Dynamic two-phase flow in porous media and its implications in geological carbon sequestration

Two-phase flow in porous media is an important subsurface process that has significant impacts on the global economy and environments. To study two-phase system in porous media, capillary pressure (Pc ), relative permeability (Kr), bulk electrical conductivity (σb) and bulk relative permittivity (εb) are often employed as characterization parameters. Interestingly, all of these parameters are functions of water saturation (S). However, the non-uniqueness in the Pc -S, Kr-S,σb-S and εb-S relationships pose considerable challenges in employing them for effective monitoring and control of the two-phase flow processes. In this work, laboratory scale experiments and numerical simulations were conducted to investigate the factors and conditions contributing to the non-uniqueness in the above relationships for silicone oil-water and supercritical CO2-water flow in porous media, with a special emphasis on geological carbon sequestration. Specifically, the dynamic capillary pressure effect, which indicates the dependence of the Pc - S relationship on the rate of change of saturation (∂S/∂t) during two-phase flow in porous media was investigated. Using a silicone oil-water system, the dynamic capillary pressure effect was quantified in term of the parameter named the dynamic coefficient, , and it was found to be dependent on the domain scale and the viscosity ratio of the two fluids. It was found that increases with the domain scale and the viscosity ratio. It is inversely affected by S t , which is related to the degree of resistance to the fluid motion, namely, viscosity. In almost all cases, was found to decrease monotonically with an increase in water saturation, S. An order increase in magnitude of was observed as the domain scale increases from 4cm scale to 8cm in height. A similar order of increase in was observed in the 12cm high domain scale. There is an order increase in the value of for the silicone oilwater system as the viscosity ratio increases from 200 to 500. For the supercritical CO2 (scCO2) and water system in porous media, the experiments and numerical simulations showed that increases with rising system temperature and decreasing porous media permeability. Dimensionless analysis of the silicone oil-water experimental results showed that by constructing non-dimensional groups of quantities expressing a relationship among different variables on which depends, it is possible to summarise the experimental results and determine their functional relationship. A generalised scaling relationship for was derived from the dimensionless analysis which was then validated against independent literature data. The exercise showed that the -S relationship obtained from the literature and the ii scaling relationship match reasonably well. This work also demonstrated the applicability of an artificial neural network (ANN) as an alternative computational platform for the prediction of the domain scale dependence of τ . The dependence of the Kr-S relationship on ∂S/∂t was also investigated. The results showed that the Kr-S curve under dynamic flow condition is different from that under the quasi-static condition. Kr for water (Krw) increases with increasing water saturation and decreases with the increase in viscosity ratio while Kr for silicone oil (Krnw) increases with decreasing water saturation as well as with the increase in viscosity ratio. Also, Krw decreases while Krnw increases with the increasing boundary pressure. However, the εb-S and σb-S relationships were found to be independent of ∂S/∂t for the scCO2-water system in carbonate and silicate porous media. Nevertheless, the εb and σb values decrease as the water saturation decreases in the two porous media samples. While εb decreases with increase in temperature in silica sand, the trend in the limestone showed a slight increase with temperature, especially at high water saturation. Also, the εb-S relationship is shown to be affected by pressure in silica sand increasing with the pressure of the domain. On the contrary, the σb-S relationship increases as the temperature increases with more significance at higher water saturation in the silica sand sample. This work further demonstrated the application of a membrane in the monitoring of the CO2 in geological sites used for carbon sequestration. Commercial silicone rubber coupled with a pressure transducer showed potential in the detection of CO2 leakage from geological sites. The response of the device in terms of the mass of permeated gas, permeability and gas flux were investigated for both CO2 and N2. In addition, the monitoring of potable water contamination in a shallow aquifer by the migrating or leaking of CO2 is demonstrated with the combination of the pH analysis, geoelectrical measurement techniques and the membrane-sensor system. Overall, the work in this PhD research demonstrated robust applications of two-phase systems’ characterization parameters under different scenarios in the porous media. Implications of the findings in this work to the monitoring and control of two-phase systems in porous media are expatiated

Experimental determination of dynamic effect for CO2-H2O flow in porous medium: application to CO2 sequestration

