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Journal articles on the topic 'Mathematical modelling of oil recovery'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Perkins, Greg. "Mathematical modelling of in situ combustion and gasification." Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 232, no. 1 (August 2, 2017): 56–73. http://dx.doi.org/10.1177/0957650917721595.

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The total worldwide resources of oil sands, heavy oil, oil shale and coal far exceed those of conventional light oil. In situ combustion and gasification are techniques that can potentially recover the energy from these unconventional hydrocarbon resources. In situ combustion can be used to produce oil, especially viscous and immobile crudes, by heating the oil and reducing the viscosity of the hydrocarbon liquids allowing them to flow to production wells. In situ gasification can be used to convert deep carbonaceous materials into synthesis gas which can be used at surface for power generation and petrochemical applications. While both in situ combustion for oil recovery and in situ gasification of coal have been developed and demonstrated over many decades, the commercial applications of these techniques have been limited to date. There are many physical processes occurring during in situ combustion, including multi-phase flow, heat and mass transfer, chemical reactions in porous media and geomechanics. A key tool in analysing and optimising the technologies involves using numerical models to simulate the processes. This paper presents a brief review of mathematical modelling of in situ combustion and gasification with an emphasis on developing a generalised framework and describing some of the key challenges and opportunities.

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MILOVANOVICH, Ekaterina V., and Svetlana N. MAKSIMOVA (KUZNETSOVA). "MODELLING OF MICROBIOLOGICAL METHOD OF OIL RECOVERY IMPROVEMENT." Periódico Tchê Química 14, no. 27 (January 20, 2017): 56–64. http://dx.doi.org/10.52571/ptq.v14.n27.2017.56_periodico27_pgs_56_64.pdf.

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The problem of energy supply has been one of the most pressing issues for the humanity at all times. Oil is one of the most desired sources of energy. However, oil reserves are being depleted, and substantial amounts of subterranean residual oil cannot be extracted with the use of traditional methods, therefore requiring implementation of new technologies. The current paper suggests two mathematical models aimed to describe and predict implications of microbiological method of oil recovery improvement based on the currently available data, as well as to assess the efficiency of this method. The first model consists of partial differential equations that describe the process of expansion of microbial population through oil formation. The second model includes ordinary differential equations, describing growth and metabolism of bacterial cultures within the bottom-hole zone of the production well. The models were studied with the use of numerical grid and Euler methods. The modeling parameters were evaluated using the least squares method. The current paper includes the results of calculations performed on basis of the proposed models. Distribution profiles of the bacterial population and the metabolic products along the reservoir were obtained and studied; provided recommendations for practical implementation of the microbiological method.

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3

Pathak, Shreekant, and Twinkle Singh. "A mathematical modelling of imbibition phenomenon in inclined homogenous porous media during oil recovery process." Perspectives in Science 8 (September 2016): 183–86. http://dx.doi.org/10.1016/j.pisc.2016.04.028.

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4

Islam, M. R., and A. Chakma. "Mathematical modelling of enhanced oil recovery by alkali solutions in the presence of cosurfactant and polymer." Journal of Petroleum Science and Engineering 5, no. 2 (February 1991): 105–26. http://dx.doi.org/10.1016/0920-4105(91)90061-q.

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5

Patel, Kinjal R., Manoj N. Mehta, and Twinkle R. Patel. "A mathematical model of imbibition phenomenon in heterogeneous porous media during secondary oil recovery process." Applied Mathematical Modelling 37, no. 5 (March 2013): 2933–42. http://dx.doi.org/10.1016/j.apm.2012.06.015.

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6

Susanti, Ari Diana, Wahyudi Budi Sediawan, Sang Kompiang Wirawan, and Budhijanto Budhijanto. "Mathematical Modelling of Micronutrient Recovery from Vegetable Oil by Silica-based Adsorption: Vitamin E from Palm Fatty Acid Distillate." Equilibrium Journal of Chemical Engineering 1, no. 1 (January 10, 2017): 15. http://dx.doi.org/10.20961/equilibrium.v1i1.40363.

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Mathematical modelling on kinetics of batch adsorption of vitamin E separation from palm fatty acid distillate (PFAD) has been set-up and then applied for literature experimental data. Since the sizes of adsorbent particles used are usually relatively small, the concentration in the particles is assumed to be uniform. Hence, the adsorption rate is controlled by the rate of solute mass transfer from the bulk fluid to the surface of particles. In this model, the rate of mass transfer is assumed to be proportional to the concentration deviation from the equilibrium state. Meanwhile, the equilibrium models applied were coefficient distribution, Freundlich, and Langmuir with the values of the parameters obtained from literature data. It turned out that the model set-up can quantitatively describe the experimental kinetics data from literature. The value of mass transfer coefficient per unit adsorbent mass (kca) is obtained by curve fitting. It is also observed that the model proposed quantitatively describes the batch adsorption process well. The three equilibrium models applied are suitable for the mathematical modelling. Adjustment of the values of equilibrium isotherm parameters from literature significantly improves the accuracy of the model.

