The field onto which AHM was applied showed that relatively modest changes were required to obtain good history match. SPE paper 74712, shows the application of AHM with streamlines; first application with streamlines alone and then with AHM. The difference in results is quite noticeable.
Two-Step Inversion Method
The two step-inversion method involves the modification of permeability distribution at streamline and based on simulated results and field data for water cut, pressure drop and flow rate. Using this process, reservoir heterogeneity capturing is attempted; this is done by matching fractional flow curve through manipulation of permeability field. The second step involves mapping the modification performed to the streamline permeability on to the grid blocks. Flow simulations are performed to check match, in which iterations are involved if desired match is not achieved.
The advantage of using the two-step inversion method is that when multi-phase displacement is considered, each streamline contributes a small amount to the fractional flow curve at the producer. Order the streamlines with respect to their breakthrough times, various sections of fractional flow curve can be related to breakthrough of individual streamlines. If there happens to be a mismatch between the simulated fractional flow curve and the field water curve, the streamline responsible for this difference is inferred, rather than going to the grid block and changing parameters in an ad-hoc manner.
Another advantage of this method compared to the AHM method is that it takes into account the error of the simulation results compared to the field data, therefore uses the objective function to minimise the error.
The draw back with this method is that it only works well for flow with unfavourable mobility ratios in heterogeneous reservoirs. Therefore it cannot account for changes in heterogeneity as the AHM method with the use of DP coefficient can.
Black-oil model
The method used in the SPE paper 66388, uses a black oil simulator for the purpose of history matching. The method here is a slight extension to the ‘Two-Step Inversion’ method; work performed by ‘Wang Kovscek’. The difference with this method compared to the one discussed previously is that it does not assume the fluid will be incompressible, rather it assumes compressibility and a pressure equation for it is solved. Also, a mass conservation equation is solved along each streamline that accounts for changes in pressure and total velocity.
For the example cases mentioned in SPE paper 66388 for the implementation of the black-oil model, it shows that match obtained was reasonable. The difference between this model and the pervious two is that it takes into account the effect if gravity and compressibility, which can have noticeable effects.
Forward simulations tend to ignore vital physics of the reservoir and although it may yield a good match, the predicted reservoir description may not be close to reality. Ignoring compressibility and gravity may give desired results, but future predictions will be worse than when correct physics is used. This is clearly shown in the examples used the work conducted by ‘Blunt and Agarwal’.
In traditional flow simulations, the flow is considered as a tracer, hence, tracer-like-flow assumption. If this is assumed, there will be no improvements on the iteration results after a few iterations and incorporating and type of production data will just add to the complexity.
With some development, the black-oil model has the potential of history matching production/water-cut data very well. Although its application on the synthetic example discussed in SPE paper 66388 is not very convincing, the application on a real field was different. In this case, the black-oil model allows for a relatively good match to be achieved.
Exact Sensitivity Coefficient Method
This method greatly reduces the amount of computational work for a history match. It also takes into account change in boundary conditions for two phase flow and non-unit mobility ratios, which the two-step inversion method does not.
The history matching method is based on gradients and on the minimisation of the objective function that quantifies the discrepancy between simulated and observed data.
The use of exact sensitivity coefficients is the most complex of the methods when it comes to history matching. The permeability and its initial saturation are considered. The pressure and velocity are also computed.
Another parameter which is calculated is the ‘gradients’ of production data, which is computed with respect to parameterisation of spatial distribution of permeabilities. This is used in inverse problems to modify the match between simulated and observed.
Due to the objective function, pressure changes, which are related to permeability, can be made to reduce the discrepancy, thus enabling better history match.
Geo-statistical Approach
The advantage of the geo-statistical approach is that it avoids the calculation of single grid block sensitivity coefficients; instead it serially perturbs the effective permeabilities of the streamlines.
Geological information is integrated within a consistent framework. Also, the algorithms spread the streamline effective permeability perturbation to the grid block level, thus accounting for any given histogram of the grid block permeability.
The methodology used in work by ‘Wang & Kovscek’, is used here; two-step inversion method is also used here. The improvement made by geo-statistical method is such that it updates the permeability field accounting for the proposed change in effective permeability consistent with model variogram and histogram of the grid cell permeability.