The presence of dynamic effects in two-phase characterization parameters has led to the modification of the traditional capillary pressure and saturation function. This modification now inlcudes the term dynamic coeffcient (τ) which indicates how far or close to equilibrium is the two-phase system. In this work, experimental techniques for the determination of the dynamic effects in the CO2-water system is presented. This is important in the characterization of the system for effective monitoring and control

Novel Linear and Nonlinear Equations for the Higher Heating Values of Municipal Solid Wastes and the Implications of Carbon to Energy Ratios

Energy recovery from municipal solid wastes (MSW) offers economic benefits together with improved management of wastes. In the literature, attempts have been made to understand and quantify the potential energy benefits of MSW but the implications of the proportion of the elemental constituents on the heating value of the wastes are rarely discussed. In this investigation, novel linear and nonlinear equations were developed from artificial neural network (ANN) to predict the higher heating values (HHV) of MSW. The new equations perform equally well in comparison with the existing models in the literature for different HHV data from various MSW sources. They also showed consistency in satisfactory performances for predicting HHV values from new data as well as altered elemental compositions. Furthermore, it was found that the change in the proportion of elemental compositions have interesting relation to the magnitude of the HHV for different wastes. Results show that a change in percent hydrogen (%H) changes the HHV in some wastes that possess the thresholds of both HHV magnitude and the carbon to energy ratio (C/HHV). For the waste with low HHV but relatively high C/HHV value, increasing the %H does not significantly alter their HHV value. For those with high HHV value and moderate C/HHV value, HHV increases as the %H increases. Wastes with high HHV value but low C/HHV undergo reverse in the trend of HHV as the %H increases. Typical example of this is found in plastic wastes with high percentage carbon (%C) but low C/HHV. In this waste, as the %H increases the corresponding HHV decreases. Keywords: Municipal solid wastes, linear, nonlinear, artificial neural network, carbon to energy ratio, higher heating values.

Artificial Neural Network (ANN) modelling of scale dependent dynamic capillary pressure effects in two-phase flow in porous media

A number of numerical simulations and experimental investigations have reported the impact of specific domain size on the dynamic capillary pressure which is one of the forces that govern two-phase flow in porous media. These investigations are often achieved with time-consuming experiments and/or costly/complex computational methods. In view of this, a computationally efficient and simple alternative platform for the prediction of the domain scale dependence of the dynamic capillary pressure effects, defined in terms of a coefficient named as dynamic coefficient ( ), is developed using artificial neural network (ANN). The input parameters consist of the phase saturation, media permeability, capillary entry pressure, viscosity ratio, density ratio, temperature, pore size distribution index, porosity and domain volume with corresponding output obtained at different domain scales. Good generalization of the model was achieved by acquiring data from independent sources comprising experiments and numerical simulations. Different ANN configurations as well as linear and non-linear multivariate regression models were tested using a number of performance criteria. Findings in this work showed that the ANN structures with two hidden layers perform better than those with single hidden layer. In particular, the ANN configuration with 13 and 15 neurons in the first and second hidden layers, respectively, performed the best. Using this best-performing ANN, effects of increased domain size were predicted for three separate experimental results obtained from literature and our laboratory with different domain scales. Results showed increased magnitude of as the domain size increases for all the independent experimental data considered. This work shows the applicability and techniques of using ANN in the prediction of scale dependence of two-phase flow parameters

Scale-dependent dynamic capillary pressure effect for two-phase flow in porous media in relation to fluid viscosity ratio

Scale-dependent dynamic capillary pressure effect for two-phase flow in porous media in relation to fluid viscosity rati

pH, geoelectrical and membrane flux parameters for the monitoring of water-saturated silicate and carbonate porous media contaminated by CO2