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7

Gołąbek, Andrzej, Wiesław Szott, Piotr Łętkowski, and Jerzy Stopa. "Similitude Analysis of Experiment and Modelling of Immiscible Displacement Effects with Scaling and Dimensional Approach." Energies 13, no. 19 (October 7, 2020): 5224. http://dx.doi.org/10.3390/en13195224.

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This paper presents the use of scaling and dimensional analysis to assess the viability of conventional modelling of immiscible displacement occurring when water is injected into the oil-saturated, porous rock—a conventional secondary oil-recovery method. A brief description of the laboratory tests of oil displacement with water performed on long core sets taken from wells operating on a Polish oil reservoir was presented. A dimensionless product generator based on dimensional analysis and Buckingham Π theorem was used to generate all possible combinatorial sets of dimensionless products for physical variables describing the phenomenon. The mathematical model of the phenomenon was transformed to its dimensionless form, using a selected set of the products. The results of the laboratory tests were analyzed as functions of the products. Statistically verified quantities describing both dependent and independent experiment variables were subject to a regression analysis to study dependencies of the experimental results upon selected dimensionless products. The degrees of the dependencies were determined and compared with the model coefficients. The conclusions are drawn for the purposes of model application to correctly describe the laboratory and, consequently, field scale processes of immiscible oil displacement by water.

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8

Lambert, Wanderson, and Maurício C. P. Loures. "A mathematical study on the viability of the geochemical flow for an enhanced oil recovery: A simplified model." Applied Mathematical Modelling 75 (November 2019): 678–91. http://dx.doi.org/10.1016/j.apm.2019.04.061.

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9

Lu, Yun-guang, Changfeng Xue, and Christian Klingenberg. "Global entropy solutions for systems modelling polymer flooding in enhanced oil recovery." Applied Mathematics Letters 122 (December 2021): 107495. http://dx.doi.org/10.1016/j.aml.2021.107495.

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10

Semanov, G. N., A. N. Gutnik, S. N. Zatsepa, A. A. Ivchenko, V. V. Solbakov, V. V. Stanovoy, and A. A. Shivaev. "Net environmental benefit analysis — a tool of decision-making at oil spill response." Arctic: Ecology and Economy, no. 1(25) (March 2017): 47–58. http://dx.doi.org/10.25283/2223-4594-2017-1-47-58.

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Development of oilfields started in Arctic requires adequate response preparedness to potential oil spills. Mechanical recovery due to specific conditions of Arctic has a lot of limitation in application and cannot prevent pollution of Special protected areas (SPA). It is necessary to consider application of dispersants and in situ burning (ISB). Oil spill dispersants are mixtures of nontoxic surface active agents in organic solvent, specifically formulated to enhance the natural dispersion of oil into the sea water column thus enhancing the biodegradation processes. Dispersed oil is practically non adhesive to feather of birds and hair of mammals. The treatment of oil with dispersants requires a cautious strategy in making decisions. It can be achieved by usage of special tool –Net Environmental Benefit Analysis (NEBA) procedures. The decision of dispersants application should be based on the following comparison: “What would be the impact of the pollution when treated with dispersant and when non treated with dispersant?” The NEBA should consider the behaviour of the treated non-treated oil, assess consequently the different resources which will be concerned either by the treated oil or by the surface film oil, assess the sensitivity of the different resources at concern towards the dispersed oil and toward the floating oil film. These analyses assist decision makers when considering whether or not the use of dispersants is appropriate to minimize the environmental/economic damage. This article describes the experience of NEBA application to substantiate decisions how to respond to potential oil spills at the sites on Aniva bay of Sakhalin-2 project at different oil spills scenarios. It was used incremental approach to choose them. Based on sensitivity maps, information about level of impact dispersed and floating oil on bioresources and results of mathematical modelling efficacy of different response methods application: monitoring (no actions to recover spilt oil), mechanical recovery and mechanical recovery together with dispersants application it was shown that SPA can be protected from pollution in most scenarios only in case of dispersants application. Amount of oil stranded on shore in case of application of response method was used as criteria of efficacy of method application level of damage.

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11

Filimonov, Sergey, Alexander Dekterev, and Andrey Minakov. "Computational modelling of flow in a microporous environment of a natural reservoir with consideration of the topological structure." E3S Web of Conferences 219 (2020): 01007. http://dx.doi.org/10.1051/e3sconf/202021901007.

