Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures

Variations in fluid density can greatly affect fluid flow and solute transport in the subsurface. Heterogeneities such as fractures play a major role for the migration of variable-density fluids. Earlier modeling studies of density effects in fractured media were restricted to orthogonal fracture networks, consisting of only vertical and horizontal fractures. The present study addresses the phenomenon of 3D variable-density flow and transport in fractured porous media, where fractures of an arbitrary incline can occur. A general formulation of the body force vector is derived, which accounts for variable-density flow and transport in fractures of any orientation. Simulation results are presented that show the verification of the new model formulation, for the porous matrix and for inclined fractures. Simulations of variable-density flow and solute transport are then conducted for a single fracture, embedded in a porous matrix. The simulations show that density-driven flow in the fracture causes convective flow within the porous matrix and that the high-permeability fracture acts as a barrier for convection. Other simulations were run to investigate the influence of fracture incline on plume migration. Finally, tabular data of the tracer breakthrough curve in the inclined fracture is given to facilitate the verification of other codes.     

Discretizing the fracture-matrix interface to simulate solute transport

This article examines the required spatial discretization perpendicular to the fracture-matrix interface (FMI) for numerical simulation of solute transport in discretely fractured porous media. The discrete-fracture, finite-element model HydroGeoSphere ( Therrien et al. 2005 ) and a discrete-fracture implementation of MT3DMS ( Zheng 1990 ) were used to model solute transport in a single fracture, and the results were compared to the analytical solution of Tang et al. (1981) . To match analytical results on the relatively short timescales simulated in this study, very fine grid spacing perpendicular to the FMI of the scale of the fracture aperture is necessary if advection and/or dispersion in the fracture is high compared to diffusion in the matrix. The requirement of such extremely fine spatial discretization has not been previously reported in the literature. In cases of high matrix diffusion, matching the analytical results is achieved with larger grid spacing at the FMI. Cases where matrix diffusion is lower can employ a larger grid multiplier moving away from the FMI. The very fine spatial discretization identified in this study for cases of low matrix diffusion may limit the applicability of numerical discrete-fracture models in such cases.     

FracKfinder: A MATLAB Toolbox for Computing Three-Dimensional Hydraulic Conductivity Tensors for Fractured Porous Media

Fractures in porous media have been documented extensively. However, they are often omitted from groundwater flow and mass transport models due to a lack of data on fracture hydraulic properties and the computational burden of simulating fractures explicitly in large model domains. We present a MATLAB toolbox, FracKfinder, that automates HydroGeoSphere (HGS), a variably saturated, control volume finite-element model, to simulate an ensemble of discrete fracture network (DFN) flow experiments on a single cubic model mesh containing a stochastically generated fracture network. Because DFN simulations in HGS can simulate flow in both a porous media and a fracture domain, this toolbox computes tensors for both the matrix and fractures of a porous medium. Each model in the ensemble represents a different orientation of the hydraulic gradient, thus minimizing the likelihood that a single hydraulic gradient orientation will dominate the tensor computation. Linear regression on matrices containing the computed three-dimensional hydraulic conductivity (K) values from each rotation of the hydraulic gradient is used to compute the K tensors. This approach shows that the hydraulic behavior of fracture networks can be simulated where fracture hydraulic data are limited. Simulation of a bromide tracer experiment using K tensors computed with FracKfinder in HGS demonstrates good agreement with a previous large-column, laboratory study. The toolbox provides a potential pathway to upscale groundwater flow and mass transport processes in fractured media to larger scales.     

Grid convergence of variable-density flow simulations in discretely-fractured porous media

Grid convergence in space and time of variable-density flow in fractured-porous rock is systematically assessed. Convergence of the flow simulation is attained using both uniform and adaptive time-stepping. This contrasts to variable-density flow in unfractured porous media where grid convergence variable-density flow problems is almost never achieved. At high discretization levels, the number of fingers in fractured-porous rock is no longer influenced by spatial-temporal grid discretization, which is not the case in unfractured porous media. However, similar to unfractured porous media, the number of fingers in fractured-porous media varies at low discretization levels. Simulated convective pattern and penetration depth of the dense plume in fractured rock depend more on spatial discretization than on temporal discretization. The appropriate spatial-temporal grid is then used to examine some aspects of mixed convection in fractured-porous rock, characterized by the mixed convection number M. The critical mixed convection number M_c = 46 represents the transition between forced and free convection in fractured porous media, which is much higher than M_c = 1 in unfractured porous media. Thus, for mixed convective flow problems, the value of M_c is not a sufficient indicator to predict the convective mode (free convection-forced convection), and the presence of vertical fractures must be included in the prediction of convective flow modes.     

