Permeability, Flow Rate, and Hydraulic Conductivity Determination for Variant Pressures and Grain Size Distributions Nick Desiderio, npd5050@psu.edu, February 18, 2014 Abstract Carbon capture and storage methods are used to decrease the amount of greenhouse gases emitted into the atmosphere such as carbon dioxide. The greenhouse gas, CO 2, is injected deep within the earth into saline aquifers, depleted oil/gas wells, and coalbeds. Permeability factors are taken into account before the injection of CO 2 and after the injection of CO 2. Geological formations must be permeable enough to allow the penetration and passage of fluid such as CO 2 through pores in rock. After the CO 2 is stored, the geological formations must have a sufficient lower permeability that will not allow for propagation of fluid back to the surface in order to prevent continued atmospheric contamination. Saline aquifers alone may account for 350 to 11,000 Gt CO 2 emissions storage. Hydraulic fracturing consists of pumping pressurized fluid into an oil/gas well to creates fractures. The fractures are held open by proppants or small granules which allows for sufficient permeability and continued oil and gas production. Core analysis of three samples, coarse, medium, and fine were analyzed in this study to determine permeability, flow rate, and hydraulic conductivity factors. Utilizing Darcy s law allowed for determination of these factors by varying pressures and grain sizes. The relationship of permeability increasing with increase of pressure and increase in particle size was illustrated in this study. The coarse particle size was the highest permeable core at 1.73 to 3.88 darcy. The fluid flow rate range through this core was 0.181 to 0.417 ± 0.0005 cm 3 /s and the hydraulic conductivity of the sample was 0.072-0.104 cm/s. The medium core had a permeability range of 0.81 to 1.54 darcy, a flow rate range of 0.085-0.165 ± 0.005 cm 3 /s, and hydraulic conductivity of 0.028 to 0.040 cm/s. The fine core sample was the lowest permeable core with a range of 0.63 to 1.11 darcy, fluid flow rate of 0.067 to 0.119 ± 0.005 cm 3 /s, and a hydraulic conductivity of 0.021 to 0.034 cm/s. Introduction Carbon dioxide sequestration along with oil and gas production highly depends on factors such as permeability and hydraulic conductivity. 1 The increase in concentration of atmospheric greenhouse gases such as carbon dioxide results in global climate change. 2 Ways of preventing CO 2 from reaching the atmosphere must be developed to stop climate change. Carbon capture and storage is a process that sequesters CO 2 emissions from power plants or other emission sources. 2 The CO 2 is then injected deep within a geological formation such as saline aquifers, depleted oil and gas wells, or coal seams. 2 The large abundance of these geological formations may allow for an easy 100 to 1000 years CO 2 storage capacity. 2 Saline aquifers in the United States offer 350 to 11,000 Gt CO 2 emission storage capacity compared to an annual production of 24 Gt CO 2 emissions. 3 Several commercial sequestration projects that use this CCS method are in operation today such as the Weyburn, Sleipner, and Salah project. 2 The goal of carbon 1
dioxide sequestration is to keep the gas contained forever and prevent any atmospheric leakage. 2 Permeability factors have a major role in ensuring minimal propagation of stored CO 2 and no leakage in the future. 2 Enhanced oil recovery is a technique used in oil and gas industries to boost the percentage of oil recovered by 30-60%. 2 This technique encompasses several methods with one method being the injection of CO 2 which can help force oil out of a reservoir by pressure expansion. 2 Hydraulic fracturing is a process where a highly pressurized fluid such as CO 2 is pumped into an oil/gas well at sufficiently high rates to create fractures. 4 Small granules known as proppants are delivered to these fractures caused by hydraulic fracturing. 4 These proppants aid by keeping the flow paths open against rock pressure. 4 The proppants ensure sufficient permeability to allow for continued oil/gas production. 