Effects of physical and chemical heterogeneities on transport and reaction processes in porous media

Open Access
Heidari, Peyman
Graduate Program:
Petroleum and Natural Gas Engineering
Doctor of Philosophy
Document Type:
Date of Defense:
December 09, 2014
Committee Members:
  • Li Li, Dissertation Advisor
  • Turgay Ertekin, Committee Member
  • Xiaofeng Liu, Committee Member
  • Jamal Rostami, Committee Member
  • Mineral Dissolution
  • Chemical Heterogeneity
  • Fluid Flow in Porous Media
  • Solute Transport
  • Non-Fickian Transport
In the natural subsurface various minerals and properties are often distributed heterogeneously. Numerous chemical and physical phenomena are influenced by heterogeneities such as contaminant transport, mineral dissolution, weathering, soil formation, nuclear waste disposal, hydrocarbon recovery, and migration of heavy metal. For example, precise modeling of transport is crucial for remediation scenario design in the event of a contaminant spill. Additionally, understanding mineral dissolution is of great importance since weathering is a common source of some elements crucial for the oceans and other ecosystems. Mineral distributions vary from random, homogenous patterns at one end of the spectrum to clustered zones and layers at the other end, which creates chemical heterogeneity. Even in a media purely made of a single mineral, physical properties such as permeability may differ spatially, resulting in physical heterogeneity. These heterogeneous distributions affect fluid flow, transport and reaction processes. Here we experimentally and numerically investigated the effect of chemical and physical heterogeneity on fluid flow, transport and reaction in porous media. We also proposed a new reactive transport model to simulate the soil formation process from Marcellus shale parent rock, which helped us in determining the key controlling parameters of the mineral dissolution and precipitation processes in natural settings. Spatial variations in subsurface physical properties have profound impacts on flow and solute transport. It is important to understand and quantify the role of heterogeneity structure in determining effective parameters at large scales in order to precisely model processes that are affected by fluid flow and transport such as mineral dissolution. There is a consensus that spatial patterns and heterogeneity structure play a critical role in determining solute transport. Various numerical studies have identified connectivity and correlation length as key parameters that determine solute breakthrough. Although connectivity and correlation length have been found to be critical in these modeling studies, they have not been systematically examined and confirmed experimentally. Existing experimental work on solute transport has mostly focused on single spatial patterns with one correlation length. The objective of the physical heterogeneity part of this work is to systematically understand and quantify the role of correlation length in determining effective permeability and solute transport using flow cell experiments and modeling approaches. In order to determine how physical heterogeneity structure, in particular correlation length, controls flow and solute transport, we used non-reactive solute transport in two-dimensional (2D) sand boxes (21.9 cm by 20.6 cm) and four modeling approaches, including 2D Advection-Dispersion Equation (ADE) with explicit heterogeneity structure, 1D ADE with average properties, and non-local Continuous Time Random Walk (CTRW) and fractional ADE (fADE). The goal of the physical heterogeneity part of the work was to answer two questions: 1) How and to what extent does correlation length control effective permeability and breakthrough curves (BTC)? 2) Which model can best reproduce data under what conditions? Sand boxes were packed with the same 20% (v/v) fine and 80% (v/v) coarse sands in three patterns that differ in correlation length. The Mixed cases contained uniformly distributed fine and coarse grains. The Four-zone and One-zone cases had four and one square fine zones, respectively. A total of 7 experiments were carried out with permeability variance of 0.10 (LC), 0.22 (MC), and 0.43 (HC). Experimental data show that the BTC curves depend strongly on correlation length, especially in the HC cases. The HC One-zone (HCO) case shows distinct breakthrough steps arising from fast advection in the coarse zone, slow advection in the fine zone, and slow diffusion, while the LCO and MCO BTCs do not exhibit such behavior. With explicit representation of heterogeneity structure, 2D ADE reproduces BTCs well in all cases. CTRW reproduces temporal moments with smaller deviation from data than fADE in all cases except HCO, where fADE has the lowest deviation. Well-mixed batch reactor reaction rate studies result in high dissolution rates, which are usually up to five orders of magnitude greater than field-scale rates. In the natural subsurface, solid materials of different properties are distributed unevenly with various spatial patterns. Numerous factors have been examined to explain the discrepancies between well-mixed laboratory rates and those measured in fields. Parameters such as chemical and physical heterogeneities, velocity, and flow distribution are commonly ignored in the well-mixed batch reactor rate measurements. Some modeling studies have shown that spatial distribution of minerals in porous media affects large-scale mineral dissolution. Experimental studies on the effect of spatial pattern of distribution of chemical heterogeneity on mineral dissolution reaction rate are scarce except for a few studies on magnesite dissolution rates. Large-scale dissolution rates can be affected by both physical and chemical heterogeneities. In the chemical heterogeneity part of the study we examined the effect of calcite spatial distribution on its dissolution rate under various flow velocities and permeability contrast conditions. Dissolution data of reactive fluid flow (pH=4) through two-dimensional (2D) flow cells (20.0 cm by 20.0 cm) was collected. The flow cells were packed with the same amount of calcite and sand with Mixed and One-zone patterns. The Mixed case contained uniformly distributed calcite and sand grains while the One-zone case had one square calcite zone in the middle of the flow cell. The experiments were carried out at three flow rates (1.435, 7.175, 14.35 m/d) and the dissolution process was simulated using reactive transport modeling. In addition to velocity, effect of parameters such as permeability ratio (calcite permeability/sand permeability), and transverse dispersivity on calcite dissolution were examined numerically. The goal of this part of the study was to answer the following questions: 1) What is the extent of the effect of physical and chemical heterogeneities on mineral dissolution? 