence.

The steps which covers the definition of the tolerance and normalization limits to the need of a new parameterization (step 2 to step 10), follow the methodological procedures presented in recent studies (e.g. Almeida et al., 2014; Maschio et al., 2015; Avansi et al., 2016) and described in the previous chapter. Additionally, and because one of the main objectives is to validate the methodology instead of achieving a perfect adjustment, the proposed methodology ends after obtaining a set of models that meet the history matching criteria. In this way, the model selection and further applications stages (steps 13 to 15) are not taken into account in this work (see Figure 2.12).

Obtaining geologically consistent models that also represent a good match regarding the observed data (production and/or seismic data) demands multiple modifications in the geological characterization of the reservoir (new parameterizations – step 11). Each new parameterization demands a complete workflow run (Figure 3.1) and includes:

 changing the uncertainty range of the different parameters;

 adding new parameters (e.g. vertical transmissibility models when in the presence of vertical stratigraphic barriers);

 generating new geostatistical models (e.g. new images guided by pilot wells).

This work proposes the generation of new geostatistical models guided by pilot wells. The methodology, based in the pilot point concept, represents an extension of the technique presented by Avansi (2014), there called virtual wells, being the porosity the main property to be adjusted. Instead of setting pilot points or pilot blocks (individual cells or blocks) as an additional synthetic dataset at selected unmeasured locations across the reservoir, in this study the pilot points take the form of synthetic wells (pilot wells). Similarly to the pilot points, the pilot wells are the fictitious data used to affect realistic modifications in the reservoir regions surrounding the pilot wells. On the other hand, each pilot well can cross the entire reservoir, being also conditioned by the estimated variogram, similarly to the measured wells. Thus, the present approach uses far fewer pilot wells when compared with the traditional pilot point method. The values in the pilot wells are the parameters to be

adjusted to modify the geological heterogeneity while minimizing the OF. At other locations, the values are found through the geostatistical modeling techniques. The total number of pilot wells and their location is one of the key issues of the method, highly dependent on the reservoir characteristics (geological scenario and reservoir flow behavior). The pilot wells methodology is chosen over other geostatistical parameterization techniques mainly due to the high flexibility in local adjustments.

In this study the pilot wells are synthetic wells with a vertical profile and a set of synthetic well logs. The facies profile is the main parameter to be manually or semi-automatically adjusted during the multiple workflow iterations, at each pilot well location. In the first case, each pilot well facies profile is entirely and manually modified (see G-segment case study in the results chapter). In the second case, a major part of the facies profile is automatically updated from the best facies models obtained during the diagnosis stages, while specific locations (i.e. specific horizons, interfaces) are manually modified (see C-segment case study). The synthetic petrophysical properties (e.g. porosity, vertical and horizontal permeability, net-to-gross, vertical transmissibility) are directly associated to the facies through an uncertainty range (Figure 3.4) and, in this way, automatically modified within the same workflow iteration and/or between iterations.

Figure 3.4. Pilot well profile and respective synthetic well logs. In this example the petrophysical parameters are conditioned by the facies log through specific uncertainty ranges.

The uncertainty ranges correspond to different distributions (e.g. normal, log-normal) with upper and lower bounds determined during the data analysis process. This procedure avoids the generation of unrealistic property values and overcomes potential instability problems that frequently affect inverse problems.

Each geological modeling workflow run generates a set of multiple 3D facies and petrophysical models. For each set of models, the facies profiles are fixed at each pilot well location, similarly to the other measured wells. On the other hand, the petrophysical logs at each pilot well location are modified before running the scale up well logs process. In this way, each model is a modified version of the input synthetic well log (curve a) (Figure 3.5).

The new log (curve b) is modified using the standard deviation curve method according to the formula:

𝐶𝑢𝑟𝑣𝑒(𝑏) = 𝑀𝑒𝑎𝑛_{Curve⁡(𝑎)}+ 𝑟𝑎𝑛𝑑 ∗ 𝑆𝑡𝐷𝑒𝑣_{𝐶𝑢𝑟𝑣𝑒(𝑎)} (3.6) where rand refers to the random distribution (normal truncated) defined according to the objectives of each parameterization run and that modifies the petrophysical logs at the pilot wells locations. The mean and the upper and lower bounds of the random distribution are also defined by taking into account the objectives of each parameterization run, which means, after the diagnosis step in the history matching workflow. The facies log is used as a control property. In this case the random value is sampled independently for each facies code. The seed value that controls the random distribution parameters is defined as a workflow variable, similarly to the facies and petrophysical modeling process. Thus, the seed value used in each model is preserved and accessible whenever necessary.

