History Matching, Forecasting and Updating

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Dr. Helmy Sayyouh

Petroleum Engineering

Cairo University

History Matching

The most practical method for testing a reservoir model’s validity and accuracy, is a process of parameter adjustment.

Its goal is to procure a set of parameters that yields the best prediction of the reservoir’s performance history.

Simulating the reservoir’s past performance is central to history matching, and the process should ideally help to identify weaknesses in and ways of improving reservoir and model description data.

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The main weakness of history matching is non-uniqueness.

Non-uniqueness arises because more than one combination of reservoir parameters may yield the same predictions.

Of course, this is not physically possible, since the actual reservoir parameters that the model is attempting to describe are unique.

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The data we build into a reservoir simulator, at best, only approximate the actual reservoir parameters.

We therefore cannot expect these data to truly represent the reservoir.

To understand why this is true, we must consider the data sources.

Permeability and porosity data may have come from laboratory core analyses, and scaling up such data to real reservoir conditions inevitably causes a problem

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The reservoir’s geometrical configuration—its shape, internal discontinuities and their descriptions (e.g., fracture and fracture geometry) is inferred from a few discrete locations, and then extrapolated over vast areas.

In light of these facts, we cannot expect these data to give more than an approximation of real conditions.

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In essence, we can describe history matching as a feedback control procedure, analogous to the classical control problem.

With the best estimates of the model parameters in hand, we run the simulator to predict the reservoir history.

We then compare this predicted performance history, using some key history matching parameters, to the actual recorded performance history.

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If we do not see an acceptable match, we adjust the model parameters and attempt a new match.

We continue this iteration process until a “good” match results.

The set of model parameters that achieves this match is the best estimate, and becomes part of the simulator for future predictions.

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The main parameters usually adjusted in history matching are:

Reservoir and fluid data.

Relative permeability function.

Capillary pressure function.

Well data.

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Permeability is the most often used reservoir variable for pressure history matching.

This is partly because permeability is the least well-defined parameter, and at the same time, the one that affects pressure distribution the most.

Porosity data are much better than permeability data and hence are not as widely used as a tuning parameter.

While permeability information from well-test analysis may be better than that obtained from other sources, its reliability depends on the representation accuracy of the well-test model.

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Parameters determines good history Match:

- PRESSURE

- FLOW RATE

- GOR - WOR

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Main Methods of History Matching:

- Linear Programming to minimize errors between calculated and observed values

- Goal Programming

- Non-Linear Programming:

Search Methods

gradient Methods

History Matching by Linear Programming

Problem

Data: Field data consists of I observations in time

0≤t≤tm : d1,d2,….,dI = di which could be , well pressure, WOR, GOR

Unknowns: Reservoir parameters : x1,x2,…,xJ = xj, which could be permeability, porosity, thickness (i.e.J unknowns)

Restrictions: Upper and lower bounds on xi are specified, otherwise assume:

x1(lower) ≤ x1 ≤x1(upper)

x2(lower) ≤ x2 ≤x2(upper)

-----

xJ(lower) ≤ xJ ≤xJ(upper)

Use xj to calculate di = di(calculated)

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Finally the problem is

To determine xi such that

Norm of the error Є = di(observed) - di (calculated)

is minimized

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In order to do this, an objective function is defined based on the history matching parameter.

This objective function is usually a function representing a measure of total error between predicted and observed data.

The strategy is to minimize this error to yield the best match.

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Forecasting

The ultimate goal of any modeling effort is forecasting.

Ensure that a model has the necessary predictive capability before using it as a forecasting tool.

We ensure predictive capability by formulating an accurate representation of the reservoir, properly solving the resulting equations, and proving the validity of the model through history matching.

Once we have taken these steps, the simulator is ready for its primary purpose of forecasting.

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Analysis of results

Must promptly analyze to obtain the information we need.

Although a simulation study could involve many runs planned in advance, we should not think that we have to complete all the runs before beginning our analysis.

It is not a sequential process—we should, in fact, conduct simulation runs and analysis simultaneously.

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Updating

Rarely do we have available all the information that we need at the beginning of a simulation study.

Basic tenet of engineering is using the available information—as inadequate as it may be—to come up with a “best” solution.

This solution is then improved as more information becomes available.

This process called updating. There are two methods of updating in reservoir simulation: updating the reservoir model itself, and revising the simulation approach.

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