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Collaborating Authors
Results
A New Stochastic Bubble Population Model For Foam In Porous Media
Zitha, Pacelli Lidio Jose (Delft University of Technology)
Abstract Foam has been widely used as a mobility control agent for Improved Oil Recover (IOR), gas blocking and acid diversion during matrix stimulation. The prediction of foam performance relies on macroscopic modeling. Foam modeling approaches include fractional flow theories and population balance models. Traditionally, fractional foam models assume implicitly that foam is incompressible and do not account directly for the evolution of bubble population. The population balance models, instead, rely on the idea that foam mobility depends on bubble density and are more comprehensive. Yet, population balance models did not gain full acceptance thus far, because of their perceived complexity, with parameters that are hard to obtain experimentally. This paper presents an improved foam model based on a simpler but realistic foam rheology and stochastic bubble generation ideas. Physical ideas in agreement with pictures emerging from recent foam studies using X-ray computed tomography form the basis for the new model. First, we provide the conservation equations for foam motion in porous media. Then we present their analytical treatment considering several cases that are likely to exist in the laboratory and in the field. We present an analysis of quasi-incompressible foam, reconciling for the first time the population balance and fractional flow ideas. We demonstrate why fingering is likely to occur during liquid injection following foam. Then we provide a solution for the coupling of liquid drainage through foam and viscous fingering. Introduction Foam motion in granular porous media is a phenomenon of common experience with applications in various fields, including oil and gas recovery,[1–6] environmental remediation[1,4–6] and water purification.[1] The description of foam behavior in porous media relies on phenomenological modeling. The available foam models aim to capture the drastic lowering of gas mobility associated with foam development. Nevertheless, they differ on their approaches to accomplish this task. With some simplification, current foam models can be grouped in (semi-) empirical,[7] fractional flow,[8,9] population balance[10–13] and percolation or network[14–16] approaches. The emphasis of this work is on fractional flow and population balance methods. The modeling of foam using fractional flow ideas was advocated by Rossen and co-workers.[2,8,9] These authors identified foam states in so-called time-distance diagrams computed from core flow experimental data. They argued that the computation is simplified when done near the critical capillary pressure.[17] Foam fractional flow theory is based on the assumption that foam is incompressible and, therefore, is valid for cases where pressure variations remain small compared with the reference pressure. However, current fractional flow models do not account for the evolution of bubble population explicitly and therefore may lack accuracy when tackling transient foam motion.
- North America > United States > Texas (0.93)
- Asia (0.68)
Mass Transfer and Gelation in Sandstone Cores of a Novel Water Shutoff Chemical
Castelijns, Henricus Jozef (Delft University of Technology) | Pel, Leo (Eindhoven University of Technology) | Huinink, Henk (Eindhoven University of Technology) | Zitha, Pacelli Lidio Jose (Delft University of Technology)
Abstract An innovative water shut-off chemicals was recently proposed. The chemical is soluble in oil without any chemical reaction and forms gel in the presence of water. When the chemical dissolved in oil is injected in the near well-bore formation it modifies selectively the two-phase flow properties in order to reduce the production of water. The gelation process involves the partitioning of the chemical from the oil phase into the water phase. Upon contact with water a heterogeneous (hydrolysis and condensation) reaction takes place between gelant and water, leading to the formation of a gel in the water phase. Recently we have demonstrated that NMR imaging is a viable technique for visualizing and quantifying the above reactive mass transfer process in bulk and glass bead systems.[1,2] Here we report a new core-flood experimental study consisting of the placement of the chemical dissolved in oil in Bentheim sandstone cores. NMR imaging and (T1 and T2) relaxation time measurements are used to monitor the reactive transport of the chemical in the core. The mass transfer of the chemical from the oil phase to the water phase is derived from the measurement of T1 related to the oil phase. The progress of hydrolysis and gelation is indicated by a decrease in T2 of the water phase. Introduction Several techniques have been proposed and applied in the field to prevent or to remediate a high water cut during hydrocarbon production.[3–7] A method often used is the placement of chemicals and gels in the near-well bore formation in order to modify the flow characteristics of the reservoir fluids.[8,9] The purpose of the gels is to reduce or to block completely the flow of water into the well without reducing the oil flow. Suitable chemicals for achieving these selective treatments are the oil-soluble chemicals (OSC) of the alkoxy-silane family. These chemicals can be mixed with oil without any chemical reaction but react upon entering in contact with water to form a gel. Plazanet and Thomere were the first to propose the use of these chemicals for the consolidation of sand in high water production wells.[10] Thompson and Fogler investigated the possibility of using these innovative chemicals for water shut-off and fluid diversion.[11,12] The OSC used in this study is a non-commercial variant of an alkoxy-silane compound, namely tetra-methyl-ortho-silicate (TMOS), or Si(OCH3)4. The reaction of TMOS with water can be classified as a sol-gel reaction and consists of two steps.13 First TMOS hydrolyzes as follows: The reaction products are silicic acid and methanol. The second step is the condensation of the silicic acid into a silica network: The rate and extend of both steps depend on temperature, pH, concentrations, and catalysts present in the sol.[13] The potential of this type of chemical as a bullhead water control agent was evaluated earlier in two inter-European cooperation projects.[14] The placement and reaction of the chemical in ceramic and limestone cores was studied by Thompson and Fogler through a series of core flood experiments.[11,12] Elewaut and Zitha reported an experimental study of OSC gel treatments in Bentheim sandstone cores, using pressure data and X-Ray computed tomography (CT) imaging to interpret the mass transfer of the flowing gelant in a macroscopic sense in the initial stages of the gel treatment.[15] An in-situ study of the reactive transport of the OSC within a natural porous medium is, however, lacking. Recently we have demonstrated that NMR imaging is a viable technique for visualizing and quantifying the above reactive mass transfer process in bulk and glass bead systems.[1,2] In this study the gel-forming chemical was injected in Bentheim sandstone cores at low water-saturation conditions. During placement and shut-in the fluids in the core were continuously monitored using NMR.