Grid refinement for modeling multiphase flow in discretely fractured porous media

A study of the effects of grid discretization on the migration of DNAPL within a discrete-fracture network embedded in a porous rock matrix is presented. It is shown that an insufficiently fine discretization of the fracture elements can lead to an overprediction of the volume of DNAPL that continues to migrate vertically at the intersection of a vertical and horizontal fracture. Uniform discretization of elements at the scale of one centimetre (or less) accurately resolved the density and capillary pressure components of the head gradient in the DNAPL. An alternative, non-uniform method of discretization of elements within the discrete-fracture network is presented whereby only fracture elements immediately adjacent to fracture intersections are refined. To further limit the number of elements employed, the porous matrix elements adjacent to the fracture elements are not similarly refined. Results show this alternative method of discretization reduces the numerical error to an acceptable level, while allowing the simulation of field-scale DNAPL contamination problems. The results from two field-scale simulations of a DNAPL-contaminated carbonate bedrock site in Ontario, Canada are presented. These simulations compare different methods of grid discretization, and highlight the importance of grid refinement when simulating DNAPL migration problems in fractured porous media.     

A test case for the simulation of three-dimensional variable-density flow and solute transport in discretely-fractured porous media

A test case has been developed for three-dimensional simulations of variable-density flow and solute transport in discretely-fractured porous media. The simulation domain is a low-permeability porous matrix cube containing a single non-planar fracture. The initial solute concentration is zero everywhere. A constant solute concentration is assigned to the top of the domain, which increases near-top fluid density and induces downward density-driven flow. The test case is therefore comparable to downwelling of a dense brine below a saline disposal basin or a waste repository. Numerous fingers and distinct convection cells develop early in the fracture but the fingers later coalesce and convection becomes less apparent. To help test other variable-density flow and transport models, results of the test case are presented both qualitatively (concentration contours and velocity fields) and quantitatively (penetration depth, mass flux, total mass stored, maximum fracture and matrix velocity).     

Numerical comparison of the equivalent continuum,non-homogeneous and dual porosity models for flow and transport in fractured porous media

The main objective of this work is to compare three different models for modelling of flow and solute transport in fractured porous media, in terms of their predictions of the flow and solute transport field variables. The three models are: the equivalent continuum model, the dual porosity model and the discrete fracture/non-homogeneous model. Though it is clear that the three models are based on different assumptions for their validity, it is not clear in which cases two or all of them would give similar results, since there are no such reported comparisons in the open literature.The three methods are compared for two different geometries: a rectangular porous domain with two parallel fractures and a square porous domain with regular mesh of three parallel fractures and another three fractures perpendicular to the first ones. The results helped to draw some conclusions in respect to the similarity of potentials as well as fluxes for the different methods for each of the two geometries.In this research the boundary element dual reciprocity method–multi domain scheme (BE DRM–MD) has been used and its implementation has been described. This numerical scheme has been used for the first time to solve a dual-porosity model. The scheme showed satisfactory accuracy and high flexibility in preparation of the discrete fracture/non-homogeneous meshes.     

Specification of Matrix Cleanup Goals in Fractured Porous Media

Semianalytical transient solutions have been developed to evaluate what level of fractured porous media (e.g., bedrock or clay) matrix cleanup must be achieved in order to achieve compliance of fracture pore water concentrations within a specified time at specified locations of interest. The developed mathematical solutions account for forward and backward diffusion in a fractured porous medium where the initial condition comprises a spatially uniform, nonzero matrix concentration throughout the domain. Illustrative simulations incorporating the properties of mudstone fractured bedrock demonstrate that the time required to reach a desired fracture pore water concentration is a function of the distance between the point of compliance and the upgradient face of the domain where clean groundwater is inflowing. Shorter distances correspond to reduced times required to reach compliance, implying that shorter treatment zones will respond more favorably to remediation than longer treatment zones in which back‐diffusion dominates the fracture pore water response. For a specified matrix cleanup goal, compliance of fracture pore water concentrations will be reached sooner for decreased fracture spacing, increased fracture aperture, higher matrix fraction organic carbon, lower matrix porosity, shorter aqueous phase decay half‐life, and a higher hydraulic gradient. The parameters dominating the response of the system can be measured using standard field and laboratory techniques.     

