MODELING OF GAS SORPTION AND DIFFUSION BEHAVIOR AND IMPLICATIONS ON COALBED METHANE PRODUCTION
Open Access
- Author:
- Yang, Yun
- Graduate Program:
- Energy and Mineral Engineering
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 12, 2020
- Committee Members:
- Shimin Liu, Dissertation Advisor/Co-Advisor
Shimin Liu, Committee Chair/Co-Chair
Derek Elsworth, Committee Member
Sekhar Bhattacharyya, Committee Member
Chris J Marone, Outside Member
Mort D Webster, Program Head/Chair - Keywords:
- Coalbed Methane
Gas Adsorption
Gas Diffusion
Pore Structure
Cryogenic Fracturing
Fractal Dimension
Sorption Models - Abstract:
- Exploration of coalbed methane (CBM) in North America started from the 1970s as the oil crisis shifted the interest to potential natural gas resources in coalbeds. Unlike conventional natural gas reservoirs, coal acts as both source and reservoir for hydrocarbon, where 90-98% of gas in the coal seam is adsorbed at its internal surface of coal matrices. Previous studies have demonstrated that pore structure is a key factor determining gas storage and transport behaviors of CBM reservoirs. This study established an analytical relationship between pore structure and gas sorption and diffusion characteristics of coal. My holistic study can be broadly divided into two parts, including theoretical modeling (Chapter 2) and experimental study (Chapter 3). Theoretical models have been proposed to quantify gas storage capacity and diffusion coefficient of coal by directly using pore structure parameters as physical inputs. The proposed models are calibrated and validated by laboratory data, and the results are presented in Chapter 4. The theoretical analysis and experimental work conducted in these three Chapters are further coupled into gas production simulator to define the unique production profile for mature CBM wells in San Juan basin (Chapter 5). The knowledge of pore structure alteration and its influence in gas-solid interactions of coal is employed to examine the applicability of a waterless fracturing technique, cryogenic fracturing in CBM reservoirs (Chapter 6). A pore structure-gas sorption model has been proposed in Chapter 2. This model is validated against experimental data measured by sorption apparatus depicted in Chapter 3, and the validation results are presented in Chapter 4. Here presents an abstract of the findings of my thesis on the relationship between pore structure and gas sorption behavior. Gas adsorption volume has long been recognized as an important parameter for CBM formation assessment as it determines the overall gas production potential of CBM reservoirs. As the standard industry practice, Langmuir volume (VL) is used to describe the upper limit of gas adsorption capacity. Another important parameter, Langmuir pressure (PL), is typically overlooked because it does not directly relate to the resource estimation. However, PL defines the slope of the adsorption isotherm and the ability of a well to attain the critical desorption pressure in a significant reservoir volume, which is critical for planning the initial water depletion rate for a given CBM well. Qualitatively, both VL and PL are related to the fractal pore structure of coal, but the intrinsic relationships among fractal pore structure, VL, and PL are not well studied and quantified due to the complex pore structure of coal. In this thesis, a series of experiments were conducted to measure the fractal dimensions of various coals and their relationship to methane adsorption capacities. The thermodynamic model of the gas adsorption on heterogonous surfaces was revisited, and the theoretical models that correlate the fractal dimensions with the Langmuir constants were proposed. Applying the fractal theory, adsorption capacity (V_L) is proportional to a power function of specific surface area and fractal dimension, and the slope of the regression line contains information on the molecular size of the adsorbed gas. We also found that P_L is linearly correlated with sorption capacity, which is defined as a power function of total adsorption capacity (V_L) and a heterogeneity factor (ν). This implies that PL is not independent of VL, instead, a positive correlation between V_L and P_L has been noted elsewhere (e.g., Pashin (2010)). In the Black Warrior Basin, Langmuir volume is inversely related to coal rank (Kim, 1977; Pashin, 2010), and Langmuir pressure is positively related to coal rank. It was also found that P_L is negatively correlated with adsorption capacity and fractal dimension. A complex surface corresponds to a more energetic system, which results in an increase in the number of available adsorption sites and adsorption potential, which raises the value of V_L and reduces the value of