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The article presents the initial stage of developing a hybrid mathematical model for describing the recovery of oil from a natural sand reservoir. The hybrid model means that part of the computational domain (microchannel structure in the space between particles) is calculated by one- dimensional models is based on the hydraulic circuit theory, and another part (large cracks and caverns) is calculated by computational fluid dynamics methods (CFD). The article also describes a unique algorithm for building a network model based on preliminary CFD calculation. The last section of the article presentation compares of results of calculation CFD and network models.

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12

Sivasankar, P., and G. Suresh Kumar. "Influence of pH on dynamics of microbial enhanced oil recovery processes using biosurfactant producing Pseudomonas putida: Mathematical modelling and numerical simulation." Bioresource Technology 224 (January 2017): 498–508. http://dx.doi.org/10.1016/j.biortech.2016.10.091.

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13

Druetta, P., and F. Picchioni. "Influence of the polymer degradation on enhanced oil recovery processes." Applied Mathematical Modelling 69 (May 2019): 142–63. http://dx.doi.org/10.1016/j.apm.2018.11.051.

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14

Vabishchevich, Petr, and Maria Vasil'eva. "ITERATIVE SOLUTION OF THE PRESSURE PROBLEM FOR THE MULTIPHASE FILTRATION." Mathematical Modelling and Analysis 17, no. 4 (September 1, 2012): 532–48. http://dx.doi.org/10.3846/13926292.2012.706655.

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Applied problems of oil and gas recovery are studied numerically using the mathematical models of multiphase fluid flows in porous media. The basic model includes the continuity equations and the Darcy laws for each phase, as well as the algebraic expression for the sum of saturations. Primary computational algorithms are implemented for such problems using the pressure equation. In this paper, we highlight the basic properties of the pressure problem and discuss the necessity of their fulfillment at the discrete level. The resulting elliptic problem for the pressure equation is characterized by a non-selfadjoint operator. Possibilities of approximate solving the elliptic problem are considered using the iterative methods. Special attention is given to the numerical algorithms for calculating the pressure on parallel computers.

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15

Li, Shurong, Yang Lei, and Xiaodong Zhang. "Optimal control of polymer flooding for enhanced oil recovery." International Journal of Modelling, Identification and Control 18, no. 2 (2013): 89. http://dx.doi.org/10.1504/ijmic.2013.052325.

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16

Carasso, C., and G. Pasa. "An optimal viscosity profile in the secondary oil recovery." ESAIM: Mathematical Modelling and Numerical Analysis 32, no. 2 (1998): 211–21. http://dx.doi.org/10.1051/m2an/1998320202111.

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17

Gagneux, Gérard, and Monique Madaune-Tort. "Three-dimensional solutions of nonlinear degenerate diffusion-convection processes." European Journal of Applied Mathematics 2, no. 2 (June 1991): 171–87. http://dx.doi.org/10.1017/s0956792500000462.

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The main objective of this work is to present, for practical use, some original results about several qualitative properties of the solutions of a large class of degenerate diffusion-convection equations arising from fluid mechanics. Current interest in models of the simultaneous motion of two immiscible incompressible liquids results from its significance for many applied fields such as, for instance, the theoretical modelling of oil reservoirs where the pores of a threedimensional porous medium contain some hydrocarbon component (oil). In secondary recovery, a second inexpensive fluid (water) is injected into the porous medium in order to push the oil towards the producing wells.

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18

Eneotu, M., and P. Grassia. "Modelling foam improved oil recovery: towards a formulation of pressure-driven growth with flow reversal." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2244 (December 2020): 20200573. http://dx.doi.org/10.1098/rspa.2020.0573.

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The pressure-driven growth model that describes the two-dimensional (2-D) propagation of a foam through an oil reservoir is considered as a model for surfactant-alternating-gas improved oil recovery. The model assumes a region of low mobility, finely textured foam at the foam front where injected gas meets liquid. The net pressure driving the foam is assumed to reduce suddenly at a specific time. Parts of the foam front, deep down near the bottom of the front, must then backtrack, reversing their flow direction. Equations for one-dimensional fractional flow, underlying 2-D pressure-driven growth, are solved via the method of characteristics. In a diagram of position versus time, the backtracking front has a complex double fan structure, with two distinct characteristic fans interacting. One of these characteristic fans is a reflection of a fan already present in forward flow mode. The second fan however only appears upon flow reversal. Both fans contribute to the flow’s Darcy pressure drop, the balance of the pressure drop shifting over time from the first fan to the second. The implications for 2-D pressure-driven growth are that the foam front has even lower mobility in reverse flow mode than it had in the original forward flow case.

