reservoir modeling and simulation - …scholar.cu.edu.eg/sayyouh/files/8-reservoir_modeling.pdf ·...

RESERVOIR MODELINGAND SIMULATION

Dr. Helmy Sayyouh

Petroleum Engineering

Cairo University

IntroductionAny problem is solvable if you can make assumptions.

The key to problem solving, then, is determining the right assumptions.

Depending on the objectives set for the reservoir study, certain models, with their inherent assumptions, are more appropriate than the others.

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The questions asked and the assumptions made are two important considerations when choosing a reservoir model for simulation.

There are many methods of modeling the reservoir.


Modeling Methods

Experimental

Experimental methods are commonly used today, either alone or with numerical methods, to predict well or reservoir performance at a small scale.


Examples:

Slim tube to investigate miscibility.

Sand-packs to study water flood tests..

Core analyses include capillary pressure, relative permeability, rock wettability, etc.


Analogy

Where no data available, performance predictions can be made by analogy.

Here, data from a field with similar geologic and PVT characteristics can be taken.


Decline Curve Analysis

Is the extrapolation of oil production rates versus time.

This method provides estimates of future rates for a well.


Methods of decline curve analysis :

Exponential decline.

Hyperbolic decline.

Harmonic decline.


Statistical Methods

Can be used to develop correlations from available data.

The correlations can the be applied as predictive tools to reservoir with limited data.


Analytical Methods

Solving differential equations, which describe fluid flow in the reservoir, by analytical methods. The boundary conditions must be defined.


Examples:

Unsteady state water influx.

Pressure build up theory.

Buckley-Leverett fractional flow analysis

Real gas flow equations.


Predictive Models

Are combinations of analytical methods and empirical correlations.

These models are used to predict reservoir performance under different recovery scenarios.

Some of the more complex methods have been made available as software.


The Stream tube Model

Simulates performance of regular and irregular pattern water floods.

Based on the concepts developed by R. Higgins and A. Leighton.


Can be used to study water flood performance when limited data is available.

Will yield reasonable results when the assumptions inherent to the solution describe the reservoir to be studied.


Material Balance Equation

Means the conservation of a mass system, which in our case is a hydrocarbon reservoir.

Can be used to predict the performance of an oil or gas reservoir.

Enables the engineer to model the reservoir better, by understanding which drive mechanisms are important.


The material balance equation

- is zero-dimensional.

- applies to gas as well as oil reservoirs.

- needs good and accurate PVT and production data.

- has many methods for applications.


Finite Difference Method

Finite difference is a process where the continuous differential equations are transformed into a discrete form.

The reservoir can be divided into any number of orthogonal blocks.

The fluid flow equations are then solved for each block.


Finite Difference Model Grids

The size of the grid or cell, and the dimensions of the simulation model depend upon:

- the objectives of the study.

- the amount and quality of available data.

- the reservoir geometry and complexity.


Selection of the type of simulator is primarily dependent upon:

-The type of reservoir fluids.

-Recovery process being modeled.

-Computer availability.

-The study budget.


The One-Dimensional Model

Flow in only one direction.

Can be used to study the recovery between an injector and producer.

The model can be rotated in either horizontal or vertical direction.

Adequate to study line drive behavior in pilot floods.


The Two-Dimensional Model

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Can be used to study areal or vertical effects in a reservoir

A two-dimensional areal model is used

- when there are wide variations in rock and fluid properties areally.-To study fluid migration across lease lines.

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Areal and Layered Model

DR.HELMY SAYYOUH

A two-dimensional cross-sectional model is used

- when there are wide variations in rock and fluid properties vertically.

- Analyze multiple-well completions, gravity segregations, and crossflow

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Two-Dimensional Cross-sectional Model

DR.HELMY SAYYOUH

The Three-Dimensional Model

Rock and fluid properties vary a really and vertically.

Requires a significant amount of data.


General Recommendations for Constructing a Grid

1.Use the coarse grid model acceptable.

2.In areal simulation when tracking saturations, use at least three cells between wells, if possible.

3.In vertical simulation, try to use three layers or more per stratigraphic layer.


4.Keep the cell dimensions as uniform as possible.

5.Align the grids with the major flow direction of the field or along the known permeability orientation.


6.Avoid cells having cross sections to flow that are extremely large relative to the flow path length.

7.Cells with very large conductance and very low pore volumes will cause numerical problems; leave such cells out of the model, if possible.

8.In real simulation without major saturation-front movement, having several wells per cell is allowable if their pressure behaviors are similar


Special Finite Difference Models

Pattern Elements

Assumption: geology is representative of the entire pattern and that the sides of the are no-flow boundary.

The pattern element grid can be aligned one of two ways: diagonal and parallel grid orientations.

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Parallel Grid Diagonal GridOne-Eighth of a Five-Spot Pattern

DR.HELMY SAYYOUH

Forecast Models

A forecast model

is a program which combines the simulation results from the various models, allocates production to the entire field based on specific criteria, and then sums the predicted production to give a fieldwide production schedule.

Is specific to a given study.


