History Matching

 The update of a model to fit the actual performance is known as history matching.

Clearly speaking, developing a model that cannot accurately predict the past perfor￾mance of a reservoir within a reasonable engineering tolerance of error is not a good

tool for predicting the future of the same reservoir. To history match a given field

data with material balance equation, we have to state clearly the known parameters to

match and the unknown parameters to tune to get the field historical production data

with minimum tolerance of error and these parameters are given in Table 10.1.

Besides, one of the paramount roles of a reservoir engineer is to forecast the future

production rates from a specific well or a given reservoir. From history, engineers

have formulated several techniques to estimate hydrocarbon reserves and future

performance. The approaches start from volumetric, material balance, decline

curve analysis techniques to sophisticated reservoir simulators. Whatever approach

taken by the engineers to predict production rates and reservoir performance pre￾dictions whether simple or complex method used relies on the history match.

The general approach by the engineer whose production history is already

available, is to determine the rates for the given period of production. The value

calculated is use to validate the actual rates and if there is an agreement, the rate is

assumed to be correct. Thus, it is then used to predict the future production rates. On

the contrary, if there is no agreement between the calculated and the actual rates, the

calculation is repeated by modifying some of the key parameters. This process of

matching the computed rate with the actual observed rate is called history matching.

It therefore implies that history matching is a process of adjusting key properties

of the reservoir model to fit or match the actual historic data. It helps to identify the

weaknesses in the available data, improves the reservoir description and forms basis

for the future performance predictions. One of these parameters that is vital in history

matching, is the aquifer parameters that are not always known. Hence, modification

of one or several of these parameters to obtain an acceptable match within reasonable

engineering tolerance of error or engineering accuracy is history matching (Donnez

2010). Therefore, to complete this chapter, the following textbooks and articles were

reviewed: Aziz & Settary (1980), Crichlow (1977), Kelkar & Godofredo (2002),

Chavent et al. (1973), Chen et al. (1973), Harris (1975), Hirasaki (1973),

Warner et al. (1979), Watkins et al. (1992).

History Matching Plan

The validity of a model should be approach in two phases: pressure match and

saturation match (oil, gas and water rates). The pressure and saturation phases

matche, follows different pattern depending on purpose (experience of the individual

carrying out the study). The simulation follows the same basic steps for the two

phases. These steps include:

• Gather data

• Prepare analysis tools

• Identify key wells/tank

Interpret reservoir behavior from observed data

• Run model

• Compare model results to observed data

• Adjust models parameters

10.3 Mechanics of History Matching

There are several parameters that are varied either singly or collectively to minimize

the differences between the observed data and those calculated data by the simulator.

Modifications are usually made on the following areas as presented by Crichlow

(1977):

• Rock data modifications (permeability, porosity, thickness & saturations)

• Fluid data modifications (compressibility, PVT data & viscosity)

• Relative permeability data

• Shift in relative permeability curve (shift in critical saturation data)

• Individual well completion data (skin effect & bottom hole flowing pressure)

The two fundamental processes which are controllable in history matching are as

follows:

1. The quantity of fluid in the system at any time and its distribution within the

reservoir, and

2. The movement of fluid within the system under existing potential gradients

(Crichlow 1977).

The manipulation of these two processes enables the engineer to modify any of

the earlier-mentioned parameters which are criteria to history matching. It is man￾datory that these modifications of the data reflect good engineering judgment and be

within reasonable limits of conditions existing in that area. History matching is

actually an act and time consuming. This implies that the total time spent on history

matching depends largely on the expertise of the engineer and his familiarity with the

particular reservoir. Here are some of the key variables to consider when conducting

history matching:

• Porosity (local)

• Water Saturation (Global)

• Permeability (Local)

• Gross Thickness (Local)

• Net Thickness (Local)

• kv/kh Ratio (Global


Local?)

• Transmissibility (x/y/z/) (Local)

• Aquifer Connectivity and Size (Regional)

• Pore Volume (Local)

• Fluid Properties (Global)

• Rock Compressibility (Global)

Relative Permeability (Global -regional with Justification)

• Capillary Pressure (Global -regional with justification)

• Mobile Oil Volume (Global or Local?)

• Datum Pressure (Global)

• Original Fluid Contact (Global)

• Well Inflow Parameters (Local)

10.4 Quantification of the Variables Level of Uncertainty

The following variables are often considered to be determinate (low uncertainty):

• Porosity

• Gross thickness

• Net thickness

• Structure (reservoir top/bottom/extent)

• Fluid properties

• Rock compressibility

• Capillary pressure

• Datum pressure

• Original fluid contact

• Production rates

The following variables are often considered to be indeterminate (high

uncertainty):

• Pore volume

• Permeability

• Transmissibility

• Kv/Kh ratio

• Rel. perm. curves

• Aquifer properties

• Mobile oil volumes

• Well inflow parameters

10.5 Pressure Match

Here are two proposed option for pressure match

Option 1

• Run the model under reservoir voidage control

• Examine the overall pressure levels

• Adjust the pore volume/aquifer properties to match overall pressure

Match the well pressures

• Modify local PVs/aquifers to match overall pressures

• Modify local transmissibility to match pressure gradient

Option 2

• Check/Initialization

• Run simulation model

• Adjust Kx for well which cannot meet target rates

• Adjust pore volume and compressibility to match pressure change with time

• Adjust Kv and Tz to capture vertical pressure gradient

• Adjust Kv and Tz to meet areal pressure

• Adjust Tx and Ty at the faults

• Adjust PI’s to meet production allocations

• Iterate

10.6 Saturation Match

Option 1

• Normally attempted once pressures matched

• Most important parameters are relative permeability curves and permeabilities

• Try to explain the reasons for the deviations and act accordingly

• Changes to relative permeability tables should affect the model globally

• Changes to permeabilities should have some physical justification

• Consider the use of well pseudos

• Assumed layer KH allocations may be incorrect (check PLTs, etc.)

