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  • 1.
    Al-Ajmi, Adel M.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics. Department of Petroleum and Chemical Engineering, Oman .
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    A new 3D stability model for the design of non-vertical wellbores2006Conference paper (Refereed)
    Abstract [en]

    The Mohr-Coulomb failure criterion is known to be too conservative in estimating the critical mud pressure required to maintain wellbore stability, due to ignoring the strengthening effect of the intermediate principal stress. To eliminate this deficiency, we have developed a new analytical model to estimate the mud pressure required to avoid shear failure at the wall of non-vertical boreholes (i.e., the collapse pressure). This has been achieved by using a linear elastic and isotropic constitutive model for the stresses, and the Mogi-Coulomb criterion to predict failure. For comparison, the stability analysis has been also carried out using Mohr-Coulomb, the modified Lade criterion, and the Drucker-Prager criterion. We have found that implementing the Mogi-Coulomb law instead of Mohr-Coulomb does indeed lessen the conservative nature of the wellbore stability analysis. In general, the Mogi-Coulomb criterion gives an estimate of the collapse pressure that is similar to that given by the modified Lade criterion in polyaxial stress states, and similar to Mohr-Coulomb in triaxial stress states. By comparison, the Drucker-Prager criterion always underestimates the required mud weight. The developed 3D stability model has been applied in a field case study.

  • 2.
    Al-Ajmi, Adel M.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Stability analysis of vertical boreholes using the Mogi-Coulomb failure criterion2006In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 43, no 8, p. 1200-1211Article in journal (Refereed)
    Abstract [en]

    A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, a, and sigma(3), and therefore assumes that the intermediate stress 92 has no influence on rock strength. As the Mohr-Coulomb criterion ignores the strengthening effect of the intermediate stress, it is expected to be too conservative in estimating the critical mud weight required to maintain wellbore stability. Recently, Al-Ajmi and Zimmerman [Relationship between the parameters of the Mogi and Coulomb failure criterion. Int J Rock Mech Min Sci 2005;42(3):431-39.] developed the Mogi-Coulomb failure criterion, and showed that it is reasonably accurate in modelling polyaxial failure data from a variety of rocks. We then develop a model for the stability of vertical boreholes, using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi-Coulomb criterion to predict failure. Our model leads to easily computed expressions for the critical mud weight required to maintain wellbore stability.

  • 3. Al-ajmi, A.M
    et al.
    Zimmerman, Robert W
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering.
    Relation between the Mogi and the Coulomb failure criteria2005In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 42, no 3, p. 431-439Article in journal (Refereed)
    Abstract [en]

    We have shown that linear Mogi criterion does a good job in representing rock failureunder polyaxial stress states. When σ2 = σ3 the linear version of Mogi's triaxial failurecriterion reduces exactly to the Coulomb criterion. Hence, the linear Mogi criterion can be thought of as a natural extension of the Coulomb criterion into three dimensions (i.e., polyaxial stress space). As Mohr's extension of the Coulomb criterion into three dimensions is often referred to as the Mohr-Coulomb criterion, we propose that the linear version of the Mogi criterion be known as the "Mogi-Coulomb" failure criterion. The classical Coulomb failure criterion can therefore be thought of as a special case, which applies only when σ2 = σ3 of the more general linear Mogi failure criterion. Furthermore, we found that the numerical values of the parameters that appear in the Mogi-Coulombcriterion can be estimated from conventional triaxial test data. Thus, this polyaxial failurecriterion can be applied even in the absence of polyaxial (true triaxial) data. This offers a great advantage, as most laboratories are equipped to conduct only traditional σ2 = σ3tests. Finally, we showed that if the linear form of the Mogi criterion is used, the parameters that appear in it can be unambiguously related to the traditional parameters appearing in the Coulomb failure law. The lack of such a relationship for the parameters appearing in the power-law Mogi criterion has been cited in [8] as a major drawback to the use of that model. 