A computational model for coupled multiphysics processes of CO2 sequestration in fractured porous media

In this paper, a computational model for the simulation of coupled hydromechanical and electrokinetic flow in fractured porous media is introduced. Particular emphasis is placed on modeling CO₂ flow in a deformed, fractured geological formation and the associated electrokinetic flow. The governing field equations are derived based on the averaging theory and the double porosity model. They are solved numerically with a mixed discretization scheme, formulated on the basis of the standard Galerkin finite element method, the extended finite element method, the level-set method and the Petrov–Galerkin method. The standard Galerkin method is utilized to discretize the equilibrium and the diffusive dominant field equations, and the extended finite element method, together with the level-set method and the Petrov–Galerkin method, are utilized to discretize the advective dominant field equations. The level-set method is employed to trace the CO₂ plume front, and the extended finite element method is employed to model the high gradient in the saturation field front. The proposed mixed discretization scheme leads to a convergent system, giving a stable and effectively mesh-independent model. The accuracy and computational efficiency of the proposed model is evaluated by verification and numerical examples. Effects of the fracture spacing on the CO₂ flow and the streaming potential are discussed.     

A practical model for fluid flow in discrete-fracture porous media by using the numerical manifold method

In this study, a numerical manifold method (NMM) model is developed to analyze flow in porous media with discrete fractures in a non-conforming mesh. This new model is based on a two-cover-mesh system with a uniform triangular mathematical mesh and boundary/fracture-divided physical covers, where local independent cover functions are defined. The overlapping parts of the physical covers are elements where the global approximation is defined by the weighted average of the physical cover functions. The mesh is generated by a tree-cutting algorithm. A new model that does not introduce additional degrees of freedom (DOF) for fractures was developed for fluid flow in fractures. The fracture surfaces that belong to different physical covers are used to represent fracture flow in the direction of the fractures. In the direction normal to the fractures, the fracture surfaces are regarded as Dirichlet boundaries to exchange fluxes with the rock matrix. Furthermore, fractures that intersect with Dirichlet or Neumann boundaries are considered. Simulation examples are designed to verify the efficiency of the tree-cutting algorithm, the calculation's independency from the mesh orientation, and accuracy when modeling porous media that contain fractures with multiple intersections and different orientations. The simulation results show good agreement with available analytical solutions. Finally, the model is applied to cases that involve nine intersecting fractures and a complex network of 100 fractures, both of which achieve reasonable results. The new model is very practical for modeling flow in fractured porous media, even for a geometrically complex fracture network with large hydraulic conductivity contrasts between fractures and the matrix.     

A new lumped-parameter model for flow in unsaturated dual-porosity media

A new lumped-parameter approach to simulating unsaturated flow processes in dual-porosity media such as fractured rocks or aggregated soils is presented. Fluid flow between the fracture network and the matrix blocks is described by a non-linear equation that relates the imbibition rate of the local difference in liquid-phase pressure between the fractures and the matrix blocks. Unlike a Warren-Root-type equation, this equation is accurate in both the early and late time regimes. The fracture/matrix interflow equation has been incorporated into an existing unsaturated flow simulator, to serve as a source/sink term for fracture gridblocks. Flow processes are then simulated using only fracture gridblocks in the computational grid. This new lumped-parameter approach has been tested on two problems involving transient flow in fractured/porous media, and compared with simulations performed using explicit discretisation of the matrix blocks. The new procedure seems to accurately simulate flow processes in unsaturated fractured rocks, and typically requires an order of magnitude less computational time than do simulations using fully-discretised matrix blocks.     