P_L. A pore structure-gas diffusion model is developed in Chapter 2. This model is validated against experimental data measured by sorption apparatus depicted in Chapter 3, and the validation results are presented in Chapter 4. Here presents an abstract of the findings of the research on the relationship between pore structure and gas diffusion behavior. Diffusion coefficient is one of the key parameters determining the coalbed methane (CBM) reservoir economic viability for exploitation. Diffusion coefficient of coal matrix controls the long-term late production performance for CBM wells as it determines the gas transport effectiveness from matrix to fracture/cleat system. Pore structure directly relates to the gas adsorption and diffusion behaviors, where micropore provides the most abundant adsorption sites and meso- and macro-pore serve as gas diffusive pathway for gas transport. Gas diffusion in coal matrix is usually affected by both Knudsen diffusion and bulk diffusion. A theoretical pore-structure-based model was proposed to estimate the pressure-dependent diffusion coefficient for fractal porous coals. The proposed model dynamically integrates Knudsen and bulk diffusion influxes to define the overall gas transport process. Uniquely, the tortuosity factor derived from the fractal pore model allowed to quantitatively take the pore morphological complexity to define the diffusion for different coals. Both experimental and modeled results suggested that Knudsen diffusion dominated the gas influx at low pressure range (< 2.5 MPa) and bulk diffusion dominated at high pressure range (>6 MPa). For intermediate pressure ranges (2.5 to 6 MPa), combined diffusion should be considered as a weighted sum of Knudsen and bulk diffusion, and the weighing factors directly depended on the Knudsen number. The proposed model was validated against experimental data, where the developed automated computer program based on the Unipore model can automatically and time-effectively estimate the diffusion coefficients with regressing to the pressure-time experimental data. This theoretical model is the first-of-its-kind to link the realistic complex pore structure into diffusion coefficient based on the fractal theory. The experimental results and proposed model can be coupled into the commercially available simulator to predict the long-term CBM well production profiles. Chapter 5 presents a field case study to model long-term production behavior for mature CBM wells. CBM wells in the fairway of the San Juan basin are in the mature stage of pressure depletion, experiencing very low reservoir pressure. These mature wells that have been successfully producing for more than 20 years exhibit long-term hyperbolic decline behavior with elongated production tails. Permeability growth during primary production is a well-known characteristic of fairway reservoirs and was historically interpreted to be the dominant factor causing the production tail. Several experimental works observed that the diffusion coefficient of the San Juan coal sample also varied with pressure. However, the pressure-dependent nature of gas diffusion in the coal matrix was neglected in most simulation works of CBM production. This may not significantly mis-predict the early and medium stage of production behavior when permeability is still the primary controlling parameter of gas flow. Prediction errors are elevated considerably for these late-stage fairway wells when diffusion mass flux takes the predominant role of the overall flowability. A novel approach to implicitly incorporate the evolution of gas diffusion during pressure depletion in the flow modeling of fairway reservoirs was proposed in this Chapter, where the derived diffusion-based matrix permeability model converts gas diffusivity into Darcy's form of matrix permeability. This modeling of matrix flow enables the direct use of lab measurements of diffusivity as input to the reservoir simulator. The calculated diffusion-based permeability also increases with pressure decrease. The matrix and cleat permeability growths are then coupled into the numerical simulator to history-match the field production of multiple CBM wells in the fairway region. The established numerical model provides satisfactory matches to field data and accurately predicts the elongated production tail in the late decline stage. Sensitivity analyses were conducted to examine the significance of accurate modeling of gas diffusion flow in CBM production throughout the life span of the fairway wells. The results show that the assumption on constant matrix flowability leads to substantial errors in the prediction of both peak gas production rate and long-term declining behavior. Accurate modeling of gas diffusive in