  • 4. Al-Marooqi, S.H
    et al.
    Grattoni, C.A
    Muggeridge, A.M
    Zimmerman, Robert W
    Department of Earth Science and Engineering, Imperial College,.
    Jing, X.D
    Pore-Scale modelling of NMR relaxation for the characterization of wettability2006In: Journal of Petroleum Science and Engineering, ISSN 0920-4105, E-ISSN 1873-4715, Vol. 52, no 1-4, p. 172-186Article in journal (Refereed)
    Abstract [en]

    Several research groups are currently investigating the determination of wettability usingNMR relaxation times. Although correlations with traditional wettability indices have been presented with some success, further effort is needed to relate the wettability atpore-scale to a core-scale measurement of NMR response. For example, a qualitative method using the arithmetic mean of relaxation times at various saturations has been presented [Guan, H., Brougham, D., Sorbie, K.S., Packer, K.J., 2002. Wettability effects in a sandstone reservoir and outcrop cores from NMR relaxation time distributions. J. Petroleum Sci. and Eng. 34, 35-54] and a wettability index that quantifies the amount of surface area that is wetted either by oil or by water, by using the T2 peak at four different saturations has been proposed [Fleury, M., Deflandre, F., 2003. Quantitative evaluation of porous media wettability using NMR relaxometry. Mag. Reson. Imaging 21, 385-387]. Our group at the Imperial College have previously shown experimentally that the T2 distribution provides valuable information about wettability and overall fluid distribution within thepore-space, which is lost if only a single value from the T2 distribution is considered [Al-Mahrooqi, S.H., Grattoni, C.A., Moss, A.K., Jing, X.D., 2003. An investigation of the effect ofwettability on NMR characteristics of sandstone rock and fluid systems. J. Petroleum Sci. and Eng. 39, 389-398]. In this paper we use a simple pore-scale model to understand the effect of wetting and its relationship with NMR relaxation times. The model uses triangular capillary pores with a given pore size distribution. The oil/water distribution within thepores is obtained as a function of capillary pressure and wettability. At a given capillary pressure, the volumes and surface areas of water and oil are calculated for each individual pore. This allows us to calculate the theoretical T2 distribution for that pore size distribution as a function of wettability and saturation. We have used the model to study the T2 distribution for a range of wettabilities and saturations. Results from the model confirmed previous observations from experiments regarding the effect of wettability onNMR T2 distributions. Based on these qualitative results, an improved index for characterising wettability from the T2 distribution has been proposed. We tested the proposed index using NMR T2 data from synthetic and real sandstone core plugs with different wettabilities, ranging from strongly water-wet to strongly oil-wet. Comparison between the proposed index and wettability for the synthetic samples and Amott-Harvey index for core plugs show good correlation. 

  • 5. Al-Wardy, W
    et al.
    Zimmerman, Robert W
    Dept. of Earth Science/Engineering, Imperial Coll. of Sci. Technol./Med., London .
    Effective stress law for the permeability of clay-rich sandstones2004In: Journal of Geophysical Research, ISSN 0148-0227, E-ISSN 2156-2202, Vol. 109, no 4, p. 1-10Article in journal (Refereed)
    Abstract [en]

    Two models of clay-rich sandstones are analyzed to explain the relative sensitivity ofpermeability to pore pressure and confining pressure. In one model the clay lines the entire pore wall in a layer of uniform thickness, and in the second model the clay is distributed in the form of particles that are only weakly coupled to the pore walls. Equations of elasticity and fluid flow are solved for both models, giving expressions for theeffective stress coefficients in terms of clay content and the elastic moduli of the rock andclay. Both models predict that the permeability will be much more sensitive to changes in pore pressure than to changes in confining pressure. The clay particle model gives somewhat better agreement with data from the literature and with new data on a Staintonsandstone having a solid volume fraction of 8% clay. 