4 Proppants are extremely important within the gas and oil industry because of their properties to withstand high pressures and stresses from rock and fluid flowing through them. 4 They are known to boost the production of oil and gas by a substantial amount. 4 The objective of this study was to quantify and evaluate factors such as absolute permeability, flow rate and hydraulic conductivity based on pressure and grain size distributions. The use of three cores of beads with different particle size distributions ranging from coarse to fine allowed for comparison of these factors. The flow rate of water through these cores allowed for exploration of absolute permeability. 5 Permeability was also quantified and evaluated to explore the correlation between permeability and porosity. Formations that transmit fluids better are described as permeable and tend to have large well connected pores and tend to be coarse. 5 Finer grained particles are known to have fewer or non-interconnected pores which results in impermeability. 5 It was expected that the fine beadpack core would have the lowest permeability and that the coarse beadpack would have the highest permeability. It was also indicated that the pressure would increase with height, and the flow rate, permeability, and hydraulic conductivity would increase with increasing pressure. 6 Flow rate, permeability, and hydraulic conductivity would also increase with an increase in average particle size. 6 Theory Permeability is a property that quantifies the ability to flow or transmit fluids through a rock when a single fluid is present in pore space. 5 Absolute permeability quantifies this relationship when the fluid being transmitted is water. 5 The use of core analysis was applied during this study in order to determine the flow rate of water through the various beadpacks. Determination of flow rate allowed for the calculation of permeability and related values. The velocity of a homogeneous fluid in a porous medium is proportional to the pressure gradient and inversely proportional to the fluid viscosity. 5 Equation 1 known as Darcy s law, illustrates the relationship between fluid flow rate and pressure drop. 5 Q = (-k/ μ)a(dp/ds) (1) In Darcy s law, Q represents the flow rate (cm 3 /s), μ is the viscosity (cp) of the fluid at 20 C and in this case water (1.0020 cp), A is the cross sectional area (cm 2 ) of the core, dp/ds is the pressure gradient in the direction of flow (atm/cm), and k is the permeability (darcy). 5 A permeability of 1 darcy allows for the passage of flow from 1 cm 3 of fluid with a viscosity of 1 cp under a pressure gradient of 1 cm 2 through a porous medium with a length 1 cm. 5 2
Hydraulic conductivity also describes the ability of fluid to flow through pore spaces and fractures of rock or particles. 6 Another version of Darcy s law shown in equation 2 provided the ability to quantify hydraulic conductivity of the different beadpack samples. Q represents the flow rate (cm 3 /s), A represents the column cross sectional area (cm 2 ), k is the hydraulic conductivity, and dh/dl is the hydraulic gradient or change in head over the length of interest. 6 Q = ka (dh/dl) (2) The quantification of pressure was needed in order to explore the relationship between the flow rate and the ability of the fluid to pass through the beadpack samples. Equation 3 was used to calculate the total pressure of the fluid and air. Equations 3 and 4 were utilized because the fluid container was exposed to the surrounding atmosphere, so the atmospheric pressure must be accounted for as well. 7 P total = P atmosphere + P fluid (3) P total = P atmosphere + (ρ g h)(9.87 10-6 ) (4) In equation 4, P atmosphere represents the pressure of the atmosphere (1atm), ρ represents the density of the fluid, in this case water (1000kg 3 /m 3 ), g is the acceleration of gravity 9.8m/s 2, h is the height of the fluid (m), and P total is the total pressure of the fluid flow. 7 The conversion value of atmospheres was needed in order to convert the fluid pressure into correct units. Increases in pressure would increase the total flow rate of the fluid. Fluid flow of geological rock formations can be affected and depend on in-situ conditions which occur naturally. 