Characteristics of potable water aquifer contaminated by CO2 are investigated using well-defined laboratory experiments. The porous media domain was prepared with silica sand and limestone in separate experiments. The investigations used combinations of techniques to measure various parameters in the water-saturated porous media domain on which pressure of CO2 was imposed, under various conditions, which correspond to different geological depths. Measured parameters included the pH, geoelectrical parameters, and the diffusion of the CO2 gas through the water-saturated porous media domain using non-porous silicone rubber sheet. Experimental results revealed the existence of three stages in the profile of pH change with time as CO2 dissolved and diffused in the water-saturated porous media domain, which was composed of silica sand. The first stage was characterised by rapid decline in the pH. This is associated with quick dissolution of CO2 and the formation of carbonic acid together with bicarbonate. The second stage showed short rise in pH value, which was attributed to the reverse reaction, i.e., the formation of aqueous and gaseous CO2 and water from the carbonic acid. The third stage was that of the equilibrium in the forward and the reverse reactions, marked by steady state in pH value, which remained unchanged till the end of the experiment. The bulk electrical conductivity (σb) of the water-saturated porous domain increased in the presence of CO2. This is attributed to the formation of ionic species, especially bicarbonate, as CO2 dissolved in the domain. The rise in σb coincided with the first stage of the change in the pH of the system. In addition, the σb was higher in limestone than silica sand, and it increased with pressure of the domain. But, the bulk dielectric constant (εb) showed no change with the dissolution of the CO2 under different conditions. Furthermore, permeation of CO2 through the silicone rubber indicated the diffusion of the CO2 gas through the water-saturated domain. CO2 flux through the membrane was shown to increase with depth or pressure of the domain. A mathematical expression derived in this work shows the dependence of σb on the pH and the initial value of σb. Predictions of the changes in the σb for different porous domains show the reliability of the mathematical expression developed in this work

Scale dependent dynamic capillary pressure effect for two-phase flow in porous media

Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well

Geoelectrical characterization of carbonate and silicate porous media in the presence of supercritical CO2-water flow

The relative permittivity (εr) and the electrical conductivity (σ) of porous media are known to be functions of water saturation (S). As such, their measurements can be useful in effective characterisations and monitoring of geological carbon sequestration using geoelectrical measurement techniques. In this work, the effects of pressure, temperature and salt concentration on bulk εr–S and σ–S relationships were investigated for carbonate (limestone) and silicate porous media (both unconsolidated domains) under dynamic and quasi-static supercritical CO2 (scCO2)-brine/water flow. In the silica sand sample, the bulk εr (εb) for scCO2–water decreases as the temperature increases. On the contrary, slight increase was seen in the εb with temperature in the carbonate sample for the scCO2-water system. These trends are more conspicuous at high water saturation. The εb–S curves for the scCO2–water flow in the silica sand also show clear dependency on the domain pressure, where εb increases as the domain pressure increases. Furthermore, the bulk σ (σb), at any particular saturation for the scCO2-brine system rises as the temperature increases with more significant increase found at very high water saturation. Both εb and σb values are found to be greater in the limestone than silica sand porous samples for similar porosity values. Based on different injection rates investigated, we do not find significant dynamic effects in the εb–S and σb–S relationships for the scCO2-brine/water system. As such, geoelectrical characteristics can be taken as reliable in the monitoring of two-phase flow system in the porous media. It can be inferred from the results that the geoelectrical techniques are highly dependent on water saturation. This dependence is more conspicuous at higher water saturation. Different mathematical models examined show their reliability at different water saturation ranges. The polynomial fit developed in this work takes into consideration the fluid pressure in the system as well as the initial bulk relative permittivity prior to the injection of CO2. The polynomial fit shows a good reliability in the prediction of the geo-electrical properties of the CO2–water–porous media system, especially at higher water saturation. In comparison, the mixing model from the literature shows more reliability in the prediction of similar property at lower water saturation

Application of artificial neural network in the prediction of scale dependency of dynamic effects in two-phase flow system

Application of artificial neural network in the prediction of scale dependency of dynamic effects in two-phase flow syste

Permeability, selectivity and distinguishing criterion of silicone membrane for supercritical CO2 and N2 in the porous media

The possibility of leakage of CO2 from a geological storage reservoir is of serious concern to stakeholders. In this work, high–pressure-temperature laboratory experiments were performed to demonstrate the application of a silicone membrane-sensor system in the monitoring of subsurface gases, especially in the leakage scenario. Mass permeation, membrane resistance to gas permeation, and the gas flux across the membrane are reported for two gases, namely, CO2 and N2. Mass permeation of CO2 through the membrane was more than ten times higher than that of N2, under similar conditions. It was also found to increase with the geological depths. The gas flux remains higher for CO2 as compared to N2. From the results, a simple criterion for distinguishing the presence of the different gases at various geological depths was formulated based on the rate of permeation of gas through the membrane. Results and techniques in this work can be employed in the detection/monitoring of subsurface gas transport, especially in geological carbon sequestration