  • 6. Al-Yaarubi, A. H.
    et al.
    Pain, C. C.
    Grattoni, C. A.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Sustainable development, Environmental science and Engineering, Land and Water Resources Engineering.
    Navier-Stokes Simulations of Fluid Flow Through a Rock Fracture2013In: Dynamic Fluids and Transport Through in Fractured Rock, American Geophysical Union (AGU), 2013, p. 55-64Chapter in book (Other academic)
    Abstract [en]

    A surface profilometer was used to measure fracture profiles every 10 microns over the surfaces of a replica of a fracture in a red Permian sandstone, to within an accuracy of a few microns. These surface data were used as input to two finite element codes that solve the Navier-Stokes equations and the Reynolds equation, respectively. Numerical simulations of flow through these measured aperture fields were carried out at different values of the mean aperture, corresponding to different values of the relative roughness. Flow experiments were also conducted in casts of two regions of the fracture. At low Reynolds numbers, the Navier-Stokes simulations yielded transmissivities for the two fracture regions that were closer to the experimental values than were the values predicted by the lubrication model. In general, the lubrication model overestimated the transmissivity by an amount that varied as a function of the relative roughness, defined as the standard deviation of the aperture divided by the mean aperture. The initial deviations from linearity, for Reynolds numbers in the range 1-10, were consistent with the "weak inertia" model developed by Mei and Auriault for porous media, and with the results obtained computationally by Skjetne et al in 1999 on a two-dimensional self-affine fracture. In the regime 10 < Re < 40, both the computed and measured transmissivities could be fit very well to a Forchheimer-type equation, in which the additional pressure drop varies quadratically with the Reynolds number.

  • 7. Bond, D.
    et al.
    Krevor, S. C.
    Muggeridge, A. H.
    Waldren, D.
    Zimmerman, Robert
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Imperial College Lectures In Petroleum Engineering: Topics In Reservoir Management2017Book (Other academic)
  • 8. David, E.
    et al.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Sliding crack model for the uniaxial compression of rock2007In: Proceedings of the 1st Canada-US Rock Mechanics Symposium - Rock Mechanics Meeting Society's Challenges and Demands, Taylor & Francis, 2007, p. 575-580Conference paper (Refereed)
    Abstract [en]

    Uniaxial compression tests on rocks, if conducted at stresses below failure, typically show non-linearity in the stress-strain curve, and hysteresis. Walsh (J. Geophys. Res., 1965) explained this behavior in terms of frictional sliding along the faces of closed cracks. Although well known and widely cited, Walsh's model has not previously been developed in sufficient detail to be used for quantitative predictions. We revisit and extend his model, by including the effect of the stress required to close an initially open crack, and we examine the unloading process in detail. Our analysis leads to closed-form expressions for the loading and unloading portions of the stress-strain curve, as functions of elastic modulus of the uncracked rock, the crack density, the characteristic aspect ratio, and the crack friction coefficient. The model provides a good fit to the loading and unloading portions of the stress-strain curves, for experimental data on sandstones taken from the literature.

  • 9.
    Ekneligoda, Thushan C.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Boundary perturbation solution for nearly circular holes and rigid inclusions in an infinite elastic medium2008In: Journal of applied mechanics, ISSN 0021-8936, E-ISSN 1528-9036, Vol. 75, no 1, p. 011015-Article in journal (Refereed)
    Abstract [en]

    The boundary perturbation method is used to solve the problem of a nearly circular rigid inclusion in a two-dimensional elastic medium subjected to hydrostatic stress at infinity. The solution is taken to the fourth order in the small parameter epsilon that quantifies the magnitude of the variation of the radius of the inclusion. This result is then used to find the effective bulk modulus of a body that contains a dilute concentration of such inclusions. The corresponding results for a cavity are obtained by setting the Muskhelishvili coefficient K equal to -1, as specified by the Dundurs correspondence principle. The results for nearly circular pores can be expressed in terms of the pore compressibility. The pore compressibilities given by the perturbation solution are tested against numerical values obtained using the boundary element method, and are shown to have good accuracy over a substantial range of roughness values.