Option 2

• Check/Initialization Model

• Run simulation model

• Check overall model water/gas movement(process physics)

• Adjust relative permeability

• Introduce and adjust well’s relative permeabilities (Krs) to match individual well

performance

• Adjust PI’s to match production allocation

• Add or delete completion layers to account for channeling, leaking plugs

• Iterate

Well PI Match

• Not usually matched until pressures and saturations are matched, unless BHP

affects production rates

• Must be matched before using model in prediction mode

• Match FBHP data by modifying KH, skin or PI directly

10.8 Problems with History Matching

• Non uniqueness of accepted match

• Lack of reliable field data

• Available data may be limited

• Errors in simulator can cause a correct set of parameters to yield incorrect result.

10.9 Review Data Affecting STOIIP

Verify that the value of STOIIP calculated by the model is in line with estimated

values by volumetric calculations and material balance. If the calculated value is too

high/low, this is normally due to errors of the following type:

• High/low porosity values (data entry format error)

• Misplace fluid contacts (gas-oil and/or water-oil)

• Inclusion/exclusion of grid blocks that belong or not to the reservoir model.

• High/low values in the capillary pressure curves.

• Errors in net sand thickness.

10.9.1 Problems and Likely Modifications

• Localised high pressure area and localised low pressure area.

– Remedies:

– Modify k to allow case of flow from high pressure region to low pressure

region

– Reduce oil in high pressure region by changing ϕ or h or So or all of them.

– If rock data are varied, there may be need for redigitizing.

• Generally high pressure in the whole system

Remedy:

• Reduce oil in place by reducing porosity in the whole system.

– Discontinuous pressure distribution

Remedy: increase k to smoothen effect

• Model runs out of fluid

Remedy:

– Increase initial fluid saturation. Fluid contacts may be varied.

• No noticeable drawdown in pressure even after considerable withdrawal.

Remedy:

– Error in compressibility entered.

• Sw increase without any injection or influx of water.

Remedy:

– Increase rock compressibility used.

• Problem with matching GOR, WOR

Remedy:

– Modify relative permeability

If simulated GOR > observed GOR, reduce Krg vale in the simulator. The reverse

is true.

If free gas starts flowing early, increase critical gas sat. The reverse is also

the case.

After everything has been done, observed pressures and production are greater

than the model.

Cause:

• Reservoir getting energy from region not defined for example, fluid influx

Remedy:

• Redefine area and model or include aquifer if observed water cut is increasing.

10.10 Methods of History Matching

The method adopted for matching a field’s historic data depends on the engineer in

question. History matching has been improved from manual turning of some param￾eters to a more sophisticated computer aided tool. Today, some engineers still use

manual turning which work well for them rather than the computer aided history

matching.

10.10.1 Manual History Matching

During manual history matching, changing one or two parameters manually by trial￾and error can be tedious and inconsistent with the geological models. To make the

parameters best fit with the simulated and observed data gives considerable uncer￾tainties and does not have the reliability for a longer period.

10.10.2 Automated History Matching

Automated history matching is much faster and requires fewer simulation runs than

manual history matching. It includes a large number of different parameters and

tackles a large number of wells without problems. In manual history matching, one

or two parameters are varied at a time and it would require preliminary analysis first

for tackling the wells.

Besides, automatic history matching could give more reliable results in the case

of complex lithology conditions with considerable heterogeneity. The basic process

in automatic history matching is to start from an initial parameter guess and then

improve it by integrating field data in an automatic loop. In this case, parameter

changes are done by computer programming to minimize the function to show

differences between simulated and observed data. This is called objective function

that includes both model mismatch and data mismatch parts.

10.10.3 Classification of Automatic History Matching

• Deterministic Algorithm

• Stochastic Algorithm

10.10.3.1 Deterministic Algorithm

Deterministic algorithms use traditional optimization approaches and obtain one

local optimum reservoir model within the number of simulation iteration constraints.

In implementation, the gradient of the objective function is calculated and the

direction of the optimization search is then determined (Liang 2007). The gradient

based algorithms minimize the difference between the observed and simulated

measurements which is called the minimization of the objective function that

considered the following loop:

• To run the flow simulator for the complete history matching period,

• To evaluate the cost function,

• To update the static parameters and go back to the first step.

The following are the list of several algorithms that are commonly used for the

basis of gradient based algorithms (Landa 1979; Liang 2007):

• Gradient based algorithms:

– Steepest Descent

– Gauss-Newton (GN)

– Levenberg-Marquardt

– Singular Value Decomposition

– Particle Swarm Optimization

– Conjugate Gradient

– Quasi-Newton

– Limited Memory Broyden Fletcher Goldfarb Shanno (LBFGS)

– Gradual Deformation

10.10.3.2 Stochastic Algorithm

The stochastic algorithm takes considerable amounts of computational time com￾pared to a deterministic algorithm, but due to the rapid development of computer

memory and computation speed, stochastic algorithms are receiving more and more

attention.

Stochastic algorithms have three main direct advantages:

• The stochastic approach generates a number of equal probable reservoir models

and therefore is more suitable to non-unique history matching problems,

• It is straight-forward to quantify the uncertainty of performance forecasting by

using these equal probable model,

• Stochastic algorithms theoretically reach the global optimum.

The following are list of several algorithms that are commonly used on the basis

of non-gradient based stochastic algorithms (Landa 1979; Liang 2007):

• Non-gradient based algorithms:

– Simulated Annealing

– Genetic Algorithm

– Polytope

– Scatter & Tabu Searches

– Neighborhood

– Kalman Filter