*Reservoir Models*

A ”reservoir model” is a mathematical representation of a specific volume of rock incorporating all the “characteristics” of the reservoir under study. It can be considered as a conceptual 3D construction of a single reservoir or in some cases of an oil/gas field.

Data derived from various sources are integrated by deterministic or geostatistical methods, or a combination of both, to construct the model. Its setting up, however, is a dynamic process, since a reservoir model must be continuously up-to-dated and revised when new data become available or inconsistencies between the predicted and real reservoir behavior are found.

The reservoir model is, therefore, the result of studies whose main objective is to understand and describe the dynamic behavior of a hydrocarbon reservoir in order to predict its future performance under different development and production strategies.

From practical point of view, the integrated reservoir modeling represents now the most valuable technical approach for estimating the oil/gas reserves and computing the future production profiles, reducing the uncertainties always associated with the static and dynamic reservoir descriptions.

*Workflows for integrated reservoir modeling*

There are several reasons why an integrated reservoir modeling has found a strong and rapid development:

- For a reliable evaluation of the bulk and net rock volumes, and the original hydrocarbons in place – which are of utmost importance in
- assessing the economics of a reservoir development project
- selecting the development schemes and exploitation strategy
- selecting the basic design and size of the production facilities
- allocating equity shares with partners

- For an assessment of the minimum well number required to produce the reservoir economically, as well as for the optimal selection of well type (e.g. vertical, slant, horizontal, multilateral, etc.) and locations
- For an economic/technical evaluation of implementing IOR/EOR processes to increase the final recovery
- For verifying the consistency of all static and dynamic data reducing the uncertainties always present in a reservoir model.

The integrated reservoir modeling finds application in different stages and phases of the reservoir life cycle.

In the case of field development it is used for:

- Estimating the HOIP
- Selecting the field development strategy
- Selecting the optimal number and locations for injector and producer wells
- Computing the production proﬁles (oil, gas, and water)
- Estimating the oil and gas technical reserves
- Obtaining some basic data required by the economic evaluation
- Identifying and quantifying the key uncertainties.

In the case of producing field it is used for:

- Calibrating the geological model by matching the past production history (fluid rates, GOR, WC, pressures, etc)
- Identifying the undrained oil/gas bearing zones
- Optimizing the production rate and the final recovery
- Keeping the right injection rate for the optimal reservoir pressure maintenance and/or for the maximum sweep efficiency of the displacement processes
- Locating infilling wells
- Modifying the well patterns
- Selecting the best well construction and completion design
- vertical vs. horizontal, completions

- Updating production proﬁles and economics.

*Dynamic reservoir model for production forecasts*

In addition, the 3D integrated reservoir modeling:

- Helps the integration in a quantitative model of soft information such as sedimentological and depositional models, faults transmissibility etc.
- Enables and promotes the joint team work of geoscientists and engineers
- Reduces the inconsistencies that can be generated by the different geo-modeling workflows
- Allows a good and reliable volumetric evaluation of fluids initially in place even in case of complex reservoir geometries
- Allows the most advanced 3D gridding techniques and the upscaling the geological models
- Helps to select in a real time the optimal final well target while drilling.

*Static Model*

A static reservoir model is the one incorporating all the geological features (i.e. structural, sedimentological, petrophysical, etc.) of an underground volume of rock that can store fluids (hydrocarbons and/or water) and can allow their movement.

In general, the static model of a reservoir is the final integrated product of the structural, stratigraphic and lithological modeling activities, where each of these steps is developed according to its specific workflow.

A static reservoir study typically proceeds through four main stages.

*1. Structural modeling*

- Reconstruction of the geometrical and structural properties of the reservoir, by defining a map of its structural top and the set of faults running through it. This stage of the work is carried out by integrating interpretations of the geophysical surveys with the available well data.

*A structural model showing faults and layering*

*2. Stratigraphic modelling *

- Definition of a stratigraphic scheme using well data, which form the basis for well to well correlations. The data consist of electrical, acoustic and radioactive wireline logs, and of results of core analysis, integrated where possible with information from specialist studies and production data.

*Example of a 3D Stratigraphic Model – L. Cosentino*

*3. Lithological modeling*

- Definition of the lithological types (basic facies), which are characterized on the basis of lithology, sedimentology, and petrophysics. This classification into facies is a convenient way of representing the geological characteristics of a reservoir, especially for the purposes of subsequent three-dimensional modelling.

*Example of a stochastic model of facies – L. Cosentino*

*4. Petrophysical modeling*

- A quantitative interpretation of well logs to determine some of the main petrophysical characteristics of the reservoir rock, (porosity, water saturation, and permeability). Core data represent the essential basis for the calibration of interpretative processes.