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19

Chakraborty, Susmit, Suresh Kumar Govindarajan, and Sathyanarayana N. Gummadi. "Influence of crucial reservoir properties and microbial kinetic parameters on enhanced oil recovery by microbial flooding under nonisothermal conditions: Mathematical modelling and numerical simulation." Journal of Petroleum Science and Engineering 195 (December 2020): 107831. http://dx.doi.org/10.1016/j.petrol.2020.107831.

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20

Lyupa, A. A., D. N. Morozov, M. A. Trapeznikova, B. N. Chetverushkin, N. G. Churbanova, and S. V. Lemeshevsky. "Simulation of Oil Recovery Processes with the Employment of High-Performance Computing Systems." Mathematical Models and Computer Simulations 8, no. 2 (March 2016): 129–34. http://dx.doi.org/10.1134/s2070048216020095.

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21

Druetta, P., and F. Picchioni. "Influence of the polymer properties and numerical schemes on tertiary oil recovery processes." Computers & Mathematics with Applications 79, no. 4 (February 2020): 1094–110. http://dx.doi.org/10.1016/j.camwa.2019.08.028.

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22

Sorbie, K. S., A. Y. Al Ghafri, A. Skauge, and E. J. Mackay. "On the Modelling of Immiscible Viscous Fingering in Two-Phase Flow in Porous Media." Transport in Porous Media 135, no. 2 (September 29, 2020): 331–59. http://dx.doi.org/10.1007/s11242-020-01479-w.

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Abstract Viscous fingering in porous media is an instability which occurs when a low-viscosity injected fluid displaces a much more viscous resident fluid, under miscible or immiscible conditions. Immiscible viscous fingering is more complex and has been found to be difficult to simulate numerically and is the main focus of this paper. Many researchers have identified the source of the problem of simulating realistic immiscible fingering as being in the numerics of the process, and a large number of studies have appeared applying high-order numerical schemes to the problem with some limited success. We believe that this view is incorrect and that the solution to the problem of modelling immiscible viscous fingering lies in the physics and related mathematical formulation of the problem. At the heart of our approach is what we describe as the resolution of the “M-paradox”, where M is the mobility ratio, as explained below. In this paper, we present a new 4-stage approach to the modelling of realistic two-phase immiscible viscous fingering by (1) formulating the problem based on the experimentally observed fractional flows in the fingers, which we denote as $$ f_{\rm w}^{*} $$ f w ∗ , and which is the chosen simulation input; (2) from the infinite choice of relative permeability (RP) functions, $$ k_{\rm rw}^{*} $$ k rw ∗ and $$ k_{\rm ro}^{*} $$ k ro ∗ , which yield the same $$ f_{\rm w}^{*} $$ f w ∗ , we choose the set which maximises the total mobility function, $$ \lambda_{\text{T}}^{{}} $$ λ T (where $$ \lambda_{\text{T}}^{{}} = \lambda_{\text{o}}^{{}} + \lambda_{\text{w}}^{{}} $$ λ T = λ o + λ w ), i.e. minimises the pressure drop across the fingering system; (3) the permeability structure of the heterogeneous domain (the porous medium) is then chosen based on a random correlated field (RCF) in this case; and finally, (4) using a sufficiently fine numerical grid, but with simple transport numerics. Using our approach, realistic immiscible fingering can be simulated using elementary numerical methods (e.g. single-point upstreaming) for the solution of the two-phase fluid transport equations. The method is illustrated by simulating the type of immiscible viscous fingering observed in many experiments in 2D slabs of rock where water displaces very viscous oil where the oil/water viscosity ratio is $$ (\mu_{\text{o}} /\mu_{\text{w}} ) = 1600 $$ ( μ o / μ w ) = 1600 . Simulations are presented for two example cases, for different levels of water saturation in the main viscous finger (i.e. for 2 different underlying $$ f_{\rm w}^{*} $$ f w ∗ functions) produce very realistic fingering patterns which are qualitatively similar to observations in several respects, as discussed. Additional simulations of tertiary polymer flooding are also presented for which good experimental data are available for displacements in 2D rock slabs (Skauge et al., in: Presented at SPE Improved Oil Recovery Symposium, 14–18 April, Tulsa, Oklahoma, USA, SPE-154292-MS, 2012. 10.2118/154292-MS, EAGE 17th European Symposium on Improved Oil Recovery, St. Petersburg, Russia, 2013; Vik et al., in: Presented at SPE Europec featured at 80th EAGE Conference and Exhibition, Copenhagen, Denmark, SPE-190866-MS, 2018. 10.2118/190866-MS). The finger patterns for the polymer displacements and the magnitude and timing of the oil displacement response show excellent qualitative agreement with experiment, and indeed, they fully explain the observations in terms of an enhanced viscous crossflow mechanism (Sorbie and Skauge, in: Proceedings of the EAGE 20th Symposium on IOR, Pau, France, 2019). As a sensitivity, we also present some example results where the adjusted fractional flow ($$ f_{\rm w}^{*} $$ f w ∗ ) can give a chosen frontal shock saturation, $$ S_{\rm wf}^{*} $$ S wf ∗ , but at different frontal mobility ratios, $$ M(S_{\rm wf}^{*} ) $$ M ( S wf ∗ ) . Finally, two tests on the robustness of the method are presented on the effect of both rescaling the permeability field and on grid coarsening. It is demonstrated that our approach is very robust to both permeability field rescaling, i.e. where the (kmax/kmin) ratio in the RCF goes from 100 to 3, and also under numerical grid coarsening.