8 Saline aquifers such as those compacted in North America are composed of sedimentary rock and show that pressure, interfacial tension, relative permeability and other displacements characteristics of CO 2 -brine systems depend on the in-situ conditions of pressure, temperature and water salinity, and on the pore size distribution of the sedimentary rock. 8 Fluid flow can be greatly affected by pressure and temperature in certain geological regions. For temperatures and pressures above the critical point (31.1 C) and (7.38MPa), CO 2 is a supercritical gas but has a density like a liquid. 8 These conditions are found at depths between 600 and 1000 meters depending on geothermal regimes. 8 To maximize pore space, CO 2 injections at these depths are recommended. 8 Methods Permeability directly relates to a porous medium or rock s ability to readily transmit fluids. Geological formations such as sandstone transmit fluids easily and are said to be permeable. Sandstone s permeability is derived from its particle s large and well interconnected pores. Formations such as shale and siltstones contain mixed and finer grained sizes which correlate to smaller and fewer interconnected pores. Permeability was explored by comparing different samples of particle size distributions. 3
Three core samples composed of different particle size distributions were used to differentiate between permeability and pore interconnectivity. The three samples ranged from coarse (30-40, medium (50-70), and fine (70-100). The three samples were used to simulate real geological rock compositions in nature and their permeability characteristics. The absolute permeability was explored in each sample by exposing the core sample to a constant fluid flow of water (750mL) and varying heights. The variance of height exposed the core sample to higher and lower pressures and ultimately differentiated the flow rate and permeability factors. The height range of water that the samples were exposed to was from 24 cm to 54 cm. Flow rate was quantified for each height point and was calculated by dividing the collected volume of the water (cm 3 ) over the course of time for each trial (s). The core diameter and length were measured in order to determine permeability and hydraulic conductivity. These measurements also allowed for greater observations in the fluid flow rate. Results and Discussion Permeability, flow rate, and hydraulic conductivity factors were compared based on the particle size distribution. Three cores composed of different mean particle sizes ranging from coarse (30-40), medium (50-70), and fine (70-100) were compared in this study. Permeability and flow rate are directly related to particle size distribution and pore connectivity. Coarser particles would result in a higher permeability and finer particles would result in a lower permeability. To determine permeability, the pressure of the fluid (water) at each height was used. Table 1 shows the results and calculations for the coarse sample. The permeability as expected increased from a range of 1.73 to 3.88 darcy compared to the height range of 24.5 to 54 cm. The flow rate varied from 1.181 to 0.417 ± 0.0005 cm 3 /s compared to the same height range. Hydraulic conductivity depended on flow rate and height differentials resulting in a range anywhere from 0.072 to 0.102 cm/s. All of these factors were indeed the greatest for the coarse sample. Table 1. Permeability, flow rate, and hydraulic conductivity for coarse sample (30-40) Water Height (cm) Pressure (atm) Absolute Permeability (darcy) Flow rate (cm 3 /s) Hydraulic Conductivity (cm/s) 24.5 ± 0.005 1.02 ± 0.005 1.73 0.181 ± 0.0005 0.072 32.0 ± 0.005 1.03 ± 0.005 2.29 0.242 ± 0.0005 0.074 38.5 ± 0.005 1.04 ± 0.005 2.80 0.297 ± 0.0005 0.102 48.0 ± 0.005 1.05 ± 0.005 3.36 0.359 ± 0.0005 0.073 54.0 ± 0.005 1.06 ± 0.005 3.88 0.417 ± 0.0005 0.074 4