*A petrophysical model showing porosity distribution and values*

The results of these different stages are integrated in a two (2D) or three-dimensional (3D) context, to build an integrated geological model of the reservoir.

This model represents the reference frame for calculating the quantity of hydrocarbons in place, and on the other, forms the basis for the initialization of the dynamic model.

*Dynamic model *

The *dynamic model* combines the static model, pressure- and saturation-dependent properties, well locations and geometries, as well as the facilities layout to calculate the pressure/saturation distribution into the reservoir, and the production profiles vs. time.

A dynamic model can be used to simulate several times the entire life of a reservoir, considering different exploitation schemes and operating conditions to optimize its depletion plan.

*Integrated reservoir modeling and simulation*

Reservoir simulation is a branch of petroleum engineering developed for predicting reservoir performance using computer programs that through sophisticated algorithms numerically solve the equations governing the complex physical processes occurring during the production of an oil/gas reservoir.

Basically, a reservoir simulation study involves five steps:

- Setting objectives
- Selecting the model and approach
- Gathering, collecting and preparing the input data
- Planning the computer runs, in terms of history matching and/or performance prediction
- Analyzing, interpreting and reporting the results.

Factors to consider in selecting the simulation model are

- The recovery process of the reservoir
- the model must be able to reproduce the main reservoir drive mechanisms

- Quality and type of the available information- which influence the level of detail to use in the modeI
- Type of answer required
- The desired accuracy of the expected results will influence the design of the simulation model

- Available resources
- human, economic and technological resources

Different types of simulators are used to represent the drive mechanisms of different types of reservoirs, and the selection depends on the type and behavior of the original reservoir ﬂuids and on the predominant process controlling the reservoir production and hydrocarbon recovery:

- Black-oil model
- It assumes that the thermodynamic behavior of the reservoir hydrocarbon system can be well represented only by two components: the ”stock-tank oil” and the “separator gas”. The classical PVT studies supply all the data required by this approach.

- Compositional model
- It assumes that the reservoir hydrocarbon system can be well represented only by a number of components and pseudocomponents (C
_{1}+N_{2}, C_{2}, …, C_{7+}, …). The thermodynamic behavior of such system is described by the use of an EOS (equation of state) that is usually calibrated with the data of PVT studies.

- It assumes that the reservoir hydrocarbon system can be well represented only by a number of components and pseudocomponents (C
- Thermal model
- It is used in case of reservoirs where an EOR process based on thermal recovery techniques is applied. This is the case of heavy oil, extra heavy oil, and bitumen reservoirs, in which the oil viscosity is so high that does not allow any primary production or the implementation of any conventional injection process (cold water, gas).
- The thermal EOR processes that can be simulated include: SAGD, cyclic steam injection, steam flooding, hot and cold water injection, and in situ combustion.

Upscaling of the geological models is key issue in the reservoir simulation. It is basically a process by which a very heterogenous region of the reservoir rock described with a huge amount of “fine grid cells” is replaced by an equivalent less heterogeneous region made up of a number of single coarse-grid cells. The “upscaled geological model” must, however, maintain the same storage and transport properties of the reservoir rock described with detail by the “fine geological model”. The upscaling process, therefore, is essentially an averaging procedure in which the static and dynamic characteristics of a fine-scale model are approximated by those of a coarse-scale model.

*Conceptual illustration of the upscaling process*

In a numerical simulation study historical production/injection data (oil, gas, and water rates) must be supplied to the mathematical model. Of course, good quality production/injection data are essential for a reliable simulation study, in terms of direct input data and reference data to evaluate the accuracy of the history match phase.

Past history matching is the most practical method for testing a reservoir model’s validity and for calibrating the geological model. Basically history matching is a process of reservoir parameter adjustment in such a way that the simulated reservoir behavior reproduces the actual reservoir behavior.

History matching process should also help to identify possible points of weaknesses in the initial reservoir model, and should help to find and evaluate the most efficient ways to overcome them.

*Two possible approach to History Matching*

Once calibrated, the simulation models are then used to compute the production forecasts considering various hypotheses for the reservoir exploitation.

In simple cases, this prediction phase can be performed in a few days, while the in more complex cases it can take several months depending on:

- the size (i.e. number of cells), the type (i.e. black oil, compositional) and geological features of the model,
- the complexity of the wellbore system and of the surface facilities layout
- the number of predictions to be run.

A general sequence for running the prediction phase can be summarized as follows:

- Input Data for predictions – definition of the cases to be run
- Setting guidelines and constraints – to simulate the future production performance of a ﬁeld
- Inﬂow and outﬂow well performance
- Running the prediction cases
- Uncertainty assessment.

*Schematic of a 3D uncertainty workflow.*

*It shows the most common inputs, stages in the 3D modelling process and corresponding outputs*