Matrix diffusion-derived plume attenuation in fractured bedrock

Matrix diffusion can attenuate the rate of plume migration in fractured bedrock relative to the rate of ground water flow for both conservative and nonconservative solutes of interest. In a system of parallel, equally spaced constant aperture fractures subject to steady-state ground water flow and an infinite source width, the degree of plume attenuation increases with time and travel distance, eventually reaching an asymptotic level. The asymptotic degree of plume attenuation in the absence of degradation can be predicted by a plume attenuation factor, beta, which is readily estimated as R' (phi(m)/phi(f)), where R' is the retardation factor in the matrix, phi(m) is the matrix porosity, and phi(f) is the fracture porosity. This dual-porosity relationship can also be thought of as the ratio of primary to secondary porosity. Beta represents the rate of ground water flow in fractures relative to the rate of plume advance. For the conditions examined in this study, beta increases with greater matrix porosity, greater matrix fraction organic carbon, larger fracture spacing, and smaller fracture aperture. These concepts are illustrated using a case study where dense nonaqueous phase liquid in fractured sandstone produced a dissolved-phase trichloroethylene (TCE) plume approximately 300 m in length. Transport parameters such as matrix porosity, fracture porosity, hydraulic gradient, and the matrix retardation factor were characterized at the site through field investigations. In the fractured sandstone bedrock examined in this study, the asymptotic plume attenuation factors (beta values) for conservative and nonconservative solutes (i.e., chloride and TCE) were predicted to be approximately 800 and 12,210, respectively. Quantitative analyses demonstrate that a porous media (single-porosity) solute transport model is not appropriate for simulating contaminant transport in fractured sandstone where matrix diffusion occurs. Rather, simulations need to be conducted with either a discrete fracture model that explicitly incorporates matrix diffusion, or a dual-continuum model that accounts for mass transfer between mobile and immobile zones. Simulations also demonstrate that back diffusion from the matrix to fractures will likely be the time-limiting factor in reaching ground water cleanup goals in some fractured bedrock environments.     

Matrix–fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media

The matrix–fracture transfer shape factor is one of the important parameters in the modeling of fluid flow in fractured porous media using a dual-porosity concept. Warren and Root [36] introduced the dual-porosity concept and suggested a relation for the shape factor. There is no general relationship for determining the shape factor for a single-phase flow of slightly compressible fluids. Therefore, different studies reported different values for this parameter, as an input into the flow models. Several investigations have been reported on the shape factor for slightly compressible fluids. However, the case of compressible fluids has not been investigated in the past. The focus of this study is, therefore, to find the shape factor for the single-phase flow of compressible fluids (gases) in fractured porous media. In this study, a model for the determination of the shape factor for compressible fluids is presented; and, the solution of nonlinear gas diffusivity equation is used to derive the shape factor. The integral method and the method of moments are used to solve the nonlinear governing equation by considering the pressure dependency of the viscosity and isothermal compressibility of the fluid. The approximate semi-analytical model for the shape factor presented in this study is verified using single-porosity, fine-grid, numerical simulations. The dependency of the shape factor on the gas specific gravity, pressure and temperature are also investigated. The theoretical analysis presented improves our understanding of fluid flow in fractured porous media. In addition, the developed matrix–fracture transfer shape factor can be used as an input for modeling flow of compressible fluids in dual-porosity systems, such as naturally fractured gas reservoirs, coalbed methane reservoirs and fractured tight gas reservoirs.     

Discontinuous Galerkin methods for advective transport in single-continuum models of fractured media

Accurate simulation of flow and transport processes in fractured rocks requires that flow in fractures and shear zones to be coupled with flow in the porous rock matrix. To this end, we will herein consider a single-continuum approach in which both fractures and the porous rock are represented as volumetric objects, i.e., as cells in an unstructured triangular grid with a permeability and a porosity value associated with each cell. Hence, from a numerical point of view, there is no distinction between flow in the fractures and the rock matrix. This enables modelling of realistic cases with very complex structures. To compute single-phase advective transport in such a model, we propose to use a family of higher-order discontinuous Galerkin methods. Single-phase transport equations are hyperbolic and have an inherent causality in the sense that information propagates along streamlines. This causality is preserved in our discontinuous Galerkin discretization. We can therefore use a simple topological sort of the graph of discrete fluxes to reorder the degrees-of-freedom such that the discretized linear system gets a lower block-triangular form, from which the solution can be computed very efficiently using a single-pass forward block substitution. The accuracy and utility of the resulting transport solver is illustrated through several numerical experiments.     