  • 10.
    Ekneligoda, Thushan C.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Zimmerman, Robert W.
    Shear compliance of two-dimensional pores possessing N-fold axis of rotational symmetry2008In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 464, no 2091, p. 759-775Article in journal (Refereed)
    Abstract [en]

    We use the complex variable method and conformal mapping to derive a closed-form expression for the shear compliance parameters of some two-dimensional pores in an elastic material. The pores have an N-fold axis of rotational symmetry and can be represented by at most three terms in the mapping function that conformally maps the exterior of the pore into the interior of the unit circle. We validate our results against the solutions of some special cases available in the literature, and against boundary-element calculations. By extrapolation of the results for pores obtained from two and three terms of the Schwarz-Christoffel mapping function for regular polygons, we find the shear compliance of a triangle, square, pentagon and hexagon. We explicitly verify the fact that the shear compliance of a symmetric pore is independent of the orientation of the pore relative to the applied shear, for all cases except pores of fourfold symmetry. We also show that pores having fourfold symmetry, or no symmetry, will have shear compliances that vary with cos 4 theta. An approximate scaling law for the shear compliance parameter, in terms of the ratio of perimeter squared to area, is proposed and tested.

  • 11.
    Ekneligoda, Thushan Chandrasiri
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Compressibility of two-dimensional pores having n-fold axes of symmetry2006In: Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, E-ISSN 1471-2946, Vol. 462, no 2071, p. 1933-1947Article in journal (Refereed)
    Abstract [en]

    The complex variable method and conformal mapping are used to derive a closed-form expression for the compressibility of an isolated pore in an infinite two-dimensional, isotropic elastic body. The pore is assumed to have an n-fold axis of symmetry, and be represented by at most four terms in the mapping function that conformally maps the exterior of the pore into the interior of the unit circle. The results are validated against some special cases available in the literature, and against boundary-element calculations. By extrapolation of the results for pores obtained from three and four terms of the Schwarz-Christoffel mapping function for regular polygons, the compressibilities of a triangle, square, pentagon and hexagon are found (to at least three digits). Specific results for some other pore shapes, more general than the quasi-polygons obtained from the Schwarz-Christoffel mapping, are also presented. An approximate scaling law for the compressibility, in terms of the ratio of perimeter-squared to area, is also tested. This' expression gives a reasonable approximation to the pore compressibility, but may overestimate it by as much as 20%.

  • 12. Grattoni, C.A
    et al.
    Luckham, P.F
    Jing, X.D
    Norman, L
    Zimmerman, Robert W.
    Polymers as relative permeability modifiers: adsorption and the dynamic formation of thick polyacrylamide layers2004In: Journal of Petroleum Science and Engineering, ISSN 0920-4105, E-ISSN 1873-4715, Vol. 45, no 3-4, p. 233-245Article in journal (Refereed)
    Abstract [en]

    Water production from oil and gas reservoirs is increasing worldwide. as more reservoirs are becoming mature. In order to control water production, polymers and gels are often injected into the formation to reduce the water permeability. These systems are known as relative permeability modifiers. Although these methods sometimes lead to significant cost savings, and many successful treatments have been reported, a wider application is hindered by the lack of understanding of the basic mechanisms of permeability modification by polymers.

    This paper presents some pore-level and basic studies on polymers, with the aim of providing a better understanding of these systems. Experiments have been performed in micro-scale glass flow models, and atomic force microscopy was used to validate the flow observations. The role of adsorption and flow of polyacrylamides in the formation of thick layers is described. The size of statically adsorbed polyacrylamide layers depends on the polymer characteristics (molecular weight, degree of hydrolysis, salinity, etc.), but is less than 250 nm for all the systems studied. On the other hand, dynamically formed polymer layers can reach several thousands of nanometres. The existence of these thick polymer layers is shown here, to our knowledge for the first time, through flow experiments and AFM measurements. While mechanical retention cannot occur under our experimental conditions, the mechanism of adsorption-entanglement gives a reasonable mechanistic description of the dynamic formation of thick layers. The implications of these mechanisms in the modelling of the flow and selection of polymer systems are discussed.