2) What are the parameters that control significance of mineral spatial pattern on overall dissolution? In general, dissolution rates were higher in cases with higher mass transfer in the reactive zone. Increase of advective mass transfer with higher velocity or higher permeability ratio increased the rates. Increase of dispersive mass transfer with increase of transverse dispersivity also increased the rate. Four orders of magnitude of change in large-scale dissolution rate (Flow cell scale) were observed in the studied cases. The effect of spatial pattern was studied through use of a parameter βZ/M, defined as the One-zone large-scale rate divided by rate of its corresponding Mixed case. The βZ/M values normally range between 0 and 1. Larger values of βZ/M mean lesser effect of the spatial pattern and smaller, closer to 0 values indicate significant role of heterogeneity. Changes of transverse dispersivity (1.4×10-3cm– 1.4×10-1cm) resulted in a βZ/M range of 0.10 – 0.37. A minimum βZ/M of 0.06 was observed numerically at high velocity with low permeability ratio. While changes of permeability ratio (9.4×10-4 – 3.7×101) induced a βZ/M change of 0.06 to 0.88, changes of velocity (1.435×10-1m/d– 1.435×102m/d) did not affect βZ/M as significantly (0.15 - 0.22). The insignificant role of velocity on rate ratio was attributed to high reactivity of calcite because the solution reaches equilibrium upon contact with the reactive material at all flow velocities. Percentage of grains that participated in the dissolution reaction effectively (saturation=IAP/Keq< 0.1) increased with increase of permeability ratio and transverse dispersivity. In most cases all the effective surface area was at the calcite-sand interface except at high velocity and high permeability ratio. Under these conditions higher percentage of the total surface area was reacting effectively because advection time scale was shorter than reaction time scale and acidic inlet penetrated deeper into the reactive zone. In addition, large-scale reaction rates were related to dimensionless Peclet (Pe) and Damkohler (Da) numbers. Higher Pe and lower Da values were correlated with higher dissolution rate. Our results quantify the significance of mineral spatial distribution on reaction rates and weathering. Our results point to potential control of underlying chemical and physical heterogeneities on mineral dissolution, which can regulate ecosystem functioning and water cycling. To understand controls of geochemical reaction rates in natural systems, we modeled soil formation from Marcellus shale parent rock using reactive transport modeling with laboratory measured rate laws. Marcellus Shale is a black shale formation that is rich in organic matter and pyrite. The dissolution of Marcellus shale can lead to release of heavy metals and cause significant environment problems, especially with the extensive use of hydraulic fracturing during the production of natural gas. Here, we use soil formation and aqueous geochemistry data as constraints to understand the processes and develop a reactive transport model during Marcellus shale weathering. The simulation was carried out from approximately 10,000 years ago when the formation was first exposed after the last glacier to the present time. Our results indicated two distinct stages during the weathering. At the first 500 ~ 1,000 years, pyrite dissolved fast and Fe(OH)3 was the main precipitate. After pyrite depletion, chlorite dissolved primarily with vermiculite being the major precipitate. Field data can only be reproduced when the specific surface areas of the reactive minerals were decreased by orders of magnitude from laboratory-measured values, indicating the significantly lesser available surface area under natural conditions. Our sensitivity analysis indicated the important role of specific surface area, flow rate, and reactive gases (CO2 and O2). It was found that CO2 accelerates the weathering process and impacts pH profile and elemental concentrations in both solid and aqueous phases. In the cases with limited source of oxygen, unreacted pyrite remained in the system even after 10,000 years and ultimately dropped pH. However, the effect of O2 on the solid phase (porosity) was less than the effect of CO2. In addition, increase of flow rate increased the extent of weathering, and vice versa. However, the effects of flow rate on both solid and aqueous phases were less significant than the effect induced by changes of surface area and reactive gases. Chemical and physical heterogeneities lead to significant spatial variations in mineralogical, geochemical, and physical properties and have profound impacts on the flow, transport, and reaction processes. Understanding these processes are crucial in many applications, including contaminant fate and transport, chemical weathering, geological carbon sequestration, environmental remediation, and energy extraction. Most studies on the effect of physical heterogeneity on solute transport have focused on porous media with short correlation length. We observed significant non-Fickian transport with long correlation length even with relatively low permeability variance. Stratified low permeability layers and clay lenses with comparable length scale as the domain length are very common in natural subsurface. In addition, we found that mineral spatial distribution can affect reaction rates up to a factor of 20. This is increasingly important in several geochemical processes that occur over geologic time. For example, weathering and soil formation directly depend on mineral dissolution. Understanding weathering can help us predict a wide variety of processes from atmospheric CO2 levels to species concentrations in oceans and ecosystems.