An efficient numerical model for incompressible two-phase flow in fractured media

Various numerical methods have been used in the literature to simulate single and multiphase flow in fractured media. A promising approach is the use of the discrete-fracture model where the fracture entities in the permeable media are described explicitly in the computational grid. In this work, we present a critical review of the main conventional methods for multiphase flow in fractured media including the finite difference (FD), finite volume (FV), and finite element (FE) methods, that are coupled with the discrete-fracture model. All the conventional methods have inherent limitations in accuracy and applications. The FD method, for example, is restricted to horizontal and vertical fractures. The accuracy of the vertex-centered FV method depends on the size of the matrix gridcells next to the fractures; for an acceptable accuracy the matrix gridcells next to the fractures should be small. The FE method cannot describe properly the saturation discontinuity at the matrix–fracture interface. In this work, we introduce a new approach that is free from the limitations of the conventional methods. Our proposed approach is applicable in 2D and 3D unstructured griddings with low mesh orientation effect; it captures the saturation discontinuity from the contrast in capillary pressure between the rock matrix and fractures. The matrix–fracture and fracture–fracture fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides, in addition to the gridcell pressures, the pressures at the gridcell interfaces and can readily model the pressure discontinuities at impermeable faults in a simple way. To reduce the numerical dispersion, we use the discontinuous Galerkin (DG) method to approximate the saturation equation. We take advantage of a hybrid time scheme to alleviate the restrictions on the size of the time step in the fracture network. Several numerical examples in 2D and 3D demonstrate the robustness of the proposed model. Results show the significance of capillary pressure and orders of magnitude increase in computational speed compared to previous works.     

A terrain-following grid transform and preconditioner for parallel,large-scale,integrated hydrologic modeling

A terrain-following grid formulation (TFG) is presented for simulation of coupled variably-saturated subsurface and surface water flow. The TFG is introduced into the integrated hydrologic model, ParFlow, which uses an implicit, Newton Krylov solution technique. The analytical Jacobian is also formulated and presented and both the diagonal and non-symmetric terms are used to precondition the Krylov linear system. The new formulation is verified against an orthogonal stencil and is shown to provide increased accuracy at lower lateral spatial discretization for hillslope simulations. Using TFG, efficient scaling to a large number of processors (16,384) and a large domain size (8.1 Billion unknowns) is shown. This demonstrates the applicability of this formulation to high-resolution, large-spatial extent hydrology applications where topographic effects are important. Furthermore, cases where the analytical Jacobian is used for the Newton iteration and as a non-symmetric preconditioner for the linear system are shown to have faster computation times and better scaling. This demonstrates the importance of solver efficiency in parallel scaling through the use of an appropriate preconditioner.     

Simulating dispersion in porous media and the influence of segmentation on stagnancy in carbonates

Understanding the transport of chemical components in porous media is fundamentally important to many reservoir processes such as contaminant transport and reactive flows involved in CO₂ sequestration. Carbonate rocks in particular present difficulties for pore-scale simulations because they contain large amounts of sub-micron porosity. In this work, we introduce a new hybrid simulation model to calculate hydrodynamic dispersion in pore-scale images of real porous media and use this to elucidate the origins and behaviour of stagnant zones arising in transport simulations using micro-CT images of carbonates. For this purpose a stochastic particle model for simulating the transport of a solute is coupled to a Lattice-Boltzmann algorithm to calculate the flow field. The particle method incorporates second order spatial and temporal resolution to resolve finer features of the domain. We demonstrate how dispersion coefficients can be accurately obtained in capillaries, where corresponding analytical solutions are available, even when these are resolved to just a few lattice units. Then we compute molecular displacement distributions for pore-spaces of varying complexity: a pack of beads; a Bentheimer sandstone; and a Portland carbonate. Our calculated propagator distributions are compared directly with recent experimental PFG-NMR propagator distributions (Scheven et al., 2005; Mitchell et al., 2008), the latter excluding spin relaxation mechanisms. We observe that the calculated transport propagators can be quantitatively compared with the experimental distribution, provided that spin relaxations in the experiment are excluded, and good agreement is found for both the sandstone and the carbonate. However, due to the absence of explicit micro-porosity from the carbonate pore space image used for flow field simulations we note that there are fundamental differences in the physical origins of the stagnant zones for micro-porous rocks between simulation and experiment. We show that for a given micro-CT image of a carbonate, small variations in the parameters chosen for the segmentation process lead to different amounts of stagnancy which diffuse away at different rates. Finally, we use a filtering method to show that this is due to the presence of spurious isolated pores which arise from the segmentation process and suggest an approach to overcome this limitation.     