Examples:

If the cost of running a 3-D model is prohibited, then combine 2-D areal and cross-sectional models using forecast models to obtain a 3-D production schedule.

Use 5-spot pattern to develop a miscible flood. Running a 3-D composional model can be very expensive. However, if 2-D areal model and cross-sectional models are used with a forecast model, the same results can be approximated.


Non-Cartesian Grids

Radial Models

Radial models (2-D) are used

1. to study single well behavior :

-determine critical production rates.

-prevent water or gas coning.

-completion effects.

-deliverability response of gas wells.

2. in a pressure build up study to determine in situ permeability.


Radial models (2-D)

should not be used to study the behavior of wells close to the boundaries of a reservoir or close to a fluid contacts in horizontal flooding where the assumption of symmetry is not valid.


Curvilinear Coordinates

The curvilinear grid models the reservoir better than the rectilinear grid because the grid blocks are aligned along the preferential path of fluid flow.

Many single and multi-phase applications were investigated using curvilinear coordinates.


Considerations for Selecting Finite Difference Grids

1. Study Objectives

Define the study objectives clearly. Understanding what questions are to be answered will facilitate selecting and designing the grid.


2. Type of Process Being Modeled

The type of process ( primary depletion – water flood – immiscible gas injection - miscible displacement ) being modeled controls which simulator is to be used.


3. Reservoir Geometry and Dimensions

The geometry and dimensions of the reservoir influence the selection of the model grid. If the reservoir is small and vertical and areal effects are important, it may be possible to use a full-field 3-D model.

It is best to use the simplest model which can meet the study objectives.


4. Grid Orientation

There are two grid orientations: parallel and diagonal.

Under certain conditions, the two orientations will yield different results. This phenomenon is known as grid orientation effects.


In steam displacement the parallel grid results in a more pronounced steam finger along the injector-producer direction than the diagonal grid.

The effects are severe in miscible floods.

In selecting a simulation model, grid orientation effects should be minimized whenever possible


5. Numerical Dispersion

Numerical dispersion of the fluids takes place when the model grid cells are large areally relative to the physical dispersion rate.

This situation causes the saturation front to be smeared over a large area.


Numerical dispersion can be minimized by decreasing the grid size.

The optimum cell size is that which gives the acceptable degree of accuracy for the money available for doing the study


6. Availability of Data

The more complex models, the more detailed are the data requirements.

The minimum amount of data required is enough to define adequately the area of interest.


7. Costs

The more complex the model, the more expensive

8. Computer Availability

The maximum size of a simulation model is controlled by which machine is available to be used.


Reservoir Simulation Aspects

Uncertainty

Simulation has inherent uncertainties. These uncertainties stem from multiple sources and for most reservoirs cannot be eliminated.

The results always carry out a band of uncertainty


High-quality field and laboratory data helps reduce the size of the uncertainty band.

Uncertainty may be introduced to reservoir simulation from various sources


Data Quantity and Quality

Data must be sufficient and accurate. This accuracy introduces error which must be accepted, because the model can never be more reliable than the data it has been based upon.


Therefore, strong data-acquisition programs must be designed and implemented to reduce data uncertainty.


Geology

Geologic descriptions are largely interpretative. Hence some degree of uncertainty will always be present.

What actually occurs between the wells can never be truly known


Issues such as sand continuity, fault orientation, and vertical communication may be more definable.

The reservoir may contain variability between one well and another; this will affect reservoir performance.


Reservoir simulation can help define parameters by numerically testing evolving geologic interpretations.

As additional data becomes available with time, the picture tends to become less homogeneous.


Scale-up

Parameters critical to reservoir performance are often measured from core samples such as vertical and lateral permeability, relative permeability, capillary pressure and irreducible saturations.


It becomes evident that the assumptions based upon these small-scale core data measurements were not entirely valid.


Different lithologies will affect the vertical communicate within the reservoir.

Reconciling field and a laboratory data is an important part of reservoir simulation.


Properties measured at the core-plug scale are insupportable at the field scale.

Scale-up error may be introduced if the layering scheme in the model is very different from the true stratification of the reservoir.


Mathematics

The uncertainty introduced by mathematical solution technique is generally regarded as being controllable and measurable.


Model Selection

Model selection must be directly tied to the objectives of the study.

Objectives frequently are revised during the course of a study.

The scope of the study will determine which model design is most suitable to meet the objectives.


Classification of Simulation models

Full-Field Models

Segment or sector models

Well Models

Cross-Sectional Models


Each of these models may be either:

Conceptual Models:

use average properties, either estimated or measured, to test the sensitivity of various parameters.


Actual Models:

use detailed geologic descriptions that are designed to provide specific performance indications.


Model refinements:

gridding and layering

Fine-Grid Models:

use small cell dimensions to provide a detailed grid to track fluid front movement.


Coarse-Grid Models:

are used to capture total reservoir energy, rather like material balance models, except that they have some dimensionality to them.


reservoir modeling and simulation - …scholar.cu.edu.eg/sayyouh/files/8-reservoir_modeling.pdf ·...

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