Darcy-scale dynamics of microscopically fluctuating interfaces
Lead Research Organisation:
University of Birmingham
Department Name: School of Mathematics
Abstract
In a recent Government report "UK Oil and Gas - Business and Government Action", it is stressed that "70% of British energy requirements [are] still likely to be met by oil and gas into the 2040s", so that strategically "maximizing domestic supplies of oil and gas [...] leads to increased resilience and security for the UK's energy needs when compared with imports". At the same time, according to the World Energy Outlook Report of 2014, existing methods of secondary oil recovery still leave from 30 to 60% of oil unrecovered when an oilfield is abandoned as 'exhausted' and the exploration moves to a new one. This is both inefficient and environmentally unfriendly. To reach the unrecovered oil and reduce the pace of expansion into new oilfields until renewable power generation becomes an economically viable alternative, it is necessary to develop efficient methods of Enhanced Oil Recovery (EOR).
EOR is focused on recovering oil blobs trapped in the porous rock, known as 'ganglia', that remain stuck after the water-flooding 'secondary recovery stage'. The aim of EOR is to mobilize the ganglia by some additional physical mechanisms. The opposite problem is carbon dioxide sequestration; a process aimed at reducing the pace of climate change. There, it is absolutely essential that carbon dioxide volumes pumped into a porous layer remain there without escaping back into the atmosphere. In each case, the trial-and-error assessment of the efficiency of recovery or storage is prohibitively expensive, so that here theoreticians have a unique role to play by developing a predictive mathematical model that would reliably describe the conditions for mobilization and the dynamics of mobilized trapped fluid volumes in different porous matrices.
The proposed research aims at addressing this dual problem. It has become possible as a result of two recent developments:
- an experimental discovery at Schlumberger Gould Research Centre, Cambridge that the ganglia trapped in a porous rock can be mobilized by fluctuations on the scale of the individual pores which can be generated even when the external forcing is steady
- a new conceptual framework for describing the propagation of wetting fronts, developed by the project's investigators, which for the first time describes highly unusual ('anomalous') regimes of invasion of liquids into porous solids, that were discovered experimentally two decades ago.
The synergy of these two developments opens a way to the first reliable predictive model describing the stability and dynamics of ganglia in porous solids. The potential for the field-transforming changes has been recognized by industry, and Schlumberger, the world's leading supplier of technology solutions for the oil and gas industry, has offered to support the project by releasing its experimental data (conservatively estimated at £715,000 to generate) and the help of its staff to interpret them (£15,000 in the staff time) as well as training of the PDRAs involved in this work.
On the theoretical side, the proposed work addresses a number of fundamental research challenges in the mechanics of multiphase systems such as the translation of the pore-scale information into the properties of a macroscopic (Darcy-scale) model and the modelling of transitions in the topology of the flow domain (breakup of ganglia, their coalescence). Advances here will make a significant methodological impact on mechanics of multiphase system well beyond the study of flows in porous media. The degree of novelty and adventure in the proposed research is best illustrated by the fact that, even knowing the two developments listed above that form the basis of the project, it is still impossible to even qualitatively predict the effect of their synergy. If supported and successful, the project offers a step-change advance in our understanding of multiphase systems and, via Schlumberger, an immediate application of results.
EOR is focused on recovering oil blobs trapped in the porous rock, known as 'ganglia', that remain stuck after the water-flooding 'secondary recovery stage'. The aim of EOR is to mobilize the ganglia by some additional physical mechanisms. The opposite problem is carbon dioxide sequestration; a process aimed at reducing the pace of climate change. There, it is absolutely essential that carbon dioxide volumes pumped into a porous layer remain there without escaping back into the atmosphere. In each case, the trial-and-error assessment of the efficiency of recovery or storage is prohibitively expensive, so that here theoreticians have a unique role to play by developing a predictive mathematical model that would reliably describe the conditions for mobilization and the dynamics of mobilized trapped fluid volumes in different porous matrices.