  • 13. Jaeger, J.C
    et al.
    Cook, N.G.W
    Zimmerman, R.W
    Fundamentals of Rock Mechanics2007 (ed. 4)Book (Refereed)
  • 14. Lock, P.A.
    et al.
    Jing, X.D.
    Zimmerman, Robert
    University of London.
    Comparison of methods for upscaling permeability from the pore scale to the core scale2004In: Journal of Hydraulic Research, ISSN 0022-1686, E-ISSN 1814-2079, Vol. 42, no SI, p. 3-8Article in journal (Refereed)
    Abstract [en]

    Several methods are compared for estimating the core-scale permeability of a rock whose pore space is idealized as consisting of a cubic network of pore tubes having a distribution of pore-scale hydraulic conductances. The conductance distribution of the pores is estimated from image analysis of scanning electron micrographs of rock sections. An explicit solution of the network equations is used as a benchmark to establish the "exact" macroscopic permeability. The other three upscaling methods used are Kirkpatrick's isotropic effective medium approximation, Bernasconi's anisotropic effective medium approximation, and the generalized perturbation ansatz (GPA) proposed by Gelhar and Axness. The analysis is carried out on a suite of petroleum reservoir sandstones from the North Sea, with measured core-scale permeabilities ranging from 20 to 500 mD. The log-variances of the pore-scale hydraulic conductance distribution were in the range of 2-3. The predictions of both the Kirkpatrick equation and the GPA are in each case within 10% of those computed by explicit network calculation, and all permeability predictions are generally within a factor of two of the core-scale values measured in the laboratory.

  • 15. Lutz, M.P.
    et al.
    Zimmerman, Robert
    Imperial College, London.
    Effect of an inhomogeneous interphase zone on the bulk modulus and conductivity of a particulate composite2005In: International Journal of Solids and Structures, ISSN 0020-7683, E-ISSN 1879-2146, Vol. 42, no 2, p. 429-437Article in journal (Refereed)
    Abstract [en]

    A model is presented of a particulate composite containing spherical inclusions, each of which are surrounded by a localized region in which the elastic moduli vary smoothly with radius. This region may represent an interphase zone in a composite, or the transition zone around an aggregate particle in concrete, for example. An exact solution is derived for the displacements and stresses around a single inclusion in an infinite matrix, subjected to a far-field hydrostatic compression, and is then used to derive an approximate expression for the effective bulk modulus of a material containing a random dispersion of these inclusions. The analogous conductivity (thermal, electrical, etc.) problem is then discussed, and it is shown that the expression for the normalized effective conductivity corresponds exactly to that for the normalized effective bulk modulus, if the Poisson ratios of both phases are set to zero.

  • 16. Makurat, A
    et al.
    Zimmerman, R W
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Special issue: Rock physics and geomechanics - Preface2005In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 42, no 7-8, p. 871-872Article in journal (Other academic)
  • 17. Tavassoli, Z
    et al.
    Zimmerman, Robert W.
    Department of Earth Science and Engineering, Imperial College, London, United Kingdom.
    Blunt, M.J
    Analysis of counter-current imbibition with gravity in weakly water-wet systems2005In: Journal of Petroleum Science and Engineering, ISSN 0920-4105, E-ISSN 1873-4715, Vol. 48, no 1-2, p. 94-104Article in journal (Refereed)
    Abstract [en]

    Counter-current imbibition in one dimension is analyzed, in which a wetting phase (water) displaces a non-wetting phase against gravity. An approximate analytical approach is used to derive an expression for the saturation profile in the case where the mobility of the displaced phase at the inlet is finite. This approach is applicable to waterflooding in hydrocarbon reservoirs, flow in geothermal systems, or the displacement of non-aqueous phase liquid (NAPL) or air by water. Solutions are developed for both gravity-dominated and capillary-dominated cases. In the capillary-dominated limit the predicted recoveries compare very well with experimental data from the literature, over all time scales. The use of this expression for field-scale dual-porosity modeling of flow in fractured systems is briefly discussed.

