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 performance 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
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taken by the engineers to predict production rates and reservoir performance predictions 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 mandatory 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
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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 parameters 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 trialand error can be tedious and inconsistent with the geological models. To make the
parameters best fit with the simulated and observed data gives considerable uncertainties 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 compared 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
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