The proposed research aims at addressing this dual problem. It has become possible as a result of two recent developments:
- an experimental discovery at Schlumberger Gould Research Centre, Cambridge that the ganglia trapped in a porous rock can be mobilized by fluctuations on the scale of the individual pores which can be generated even when the external forcing is steady
- a new conceptual framework for describing the propagation of wetting fronts, developed by the project's investigators, which for the first time describes highly unusual ('anomalous') regimes of invasion of liquids into porous solids, that were discovered experimentally two decades ago.
The synergy of these two developments opens a way to the first reliable predictive model describing the stability and dynamics of ganglia in porous solids. The potential for the field-transforming changes has been recognized by industry, and Schlumberger, the world's leading supplier of technology solutions for the oil and gas industry, has offered to support the project by releasing its experimental data (conservatively estimated at £715,000 to generate) and the help of its staff to interpret them (£15,000 in the staff time) as well as training of the PDRAs involved in this work.
On the theoretical side, the proposed work addresses a number of fundamental research challenges in the mechanics of multiphase systems such as the translation of the pore-scale information into the properties of a macroscopic (Darcy-scale) model and the modelling of transitions in the topology of the flow domain (breakup of ganglia, their coalescence). Advances here will make a significant methodological impact on mechanics of multiphase system well beyond the study of flows in porous media. The degree of novelty and adventure in the proposed research is best illustrated by the fact that, even knowing the two developments listed above that form the basis of the project, it is still impossible to even qualitatively predict the effect of their synergy. If supported and successful, the project offers a step-change advance in our understanding of multiphase systems and, via Schlumberger, an immediate application of results.
Planned Impact
The continuing increase in demand for hydrocarbons both for energy (85% of supply) and for chemical feedstock (15% of supply) combined with gradual depletion of known oil and gas reserves as well as the reduced rate of discovery of new reserves mean that nurturing currently known fields to maximise recovery is becoming the necessity. The situation also has an important environmental dimension as currently, according to estimates, from 30-60% of oil is left unrecovered when an oil field is abandoned as 'exhausted' and the exploration moves to a new one. More efficient oil recovery would help to reduce the pace of this expansion until renewable power generation will be able to take over. All these factors make it necessary and economically viable to develop efficient methods of Enhanced Oil Recovery (EOR).
This project will explore a new mechanism of mobilization of oil that currently remains unrecovered and hence make a major advance in the development of novel EOR strategies, thus addressing the strategic objectives identified in the Government report "UK Oil and Gas - Business and Government Action".
The impact of this project is ensured (a) by the power of combining theoretical modelling, numerical simulation and, importantly, experimental verification of the results with the complementary benefits of academia and industrial environments, and (b) by the direct involvement of Schlumberger, the world's leading supplier of technology, integrated project management and information solutions to customers working in the oil and gas industry worldwide. The technological solutions that are expected to come out of this project will find immediate use via Schlumberger Gould Research Cenre (Cambridge), which contributes £730,000 in terms of information and manpower towards this project.
Thus, in the short term, the project's findings will be implemented into and have an impact via Schlumberger's EOR strategies, with the obtained knowledge becoming part of the computational platforms used to predict and estimate the efficiency of EOR. This will ensure an immediate impact on the oil-recovery companies served by Schlumberger to increase their productivity and efficiency of their operations. For the UK, being world-leading in this direction of research will bring significant economic gains, such as through the creation of high-skilled jobs in industry, as well as societal impact, by optimizing the recovery of our own reserves of oil in the North Sea and thus bolstering our energy security.
Longer term impact will come from the theoretical advances made in the modelling of flow through porous media, which is central to fields as diverse as carbon dioxide sequestration through to understanding the spread of contaminants via groundwater flow, as well as in related strands of multiphase systems, such as the spreading of liquids across rough or inhomogeneous solids. Here, fundamental advances will stimulate research in academia (mathematicians, engineers, physicists, computer scientists, etc) by applying the methods developed during the project's duration to related branches of science. This transfer of knowledge will be facilitated through publications, conference talks and a workshop designed specifically with this aim in mind.