Table 2 shows permeability, flow rate, and hydraulic conductivity factors for the medium sample (50-70). These factors were the second greatest compared to all of the samples as expected. The permeability ranged from 0.81 to 1.54 darcy. The flow rate ranged from 0.085 to 0.165 ± 0.0005 cm 3 /s. The hydraulic conductivity ranged anywhere between 0.028 and 0.040 cm/s. Table 2. Permeability, flow rate, and hydraulic conductivity for medium sample (50-70) Water Height (cm) Pressure (atm) Absolute Permeability (darcy) Flow rate (cm 3 /s) Hydraulic Conductivity (cm/s) 24.5 ± 0.005 1.02± 0.005 0.81 0.085 ± 0.0005 0.034 32.0 ± 0.005 1.03± 0.005 0.86 0.090 ± 0.0005 0.028 38.5 ± 0.005 1.04± 0.005 1.09 0.116 ± 0.0005 0.040 48.0 ± 0.005 1.05± 0.005 1.38 0.147 ± 0.0005 0.030 54.0 ± 0.005 1.06± 0.005 1.54 0.165 ± 0.0005 0.029 Table 3 shows all the same factors for the fine samples (70-100). They were the lowest compared to the other particle samples because of the sample s fine nature and smaller or less connected pores. The permeability ranged from 0.63 to 1.11 darcy. The flow rate ranged from 0.067 to 0.119 ± 0.005 cm 3 /s, and the hydraulic conductivity ranged from 0.021 to 0.034. Table 3. Permeability, flow rate, and hydraulic conductivity for fine sample (70-100) Water Height (cm) Pressure (atm) Absolute Permeability (darcy) Flow rate (cm 3 /s) Hydraulic Conductivity (cm/s) 24.5± 0.005 1.02 ± 0.005 0.63 0.067 ± 0.005 0.026 32.0 ± 0.005 1.03 ± 0.005 0.80 0.084 ± 0.005 0.026 38.5 ± 0.005 1.04 ± 0.005 0.93 0.099 ± 0.005 0.034 48.0 ± 0.005 1.05 ± 0.005 0.99 0.106 ± 0.005 0.022 54.0 ± 0.005 1.06 ± 0.005 1.11 0.119 ± 0.005 0.021 5
Overall, there was a significant amount of human error within the experiment. The height incrementing was done by hand which provided uncertainty of height measurement. The uncertainty of height then had to be factored into the calculation of pressure. Flow rate was measured by hand as well which produced uncertainty in the calculation of flow rate. The graduated cylinder was judged by eye which caused imprecision. The core samples were judged by eye as well which would produce the same problem of uncertainty. All of the uncertainty from direct measurements is accounted for within the data tables 1-3. There was also lag time between the timing of trials which probably accounted for small to negligible error. Conclusions The permeability, flow rate, and hydraulic conductivity are all desirable properties within oil and gas industry. They are factors in quantifying a geological formation s ability to transmit fluid through pore connectivity. Three core samples were analyzed in the study; coarse (30-40), medium (50-70), and fine (70-100). Permeability and flow rate were expected to increase with increasing pressure. The permeability and flow rates of each sample all increased gradually with pressure and resulted in linear relationships. Hydraulic conductivity was not dependent directly on the pressure. Conductivity was dependent on the height of water flow and the flow rate of water. This resulted in an inconsistent range of hydraulic conductivity, but it tended to generally increase with an increase in height. The most permeable particle size was the coarse sample with a permeability range of 1.73 to 3.88 darcy. The flow rate of sample one was also the greatest in the range of 0.181 to 0.417 ± 0.0005 cm 3 /s. The least permeable particle size was the fine sample with a permeability range of 0.63 to 1.11 darcy and a flow rate range from 0.067 to 0.119 ± 0.005 cm 3 /s. The medium grain size core was in the middle with a permeability range of 0.81 to 1.54 darcy and a flow rate of 0.085-0.165 ± 0.005 cm 3 /s. The hydraulic conductivity of the samples was not dependent on the fluid pressure. The ranges were not linearly consistent, but for the most part tended to increase with increasing water height. The coarse sample again had the largest conductivity range at 0.072-0.104 cm/s. The fine sample had the lowest hydraulic conductivity range, 0.021 to 0.034 cm/s. The medium sample was in the middle again with a range of 0.028 to 0.040 cm/s. The permeability and hydraulic conductivity of these samples further showed the importance of these factors for use in oil and gas industry as well as sequestering CO 2. CCS and EOR require ways of manipulating these factors to fulfil commercial purposes. Lower permeability of geological formations may allow for thousands of years CO 2 injection and storage. Higher permeability of geological formations can be utilized to recover oil greater, up to 30-60%. 6
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