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23

Christov, Ivan C., and Hari S. Viswanathan. "Introduction: energy and the subsurface." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2078 (October 13, 2016): 20150430. http://dx.doi.org/10.1098/rsta.2015.0430.

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This theme issue covers topics at the forefront of scientific research on energy and the subsurface, ranging from carbon dioxide (CO 2 ) sequestration to the recovery of unconventional shale oil and gas resources through hydraulic fracturing. As such, the goal of this theme issue is to have an impact on the scientific community, broadly, by providing a self-contained collection of articles contributing to and reviewing the state-of-the-art of the field. This collection of articles could be used, for example, to set the next generation of research directions, while also being useful as a self-study guide for those interested in entering the field. Review articles are included on the topics of hydraulic fracturing as a multiscale problem, numerical modelling of hydraulic fracture propagation, the role of computational sciences in the upstream oil and gas industry and chemohydrodynamic patterns in porous media. Complementing the reviews is a set of original research papers covering growth models for branched hydraulic crack systems, fluid-driven crack propagation in elastic matrices, elastic and inelastic deformation of fluid-saturated rock, reaction front propagation in fracture matrices, the effects of rock mineralogy and pore structure on stress-dependent permeability of shales, topographic viscous fingering and plume dynamics in porous media convection. This article is part of the themed issue ‘Energy and the subsurface’.

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24

van Tatenhove-Pel, Rinke J., Daan H. de Groot, Anjani S. Bisseswar, Bas Teusink, and Herwig Bachmann. "Population dynamics of microbial cross-feeding are determined by co-localization probabilities and cooperation-independent cheater growth." ISME Journal 15, no. 10 (May 5, 2021): 3050–61. http://dx.doi.org/10.1038/s41396-021-00986-y.

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AbstractAs natural selection acts on individual organisms the evolution of costly cooperation between microorganisms is an intriguing phenomenon. Introduction of spatial structure to privatize exchanged molecules can explain the evolution of cooperation. However, in many natural systems cells can also grow to low cell concentrations in the absence of these exchanged molecules, thus showing “cooperation-independent background growth”. We here serially propagated a synthetic cross-feeding consortium of lactococci in the droplets of a water-in-oil emulsion, essentially mimicking group selection with varying founder population sizes. The results show that when the growth of cheaters completely depends on cooperators, cooperators outcompete cheaters. However, cheaters outcompete cooperators when they can independently grow to only ten percent of the consortium carrying capacity. This result is the consequence of a probabilistic effect, as low founder population sizes in droplets decrease the frequency of cooperator co-localization. Cooperator-enrichment can be recovered by increasing the founder population size in droplets to intermediate values. Together with mathematical modelling our results suggest that co-localization probabilities in a spatially structured environment leave a small window of opportunity for the evolution of cooperation between organisms that do not benefit from their cooperative trait when in isolation or form multispecies aggregates.

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25

Matthai, Stephan K. "Reservoir Simulation: Mathematical Techniques in Oil Recovery." Geofluids 8, no. 4 (November 2008): 344–45. http://dx.doi.org/10.1111/j.1468-8123.2008.00220.x.

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26

Anferov, Sergey, and Oleg Skul’skiy. "Mathematical modelling of vegetable oil plunger extraction." PNRPU Mechanics Bulletin 1 (March 30, 2014): 31–56. http://dx.doi.org/10.15593/2224-9893/2014.1.02.

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27

SIVALA, K., V. VASUDEVA RAO, S. SARANGI, R. K. MUKHERJEE, and N. G. BHOLE. "MATHEMATICAL MODELLING of RICE BRAN OIL EXPRESSION." Journal of Food Process Engineering 14, no. 1 (January 1991): 51–68. http://dx.doi.org/10.1111/j.1745-4530.1991.tb00081.x.