  • 18. Tavassoli, Z.
    et al.
    Zimmerman, Robert W.
    Dept. of Earth Science/Engineering, Imperial College, London, United Kingdom.
    Blunt, M.J.
    Analytic analysis for oil recovery during counter-current imbibition in strongly water-wet systems2005In: Transport in Porous Media, ISSN 0169-3913, E-ISSN 1573-1634, Vol. 58, no 1-2, p. 173-189Article in journal (Refereed)
    Abstract [en]

    We study counter-current imbibition, where a strongly wetting phase ( water) displaces non-wetting phase spontaneously under the influence of capillary forces such that the non-wetting phase moves in the opposite direction to the water. We use an approximate analytical approach to derive an expression for saturation profile when the viscosity of the non-wetting phase is non-negligible. This makes the approach applicable to water flooding in hydrocarbon reservoirs, or the displacement of non-aqueous phase liquid (NAPL) by water. We find the recovery of non-wetting phase as a function of time for one-dimensional flow. We compare our predictions with experimental results in the literature. Our formulation reproduces experimental data accurately and is superior to previously proposed empirical models.

  • 19.
    Zimmerman, Robert
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Introduction to Rock Properties2017In: Imperial College Lectures In Petroleum Engineering, The - Volume 3: Topics In Reservoir Management, World Scientific Pub Co Pte Ltd , 2017, p. 1-46Chapter in book (Other academic)
  • 20.
    Zimmerman, Robert
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Preface2017In: Imperial College Lectures In Petroleum Engineering, The - Volume 3: Topics In Reservoir Management, World Scientific Pub Co Pte Ltd , 2017, p. v-viChapter in book (Refereed)
  • 21.
    Zimmerman, Robert W.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    The Imperial College lectures in petroleum engineering2018Collection (editor) (Other academic)
    Abstract [en]

    This book presents, in a self-contained form, the equations of fluid flow in porous media, with a focus on topics and issues that are relevant to petroleum reservoir engineering. No prior knowledge of the field is assumed on the part of the reader, and particular care is given to careful mathematical and conceptual development of the governing equations, and solutions for important reservoir flow problems. Fluid Flow in Porous Media starts with a discussion of permeability and Darcy's law, then moves on to a careful derivation of the pressure diffusion equation. Solutions are developed and discussed for flow to a vertical well in an infinite reservoir, in reservoirs containing faults, in bounded reservoirs, and to hydraulically fractured wells. Special topics such as the dual-porosity model for fractured reservoirs, and fluid flow in gas reservoirs, are also covered. The book includes twenty problems, along with detailed solutions. As part of the Imperial College Lectures in Petroleum Engineering, and based on a lecture series on the same topic, this book provides the introductory information needed for students of the petroleum engineering and hydrology.

  • 22.
    Zimmerman, Robert W.
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Land and Water Resources Engineering, Engineering Geology and Geophysics.
    Lutz, M.P
    Thermal and electrical conductivity of composites with graded interfaces2006In: International Journal of Advances in Science and Technology, ISSN 2229-5216, Vol. 45, p. 1097-1102Article in journal (Refereed)
  • 23.
    Zimmerman, R.W.
    et al.
    Dept. of Earth Science/Engineering, Imperial College, London.
    Al-Yaarubi, A
    Pain, C.C
    Grattoni, C.A
    Non-linear regimes of fluid flow in rock fractures2004In: International Journal of Rock Mechanics And Mining Sciences, ISSN 1365-1609, E-ISSN 1873-4545, Vol. 41, no 3, p. 384-384Article in journal (Refereed)
    Abstract [en]

    We have conducted high-resolution Navier-Stokes simulations and laboratory measurements of fluid flow in a natural sandstone fracture. First, epoxy casts were made of the two opposing fracture surfaces. The surface profiles of the two surfaces were then measured at a vertical resolution of ±2 μm, every 20 μm in the x and y-directions, over 2 cm × 2 cm regions of the fracture. These data were then used to create a finite-element mesh for the fracture void space, and the Navier-Stokes equations were solved within this domain. Flow experiments were also conducted within the same fracture casts, over a range of flowrates. The simulations confirm the existence of a weak inertia regime for Reynolds numbers in the range of 1-10, in which the non-Darcy pressure drop varies with the cube of the flowrate. Although of theoretical interest, this effect is, however, probably too small to be of engineering interest. At Reynolds numbers above about 20, both the simulations and experiments exhibit a Forchheimer-type regime, in which the non-Darcy pressure drop is quadratic in the flowrate.

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