This project will explore a new mechanism of mobilization of oil that currently remains unrecovered and hence make a major advance in the development of novel EOR strategies, thus addressing the strategic objectives identified in the Government report "UK Oil and Gas - Business and Government Action".
The impact of this project is ensured (a) by the power of combining theoretical modelling, numerical simulation and, importantly, experimental verification of the results with the complementary benefits of academia and industrial environments, and (b) by the direct involvement of Schlumberger, the world's leading supplier of technology, integrated project management and information solutions to customers working in the oil and gas industry worldwide. The technological solutions that are expected to come out of this project will find immediate use via Schlumberger Gould Research Cenre (Cambridge), which contributes £730,000 in terms of information and manpower towards this project.
Thus, in the short term, the project's findings will be implemented into and have an impact via Schlumberger's EOR strategies, with the obtained knowledge becoming part of the computational platforms used to predict and estimate the efficiency of EOR. This will ensure an immediate impact on the oil-recovery companies served by Schlumberger to increase their productivity and efficiency of their operations. For the UK, being world-leading in this direction of research will bring significant economic gains, such as through the creation of high-skilled jobs in industry, as well as societal impact, by optimizing the recovery of our own reserves of oil in the North Sea and thus bolstering our energy security.
Longer term impact will come from the theoretical advances made in the modelling of flow through porous media, which is central to fields as diverse as carbon dioxide sequestration through to understanding the spread of contaminants via groundwater flow, as well as in related strands of multiphase systems, such as the spreading of liquids across rough or inhomogeneous solids. Here, fundamental advances will stimulate research in academia (mathematicians, engineers, physicists, computer scientists, etc) by applying the methods developed during the project's duration to related branches of science. This transfer of knowledge will be facilitated through publications, conference talks and a workshop designed specifically with this aim in mind.
Organisations
Publications
Belozerov AA
(2022)
The onset of solidification: From interface formation to the Stefan regime.
in The Journal of chemical physics
Shikhmurzaev Y
(2017)
Darcy's law for two-dimensional flows: Singularities at corners and a new class of models
in AIChE Journal
| Description | It has been found that in essentially two-dimensional flows, like flows past an edge, the classic Darcy model gives rise to a singularity in the flow field, which, unlike similar singularities in the Fourier model of heat conduction and the Fick model for diffusion, is unphysical. In the latter, a mathematically similar singularity is a 'price' for a simplification of the flow geometry whilst in the case of the Darcy model it shows a flaw in the model itself. In practical terms, the singularity does not allow one to consider two-phase flows in porous media in the situation where the flow domain is confined by non-smooth boundaries. By analysing the nature of this singularity it has been shown that the only justifiable way of removing it and generalize the Darcy model is by taking into account the dependence of permeability of the porous matrix on the flow, more specifically, on the curvature of the flow's streamlines. This applies to both homogeneous and inhomogeneous porous matrices. Then, in 2D flows the unphysical singularity is removed whilst for unidirectional flows, for which the classic Darcy model is well verified experimentally, it remains intact. This approach, unique in the scientific literature, introduces an essentially new class of mathematical models where the transport coefficient (permeability) is intrinsically linked with the flow and has to be found simultaneously with it. Mathematically, the new class of models leads to mathematical problems which fall outside existing classification of problems with partial differential equations and hence require both (a) an analysis of how to formulate problems for these PDEs and (b) how to solve the resultant strongly nonlinear problems numerically. It has been shown, rather paradoxically, that, although the system of PDE implementing the model formally has a higher order that the Darcy model (which, in the simplest case, boils down to Laplace's equation), it requires the same boundary conditions as the latter. The development of a numerical method to solve the model had to overcome a major difficulty arising from the fact that, as follows from the physical essence of the model, the permeability depends on the absolute value of the curvature of the streamlines while implicit numerical methods are unable to deal with absolute values whilst explicit methods for this highly nonlinear problem are unstable. Nevertheless, an efficient numerical method has been developed and tested. The first results obtained using the developed method show that the classical Darcy model invariably overpredicts the flow rate. This fact has profound implications for the potential end-users of the modelling as even an estimate of the error could be used to correct predictions and estimates, say, for oil reservoir exploration. The impact of COVID-19 has slowed down exploration of the model and hindered interaction with Schlumberger, so a correction to the original research plans had to be made. |
