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Understanding reservoirs from measured data

Wednesday, November 26, 2014

You might be able to get a better understanding of reservoirs if you only analyse the 'measured data', such as pressure and temperature, use basic physical principles using the conservation laws, and forget about reservoir simulation, said Henk Poulisse

When geologists and reservoir engineers forget that they do not know upfront how the production system works, and what it looks like, it is common to see desperately low ultimate recoveries and low success rates in exploration, said Henk Poulisse, mathematical consultant with Communicative Algebra, and a former Principal Research Mathematician with Shell.

Henk Poulisse is credited with inventing a method for production metering of oil wells, to calculate the flow from individual wells when the fluid streams from different wells are co-mingled upstream of the first flowmeter.

An alternative starting point is to start by understanding that the only information you
know for sure is the measured data, and the only knowledge you have for sure about the production system are the governing physical principles, such as the conservation laws (energy in = energy out).

You can argue that for any running physical system, there are relations among the measured variables which hold over the measured data, in other words when substituting the values of these variables in those relations the result will be zero, and such relations are called vanishing relations, he said. may be algebraic - or differential equations.' 'In order to cope with this type of relations, the measured data is interpreted as the evalu- ations of mathematical objects living in environments in which non-linearity and 'derivation' are natural elements, notably a differential polynomial ring.'

'The algebraic algorithm extracts vanishing relations hidden in the data.'

'The vanishing relations that are extracted from the data depend on the perspective, on the geometry in which the production system is observed.'

Mr Poulisse illustrated this with a case study of a tight gas well.

If you call the cumulative production X, then the production rate is a time derivative of X. 'This means observing it in the symplectic geometry,' he said.

'The extracted vanishing relations may be interpreted as representing equilibrium situations.'

For further analysis, the principle of D'Alembert is applicable in that the vanishing relations can be decomposed into two non-vanishing relations, in this way moving from equilibrium to dynamics.

'The graphical representation of the pairs of non-vanishing relations reveals the dynamical symmetry portrait of the production system, that is symmetry that exists by virtue of the dynamics in the production system,' he said. 'The dynamical symmetry portrait generates a wealth of information about the production system. It gives an expression for the kinetic energy, related to the flow of gas through the reservoir. It gives an expression for the en- ergy push from the reservoir.'

'It gives information about work done by forces not derived from a potential, which is crucial information in relation with hydraulic fracking.

'It gives an equation of motion, a second order, nonlinear differential equation in X - describing the flow of gas through the reservoir.

'This can be used to compute numerical predictions (of the cumulative production and the production rate) and structural predic- tions (changes in the flow state of the production system).'

'The critical point of the equation of motion gives an estimate of the volume-in-place.'

'An abundance of new ideas is obtained by this radical change of view in addressing production problems, and the same holds true for exploration problems,' he said.

For companies and research institutes in the UK there is a good opportunity to explore these ideas further by joining the SAMBa (Statistical and Applied Mathematics at Bath) initiative, he said. This is a project supported by the British government, for the University of Bath to collaborate with industrial partners.

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» Communicative Algebra

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