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28

Abasova Inara Afrail. "PROCESSING OF OIL WELL PRESSURE RECOVERY CURVES." Science Review, no. 1(18) (January 31, 2019): 18–20. http://dx.doi.org/10.31435/rsglobal_sr/31012019/6336.

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In the article the development of a mathematical model describing the PRC is studied on the base of pressure recovery curve method.Detailed processing of the pressure recovery curve made it possible to determine the deterioration of reservoir permeability in many wells. Here two methods are considered - stationary (steady conditions of selection) and non- stationary.The article proves that the use of these methods allows to develop a mathematical model to increase the determination of this task.On the base of numerical simulation, the following facts had impact on the results of the pressure recovery curve: well shutdown time, taking into account the initial transition section, taking into account curve change section before well shutdown.The study of variable factors impact on the results is carried out by interval estimation.The mathematical model describing the pressure recovery curve is local and changes its structures. This model can be used in industry conditions.

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29

Valis, David, Libor Zak, Josef Glos, and Agata Walek. "Contribution to Mathematical Modelling of Oil Field Data." Applied Mechanics and Materials 332 (July 2013): 455–62. http://dx.doi.org/10.4028/www.scientific.net/amm.332.455.

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The paper deals with application of selected suitable analytical methods use to analyse field data from medium off-road military vehicles. Some pieces of information from oil are interpreted thank to diagnostics in form of polluting particles. Such particles represent processes in the engine like wear (e.g. Fe, Cu, Pb, etc.) and oil condition (like e.g. Mn, Si, Zn, etc.). These particles can give us information both about system state and about oil state. Thank to good recording system we have data from field operation available. Therefore we decided to use selected analytical – algebraic methods for determining the specific particles generating trend. Based on the outcomes we hope to be able to determine the system condition (e.g. residual operation life, maintenance modifications in the intervals, etc.). Selected methods like regression analysis, base functions and fuzzy inference system will be used for the data assessment. The results itself might be beneficial in other forthcoming analysis like quality, risk and dependability management processes, e.g. for optimization during an operation and maintenance phase, logistics and spare parts planning, life cycle costing, mission planning, etc.

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Jacovkis, Pablo M., Gabriela B. Savioli, and M. Susana Bidner. "Mathematical modelling of flow towards an oil well." International Journal for Numerical Methods in Engineering 46, no. 9 (November 30, 1999): 1521–40. http://dx.doi.org/10.1002/(sici)1097-0207(19991130)46:9<1521::aid-nme710>3.0.co;2-2.

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31

Yue, L. L., and L. Taerwe. "Creep recovery of plain concrete and its mathematical modelling." Magazine of Concrete Research 44, no. 161 (December 1992): 281–90. http://dx.doi.org/10.1680/macr.1992.44.161.281.

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32

Stevens, D., P. J. Oades, N. Armstrong, and C. A. Williams. "Mathematical modelling of oxygen uptake during recovery from exercise." Journal of Cystic Fibrosis 8 (June 2009): S70. http://dx.doi.org/10.1016/s1569-1993(09)60277-0.

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33

Leone, A., R. Romaniello, and A. Tamborrino. "Mathematical modelling of the decanter for olive oil extraction." Acta Horticulturae, no. 1311 (May 2021): 411–16. http://dx.doi.org/10.17660/actahortic.2021.1311.52.

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34

Mas Hernández, Elizabeth, Paul Grassia, and Nima Shokri. "Modelling foam improved oil recovery within a heterogeneous reservoir." Colloids and Surfaces A: Physicochemical and Engineering Aspects 510 (December 2016): 43–52. http://dx.doi.org/10.1016/j.colsurfa.2016.07.064.

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35

Desouky, S. M., M. M. Abdel-Daim, M. H. Sayyouh, and A. S. Dahab. "Modelling and laboratory investigation of microbial enhanced oil recovery." Journal of Petroleum Science and Engineering 15, no. 2-4 (August 1996): 309–20. http://dx.doi.org/10.1016/0920-4105(95)00044-5.

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36

Settari, A., Y. Ito, N. Fukushima, and H. Vaziri. "Geotechnical aspects of recovery processes in oil sands." Canadian Geotechnical Journal 30, no. 1 (February 1, 1993): 22–33. http://dx.doi.org/10.1139/t93-003.

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The geomechanical aspects of oil sand behaviour are important for the understanding of the thermal processes for bitumen recovery from oil sands. The paper describes the study of the geomechanical response of oil sand to fluid injection, which causes formation parting in oil sands. The behaviour of constitutive models in the low effective stress range is examined, and it is shown by modelling that the frictional properties at low effective stress control the development of the failure zone around injection wells and fractures. Based on the matching of laboratory data for the PetroCanada–CanOXY–Esso–JACOS (PCEJ) project, a generalized hyperbolic model is proposed. Modelling of a field design involving horizontal fracture shows that the stress paths and the amount of dilation experienced by the formation can be very different from those measured in standard laboratory tests. Laboratory measurements should be done at the very small stresses and along the stress paths expected in the field. These can be predicted by modelling. Key words : oil sands, constitutive models, fluid injection, hyperbolic model, sand dilation, horizontal fracture, oil sands modelling, bitumen recovery, sand failure.