The effect of the pilot wells in the reservoir properties redistribution is conditioned by the pilot wells configuration. Additionally, the geostatistical method, the variogram and the vertical and/or horizontal trends between properties also influence the efficiency of the pilot wells. The zone of influence of the pilot well can also be adjusted during the geostatistical modeling process by modifying the number of neighbors that are used for the Kriging.

Figure 3.5. Example of the input and output synthetic data on a pilot well. The input petrophysical property (vertical transmissibility) is modified at each model realization (Tm_v1 and Tm_v2) using the input

facies log as a control.

The correct choice of the pilot wells configuration (number and location of the pilot wells) remains one of the main issues. In this study, the configuration takes into account:

 Geological framework: sedimentary features with a significant impact in the reservoir flow behavior (e.g. channels, stratigraphic barriers). As a general guideline when selecting the number of pilot wells, the distance between pilot wells must be smaller than the structure to be represented. Thus, if the objective is to represent a sedimentary channel, the distance must be smaller than the channel width;

 Other datasets: 3D and/or 4D seismic data that could add new information to the geological knowledge of the reservoir (depositional/stratigraphic features);

 Streamline simulations: The streamlines describe the direction of flow at the time that they are computed. They can be seen as a set of tubes representing the total

reservoir volume and through which the fluids are moving. Since each streamline carries about the same volume, their density is an indication of the fluids velocity. One of the advantages of the streamline method is the visual information regarding the fluid flow pattern and connectivity in the reservoir. In this study, the streamline method is used to define zones-of-influence of producers and, between injectors and producers, allowing the jointly history match of multiple wells using the pilot wells method. The main streamlines paths between the pairs injector/producer are settled as the preferred locations to manually spread the pilot wells. Additionally, different pilot wells groups are defined accordingly to the different pairs injector/producer. In this way, the pilot well properties within each group are independently handled and jointly history matched (Figure 3.6). The number of pilot wells and their properties take into consideration the geological characteristics, the analysis of the NQDS values and the desired level of uncertainty, as detailed in the results chapter.

Figure 3.6. Example of two pilot wells configuration: (a) the streamlines that were in the base of the two pilot wells configuration (b) pilot wells configuration, showing two groups of pilot wells, each one adapted

according streamline paths.

 Production data: the outcome analysis of the NQDS values and production curves during diagnosis step. Taking the example shown in Figure 3.7a, the production curves reveal the earlier breakthrough, and the NQDS values the lower Qw, highlighting the importance of the cross plots analysis and the complexity of the flow behavior. For this well, the best models show severe deviations and in that sense the properties distributions of those models are not very useful. To correct these deviations, the pilot wells configuration should lead to profound modifications in the geological framework of the region such as, adding or eliminating stratigraphic barriers, building new

sedimentary features. Each action must take into account the set of information’s previously described. The streamlines method would reveal if the water production is influenced by one or more injectors and/or by the OWC, and if so, in which periods and what are the main flow patterns. The geological background would inform the sedimentary features that could act as a preferred path to the fluids flow or as a barrier (e.g. sedimentary channel and a stratigraphic barrier, respectively). Figure 3.7b shows a less complicated example. Although most models record a lower Qw, the production curves and the NQDS plot show only few models approaching the observed flow behavior (models inside the black rectangle). For these cases and as a first approach, the pilot wells are used to fix and mimic the facies and petrophysical properties observed in these best models, that is, the pilot wells properties are extracted from best models at each pilot well location. Nevertheless, the pilot wells configuration is mainly determined by the streamline analysis.

Figure 3.7. Production curves and NQDS values: (a) well B-2H, showing a generalized earlier water breakthrough and lower Q ; (b) well B-4DH, showing a lower Q for most models.

In this study, the main goal of the pilot wells method is to modify the geological heterogeneity by including new sedimentary features or changing existing ones. This is done by handling the facies logs at the pilot wells locations and, consequently, altering and adjusting the reservoir petrophysical properties.

At the end of the methodology, all the OF included in the matching process should have models inside the acceptance range.

4. Application

The methods presented in this work are applied to the Norne field benchmark case, based on real field data. The Norne project is established between the IO Center, NTNU, and Norne field Operations (Statoil, ENI and Petoro) to provide a real dataset to different research groups in order to evaluate and compare different methods for history matching and ultimately closed-loop reservoir management (Rwechungura et al., 2010). This study is limited to the information’s and datasets that are available in the Norne field benchmark case that somehow is incomplete. In this way, one of the goals of this work is also to improve and add new information to this dataset. The application presents the main features of the Norne field (geological framework and simulation model).