With the ‘Two-Step Inversion’ method the problem comes when honouring the harmonic averages; this has been deemed as an ill-poised problem. The geo-statistical approach to this is an iterative solution by means of Gauss-Marker random fields (GMrF) for conditioning to these harmonic averages. Also, the method works well for unit and unfavourable mobility ratios.
The disadvantage with this method is that because streamlines are being used, the method will work best for cases of no or slight compressibility, no gravity and capillary forces. And frequently changing well conditions or changes in heterogeneity are hard to accommodate, which the ‘Exact Sensitivity Coefficients’ and the AHM technique are able to do.
Generalised Travel Time Inversion
Out of all the methods discussed in this report, the ‘generalised travel time inversion’ method has to be the most robust and efficient. It is able to account for changing field conditions; which includes change in heterogeneity, changes in drilling pattern and also takes into account of the different times at which production may begin.
Sensitivities are used in this method similar to that of the use of ‘Exact Sensitivity Coefficient’; they are both related to production data response. The sensitivities used in this area are more uniform between wells, which prevents over correction in near well bore regions.
It has been stated in the literature that the use of amplitude matching of production response or water breakthrough is a long tedious process and is considered to be inefficient when it comes to rapid history matching. The amplitudes are used in the generalised travel time inversion method, but in a different way; it being non-linear, match can be achieved with relatively little error.
The applications of this method have proved to be successful; where matches were considered unsatisfactory the method have improved it a great deal, and with history matches that were initially good, further improvements have been made to it. This can be seen in the application on the Goldsmiths Field of SPE literature 71333.
Which Method to Use Now?
For the methods discussed above, advantages and disadvantages have been given. The most promising of the six methods are ‘Black-Oil’ method and the ‘Generalised Travel Time Inversion’ method. In terms of matching, they both perform the job equally well. The black-oil method uses three-phase compressibility model and the geological parameters and anisotropy can all be honoured and modified as it is related to TOF. The model takes into account the gravitational and the compressibility effects on production performance and can give accurate estimates rather than overestimated ones.
It is also arguable that the AHM model can be included in the category of the ‘most promising method’. It too takes into account the compressibility of the fluid and recognises three-phase flow. As of the black-oil method, geological parameters and anisotropy can all be honoured by the AHM. For the synthetic case, the match was not as good as the match performed by the black-oil model and Generalised travel time inversion method for the synthetic cases, which means that for certain field conditions the AHM model will not work. The synthetic case worked on by the AHM model was not of a complicated one; the aquifer present in the model was replaced by water injector wells.
Going back to the Black-oil and the Generalised Travel Time Inversion method, they both work equally well. The amplitude misfits in the generalised travel time inversion method reduce per iterative step, at the same time water cut misfit is also reduced. The black-oil model does not use amplitude matching method, but as the number iterations are increased, the history match is improved; the same can be said about the predictions.
If the choice had to be between the black-oil method and the generalised travel time inversion method, then I would choose the inversion method for reason stated above. The black-oil method has a lot of potential, if it was to be developed further.
Issues Concerning Future Use
The examples used in the literature (that’s all of them) have been especially picked for the use of the technique used. Issues that concern the use of streamlines in history matching are as follows:
Noisy data
Data available for history matching is generally quite noisy, this leads to further discrepancy between the match. Noisy data must be filtered and processed to obtain a good match. Actual production data is never as smooth as that of synthetic examples.
Having an accurate reservoir description
To begin with most of the reservoir description data used will be quite old and a lot of inconsistencies will be present, which means that it will be up to the simulation engineer to input processed data.
Matches obtained are non-unique
Due to the two points mentioned above the match obtained will not of a unique one. It may have a similar profile as the initial production/water-cut profile but the properties and production responses have been modified to achieve this result and may not represent the actual properties of the reservoir.
At present the method discussed in the paper have not been put into real use in industry; as the techniques are very complex and they have not been applied to many fields except for the example case, which as stated earlier has been especially chosen for that purpose and may not produce desired results for other field. The challenge is to use these techniques for applications to more field and see how effective they are.
The question that faces us now is can it be used as a routine tool? The answer if one wants can be yes. Different people will use different methods depending on the degree of accuracy wanted and how much time they are willing to spend on it. The generalised travel time inversion method is able to perform matches in a relatively short period of time with good deal of accuracy. Again, emphasis has to be placed on the matter of the methods not being tested with other wells. If the test can prove that the method(s) can work for any given field condition then it may be seen as a routine tool.