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Reis-Vasco, E. M. C., J. A. P. Coelho, A. M. F. Palavra, C. Marrone, and E. Reverchon. "Mathematical modelling and simulation of pennyroyal essential oil supercritical extraction." Chemical Engineering Science 55, no. 15 (August 2000): 2917–22. http://dx.doi.org/10.1016/s0009-2509(99)00561-8.

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Jokić, Stela, Sandra Svilović, Zoran Zeković, and Senka Vidović. "Mathematical modelling of soybean oil solubility in supercritical carbon dioxide." International Journal of Food Science & Technology 46, no. 5 (March 25, 2011): 1031–37. http://dx.doi.org/10.1111/j.1365-2621.2011.02571.x.

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Xiu, Jianlong, Tianyuan Wang, Ying Guo, Qingfeng Cui, Lixin Huang, Yuandong Ma, and Weiyao Zhu. "A MATHEMATICAL MODEL OF MICROBIAL ENHANCED OIL RECOVERY IN POROUS MEDIA." Special Topics & Reviews in Porous Media: An International Journal 8, no. 4 (2017): 263–72. http://dx.doi.org/10.1615/specialtopicsrevporousmedia.2017020279.

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Khuramshina, R. A., and V. V. Sokolova. "Mathematical modelling of ultrasonic treatment of asphaltene deposits." Herald of Dagestan State Technical University. Technical Sciences 48, no. 2 (July 31, 2021): 60–72. http://dx.doi.org/10.21822/2073-6185-2021-48-2-60-72.

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Objective. The removal of asphaltene deposits at oil and gas facilities is one of the urgent and important problems and requires significant material and labor costs. It is possible to reduce costs by creating and implementing effective technical means, which requires an in-depth study of the processes of organic matter deposition at oil and gas facilities and their use as a secondary raw material. Methods. This paper discusses modern views on the state of the problem of asphaltene deposits in oil shipping and storage equipment and possible ways to solve it. The paper provides an overview of various ways to clean shipping and storage objects from asphaltene deposits: chemical (adding additives, solvents), thermal (heating by special devices or injection of superheated steam during exploitation), mechanical (using scrapers and pistons), and refers, among other things, to scientific works on the use of ultrasound to accelerate the removal of deposits. Results. The paper considers methods for removing deposits, as well as using the positive effect of the removed layer as a secondary energy source. A procedure for model calculation of the use of ultrasonic equipment to remove deposits has been developed. As a result, the deposit melting front velocity was determined depending on the duration of exposure. Conclusion. Taking into account the positive world experience, the level of development of the ultrasonic method for removing asphaltene deposits in the oil and gas industry and the use of asphaltene deposits as a secondary raw material, this area needs further development. The widespread implementation of equipment and, from the standpoint of rational use of natural resources, the use of deposits as a secondary raw material will increase cost efficiency and equipment efficiency, and reduce environmental impact.

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Owolarafe, O. K., A. S. Osunleke, O. A. Odejobi, S. O. Ajadi, and M. O. Faborode. "Mathematical modelling and simulation of the hydraulic expression of oil from oil palm fruit." Biosystems Engineering 101, no. 3 (November 2008): 331–40. http://dx.doi.org/10.1016/j.biosystemseng.2008.08.007.

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Luk, G. K., and H. F. Kuan. "Modelling the behaviour of oil spills in natural waters." Canadian Journal of Civil Engineering 20, no. 2 (April 1, 1993): 210–19. http://dx.doi.org/10.1139/l93-026.

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This paper is a state-of-the-art review of the formulations for the different processes responsible for the transport and mixing of petroleum oil spilled in natural waters. Processes accounting for the transfer and loss of the surface oil, such as initial spreading, evaporation, dissolution, emulsification, dispersion, photo-oxidation, and sedimentation, are included. Based on the findings, a dynamic mathematical model describing the fate of spilled oil was developed. To reflect field observations, the surface oil composition in the model is allowed to vary with time as a result of weathering. Initial results for model testing are presented. Key words: oil spill, mathematical model, fate model, weathering processes.

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Irfan, Sayed Ameenuddin, Afza Shafie, Noorhana Yahya, and Nooraini Zainuddin. "Mathematical Modeling and Simulation of Nanoparticle-Assisted Enhanced Oil Recovery—A Review." Energies 12, no. 8 (April 25, 2019): 1575. http://dx.doi.org/10.3390/en12081575.