| Exploitation Route | An essentially new class of models introduced in the course of this project opens an entirely new direction in the mathematical modelling. At the moment, it is difficult even to predict where this outcome could lead once/if it is digested by the scientific community. The new numerical method developed to solve the mathematical problems arising in the use of the new models can have even wider applications as it allows one to solve problems with PDEs that fall outside existing classifications of PDEs. |
| Sectors | Digital/Communication/Information Technologies (including Software),Education,Energy,Other |
| Description | The qualitative outcome of this research has been reported to Schlumberger, the world's leading provide of the oil and gas recovery technology. The fundings indicated that the existing modelsused to describe the oil flow overpredict the flow rate and hence one should make a correction to the estimates of the unrecovered oil reserves. At the moment, this impact is impossible to quantify as there is a considerable lag between the new theoretical findings and their material implementation in technological processes. |
| First Year Of Impact | 2022 |
| Sector | Education,Energy |
| Impact Types | Economic |
| Description | A presentation at the 72nd Annual Meeting of the American |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | This talk presented a new numerical method developed for a new class of problems emerging in the singularity-free modelling of two-dimensional Darcy flows. The method is highly original as the kind of problem it considers has never been dealt with before, neither analytically nor numerically. Although only some preliminary results have been reported, the talk generated considerable interest and was followed by many questions. |
| Year(s) Of Engagement Activity | 2019 |
| Description | A webinar at Institute of Mechanics |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | A webinar was given with the Institute of Mechanics, Moscow State University as the host and an international audience. The purpose of the webinar was to inform the practitioners of the new results obtained in the field and seek their feedback in terms of critical approbation and the ways of further development. |
| Year(s) Of Engagement Activity | 2022 |
| Description | Presentation at Darmstadt |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Professional Practitioners |
| Results and Impact | A presentation of the first results obtained in the framework of this project was given at the Collaborative Research Center (TU Darmstadt, Germany). The purpose was to introduce theoreticians and experimentalists, as well as graduate students, to the new approach to the modelling of flows in porous media for 2D and 3D flows. The presentation seems to have generated considerable interest as a fresh idea in a classical research area. |
| Year(s) Of Engagement Activity | 2018 |
| Description | Talk at Lincoln |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | National |
| Primary Audience | Professional Practitioners |
| Results and Impact | A talk was given at University of Lincoln covering a range of topics, including the new ideas in the modelling of flows in porous media and applications of the interface formation model to the spinning disc atomisation process. The talk engaged a new audience and generated a lively discussion. |
| Year(s) Of Engagement Activity | 2018 |
| URL | https://comp-physics-lincoln.org/2018/10/26/yulii-d-shikhmurzaev-visiting/ |
| Description | Webinar at Schlumberger |
| Form Of Engagement Activity | A talk or presentation |
| Part Of Official Scheme? | No |
| Geographic Reach | International |
| Primary Audience | Industry/Business |
| Results and Impact | The webinar was aimed at Special Interest Groups (SIGs) within Schlumberger Corporation and its objetive was to introduce a new mathematical model regularizing the singularities present in the classical Darcy model that forms the basis of Schlumberger's (and other companies) modelling platforms and to describe a numericalgorithm developed to solve problems formulated in the framework of this model. Importantly, it has been shown that for all non-unidirectional flows, even those where Darcy's model exhibits no singularities, the Darcy model overpredicts the flow rate. This implies that assessments made on the basis of Darcy's model err on one side and need to be corrected. The webinar was followed by a discussion and its recording was placed on Schlumberger's intranet for internal use. Subsequently, a number of questions were received (via the webinar's coordinator) and answered. |
| Year(s) Of Engagement Activity | 2022 |