Direct numerical simulation of pore-scale flow in a bead pack: Comparison with magnetic resonance imaging observations

A significant body of current research is aimed at developing methods for numerical simulation of flow and transport in porous media that explicitly resolve complex pore and solid geometries, and at utilizing such models to study the relationships between fundamental pore-scale processes and macroscopic manifestations at larger (i.e., Darcy) scales. A number of different numerical methods for pore-scale simulation have been developed, and have been extensively tested and validated for simplified geometries. However, validation of pore-scale simulations of fluid velocity for complex, three-dimensional (3D) pore geometries that are representative of natural porous media is challenging due to our limited ability to measure pore-scale velocity in such systems. Recent advances in magnetic resonance imaging (MRI) offer the opportunity to measure not only the pore geometry, but also local fluid velocities under steady-state flow conditions in 3D and with high spatial resolution. In this paper, we present a 3D velocity field measured at sub-pore resolution (tens of micrometers) over a centimeter-scale 3D domain using MRI methods. We have utilized the measured pore geometry to perform 3D simulations of Navier–Stokes flow over the same domain using direct numerical simulation techniques. We present a comparison of the numerical simulation results with the measured velocity field. It is shown that the numerical results match the observed velocity patterns well overall except for a variance and small systematic scaling which can be attributed to the known experimental uncertainty in the MRI measurements. The comparisons presented here provide strong validation of the pore-scale simulation methods and new insights for interpretation of uncertainty in MRI measurements of pore-scale velocity. This study also provides a potential benchmark for future comparison of other pore-scale simulation methods. © 2012 Elsevier Science. All rights reserved.     

A numerical Eulerian method of moment for solute transport in a nonstationary dual-porosity medium

An Eulerian perturbation approach was applied to develop a method of moment for solute transport in a nonstationary, fractured medium. The conceptualized fractured medium is described through a dual-porosity model. Stochastic governing equations for mean concentration and concentration covariance were analytically derived to the first-order accuracy of log-conductivity variance and solved with a numerical method––a finite difference method. The developed method is called a numerical Eulerian method of moment (NEMM). This method was compared with the stationary transport theory [Water Resour. Res. 36(7) (2000) 1665] for predicting mean concentration and its spatial moments. The comparison indicated that the two methods matched very well in predicting first and second spatial moments. NEMM solutions were also compared with Monte Carlo simulations for solute transport in stationary fractured media. The results of the two methods were consistent for calculating small log conductivity variance. The theory was then used to study effects of various parameters and nonstationarity of the medium on flow and transport processes. Results indicated that medium nonstationarity would significantly influence the solute transport process. The nonstationary transport theory relaxes many assumptions adopted in stationary theories and paves the way for applying the NEMM to many environmental projects, especially in analyzing uncertainty of solute transport.     

Weathering and erosion of fractured bedrock systems

We explore the contribution of fractures (joints) in controlling the rate of weathering advance for a low‐porosity rock by using methods of homogenization to create averaged weathering equations. The rate of advance of the weathering front can be expressed as the same rate observed in non‐fractured media (or in an individual block) divided by the volume fraction of non‐fractured blocks in the fractured parent material. In the model, the parent has fractures that are filled with a more porous material that contains only inert or completely weathered material. The low‐porosity rock weathers by reaction‐transport processes. As observed in field systems, the model shows that the weathering advance rate is greater for the fractured as compared to the analogous non‐fractured system because the volume fraction of blocks is < 1. The increase in advance rate is attributed both to the increase in weathered material that accompanies higher fracture density, and to the increase in exposure of surface of low‐porosity rock to reaction‐transport. For constant fracture aperture, the weathering advance rate increases when the fracture spacing decreases. Equations describing weathering advance rate are summarized in the ‘List of selected equations’. If erosion is imposed at a constant rate, the weathering systems with fracture‐bounded bedrock blocks attain a steady state. In the erosional transport‐limited regime, bedrock blocks no longer emerge at the air‐regolith boundary because they weather away. In the weathering‐limited (or kinetic) regime, blocks of various size become exhumed at the surface and the average size of these exposed blocks increases with the erosion rate. For convex hillslopes, the block size exposed at the surface increases downslope. This model can explain observations of exhumed rocks weathering in the Luquillo mountains of Puerto Rico. Published 2017. This article is a U.S. Government work and is in the public domain in the USA