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In the last two decades, nanotechnology has flourished due to its vast number of applications in many fields such as drug delivery, oil and gas, and thermal applications, like cooling and air-conditioning. This study focuses on the applications of nanoparticles/nanofluids in the Enhanced Oil Recovery (EOR) process to increase oil recovery efficiency. To understand the nanoparticle-assisted EOR process, the first step is to understand the flow characteristics of nanoparticles in porous media, including entrapment and release in the pores and the behavior of nanoparticles under high temperatures, pressures, and salinity levels and in the presence of external electric and magnetic fields. Also, the process looks at the roles of various pore distributions during their application as EOR agents. The experimental approaches are not only time consuming, but they are also cumbersome and expensive. Hence, the mathematical models could help to facilitate the understanding of the transport and interaction of nanofluids in a reservoir and how such processes can be optimized to get maximum oil recovery and, in turn, reduce the production cost. This paper reviews and critically analyzes the latest developments in mathematical modeling and simulation techniques that have been reported for nanofluid-assisted EOR. One section is dedicated to discussing the challenges ahead, as well as the research gaps in the modeling approach to help the readers to also contribute to further enlightening the modeling nanofluid-assisted EOR process.

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Wang, Tianyuan, Li Yu, Jianlong Xiu, Yuandong Ma, Wei Lin, Ting Ma, Xiangyang Wang, and Lin Wang. "A mathematical model for microbial enhanced oil recovery using biopolymer-producing microorganism." Fuel 216 (March 2018): 589–95. http://dx.doi.org/10.1016/j.fuel.2017.12.058.

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Marotto, Tamires A., and Adolfo P. Pires. "Mathematical modeling of hot carbonated waterflooding as an enhanced oil recovery technique." International Journal of Multiphase Flow 115 (June 2019): 181–95. http://dx.doi.org/10.1016/j.ijmultiphaseflow.2019.03.024.

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Gerasimenko, Yuri. "MATHEMATICAL MODELLING OF HYDRODYNAMIC PROCESSES IN THE LENGTH OF OIL PIPELINES." University News. North-Caucasian Region. Technical Sciences Series, no. 3 (September 2015): 10–16. http://dx.doi.org/10.17213/0321-2653-2015-3-10-16.

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Reverchon, E., A. Kaziunas, and C. Marrone. "Supercritical CO2 extraction of hiprose seed oil: experiments and mathematical modelling." Chemical Engineering Science 55, no. 12 (June 2000): 2195–201. http://dx.doi.org/10.1016/s0009-2509(99)00519-9.

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Emenike, C. O. "Mathematical modelling of cathodic protection systems for oil and gas facilities." Anti-Corrosion Methods and Materials 42, no. 4 (April 1995): 6–8. http://dx.doi.org/10.1108/eb007362.

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Kok, M. V., and R. O. Saracoglu. "MATHEMATICAL MODELLING OF WAX DEPOSITION IN CRUDE OIL PIPELINES (COMPARATIVE STUDY)." Petroleum Science and Technology 18, no. 9-10 (November 2000): 1121–45. http://dx.doi.org/10.1080/10916460008949895.

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Yuliansyah, Ahmad Tawfiequrahman, Bardi Murachman, and Suryo Purwono. "Mathematical Model for Water Flooding and HPAM Polymer Flooding in Enhanced Oil Recovery." ASEAN Journal of Chemical Engineering 21, no. 1 (June 30, 2021): 124. http://dx.doi.org/10.22146/ajche.65531.

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The need for energy, especially the petroleum-based one, is steadily increasing along with population growth and technological advancement. Meanwhile, oil exploitation from oil reservoirs using primary and secondary techniques can only obtain about 30%-50 % out of the original oil in place. Enhanced Oil Recovery (EOR) is a method for increasing oil recovery from a reservoir by injecting materials that are not found in the reservoir, such as surfactant, polymer, etc. This research aims to develop a mathematical model representing two-phase flow through porous media in the EOR process. This model was extended from mass balance and fluid flow in porous media equations. The reliability of the model was then validated by water flooding and polymer flooding experiment. A porous media, constituted by a silica sand pack, was saturated with 2 % brine and sequentially flooded with HPAM polymer solution at various concentrations (5,000-15,000 ppm). The volume of the oil coming out from the media at any time intervals was measured. Validation of the model was carried out by optimizing the model parameters to obtain the best curve-fitting on the plot of the percentage of cumulative recovered oil against time. The results showed that the proposed mathematical model was reliable enough to express both water and polymer-flooding processes.

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