the matrix is essential in production projection for the mature fairway CBM wells. The integration of gas diffusivity growth into production simulation improves the prediction of gas production rates and the estimation of ultimate recovery for the late-stage fairway reservoirs. Chapter 6 investigates the applicability of cryogenic fracturing in exploiting CBM plays using the theoretical and experimental analyses conducted in Chapter 2 and Chapter 3. Cryogenic fracturing using liquid nitrogen is a waterless and environmentally-friendly formation stimulation method to effectively create a complex fracture network and dilatated nano- and micro- pores within coal matrix that greatly enhances gas transport in coal matrix as well as cleats. However, the development of cryogenic fracturing is still at its infancy. Before large-scale field implementation, a comprehensive understanding of the fracture and pore alteration will be essential and required. For pore-scale investigation, this chapter focuses on the induced pore structural alterations due to cryogenic treatment and their effects on gas sorption and diffusion behaviors. The changes in the pore structure of coal induced by cyclic nitrogen injections were studied by physical adsorption at low temperatures. A micromechanical model was proposed to simulate the microscopic process and predict the degree of deterioration due to low temperature treatments. As a common characteristic of modeled results and experimental results, the total volume of mesopore and macropore increased with cryogenic treatment, but the growth rate of pore volume became much smaller as freezing-thawing were repeated. Pores in different sizes experienced different degrees of deterioration. In the range of micropores, no significant alterations of pore volume occurred with the repetition of freezing and thawing. In the range of mesopore, pore volume increased with the repetition of freezing and thawing. In the range of macropores, pore volume increased after the first cycle of freezing and thawing but decreased after three cycles of freezing and thawing. Because of pore structural alterations, cryogenic treatment enhanced gas transport process as the diffusion coefficients of the freeze-thawed coal samples were increased by 18.76% and 30.18% in the adsorption and desorption process. For the studied Illinois coal sample, repetitive applications of cryogenic treatment reduced macropore volume and increase mesopore volume. For the tested sample, the diffusion coefficient of the coal sample that underwent three cycles of freezing-thawing was lower than that of the coal sample that underwent a single cycle of freezing and thawing. The outcome of this study provides a scientific justification for post-cryogenic fracturing effect on diffusion improvement and gas production enhancement, especially for high “sorption time” CBM reservoirs. For fracture-scale investigation, Chapter 6 develops a non-destructive geophysical technique using seismic measurements to probe fluid flow through coal and ascertain the effectiveness of cryogenic fracturing. A theoretical model was established to determine fracture stiffness of coal inverted from wave velocities, which serves as the nexus that correlates hydraulic with seismic properties of fractures. In response to thermal shock and frost forces, visible cracks were observed on coal surfaces that deteriorated the mechanical properties of the coal bulk. As a result, the wave velocity of the frozen coal specimens exhibited a general decreasing trend with freezing time under both dry and saturated conditions. For the gas-filled specimen, both normal and shear fracture stiffness monotonically decreased with freezing time as more cracks were created to the coal bulk. For the water-filled specimen, the formation of ice provoked by cryogenic treatment leads to the grouting of the coal bulk. Accordingly, fracture stiffness of the wet coal initially increased with freezing time and then decreased for longer freezing time. Coalbed with higher water saturation is preferred in the application of cryogenic fracturing because fluid-filled cracks can endure larger cryogenic forces before complete failures, and the contained water aggravates breaking coal as ice pressure builds up from volumetric expansion of water-ice phase transition and adds additional splitting forces on the pre-existing or induced fractures/cleats. This study also confirms that the stiffness ratio is sensitive to fluid content. The measured stiffness ratio varied between 0.7 and 0.9 for the dry coal, and it was less than 0.3 for the saturated coal. The outcome of this study provides a basis for a realistic estimation of stiffness ratio for coal for future discrete fracture network modeling.