- Europe > Netherlands > North Sea > Dutch Sector (0.65)
- North America > United States > Texas (0.28)
- North America > United States > Oklahoma (0.28)
- Energy > Oil & Gas > Upstream (1.00)
- Water & Waste Management > Water Management > Lifecycle > Conformance/Minimization (0.40)
Abstract Foam flow in porous media plays an important role in oil and gas recovery. Besides experimental studies, the prediction of foam behavior in the applications relies on macroscopic modeling. In this paper, we present a numerical analysis of foam flow in porous media using a new stochastic bubble population (SBP) model. We also present a sensitivity analysis to the main parameters. The idea that foam flow in porous media can be described as a stochastic process emerged from recent studies of foam flow through porous media using X-ray computed tomography (CT). The model is simple as it describes the bubble generation using mainly two parameters, the maximum bubble density and a foam generation constant. It is also robust because it grasps the essence of foam physics in homogeneous porous media. A good qualitatively agreement exists between the numerical predictions and the water saturation profiles obtained from the CT scan experiments. Introduction Over the last decades, foam has been widely used as a mobility control agent in Enhanced Oil Recovery (EOR),[1–4] gas blocking[5] and acid diversion during matrix stimulation.[2] Foam remains one of the best EOR options, especially in maturing reservoirs. Besides experimental studies, the description of foam behavior in porous media relies on macroscopic modeling. Among the existing foam modeling approaches, the most documented ones are the fractional flow and the population balance models. The foam fractional flow modeling was initiated by Rossen and et al..[2,6,7] It assumes implicitly that foam is incompressible. This approach is valid when pressure variations are small, compared with the reference pressure (backpressure). The classical fractional flow models do not account explicitly for the evolution of bubble population and, therefore, might not be accurate when describing transient foam motion. The population balance approach introduced by Patzek[8] and further elaborated by Kovscek et al.[3,9–11] and Falls et al.,[12] starts from the principle that foam mobility depends on the bubble density (number of bubbles per unit gas volume). The population balance model splits gas saturation into flowing and trapped fractions. Although this appears to be in agreement with the early experimental work of Bernard et al.[13,14] and Holm,[15,16] it turns out to be disadvantageous, as it leads to the introduction of parameters that may be difficult to determine experimentally. The petroleum community, therefore, perceives the population balance models as being comprehensive but complex. Recently Zitha[17] developed an alternative population balance theory for foam motion in porous media (other paper in this conference). The theory is build upon the following basic postulates:Foam is a complex fluid, characterized by a yield stress and, above the yield stress, by a power law behavior; its rheology is described using the Herschel-Bulkley model. Foam rheology depends essentially on the bubble density (number of bubbles per unity volume of porous medium). Finally, on the macroscopic level, we can treat the bubble generation as a stochastic process; we describe the kinetics of foam generation using a simple exponential growth function. The bubble generation involves essentially two parameters that are in principle easier to determine experimentally. During foam development, we expect the bubble density to be small. From the above it follows therefore that, the yield stress of foam is low and, consequently, foam trapping is unlikely.[17] Hence, in the model for foam propagation, foam trapping is not taken into account. This is in good agreement with foam experiments performed using X-ray computed tomography (CT).]18–22] These experiments showed no evidence of gas trapping during co-injection of gas and a surfactant solution in sandstone cores containing surfactant solution (transient foam flow). The new stochastic bubble population model lies therefore upon a more realistic picture of foam physics. The model is simpler and more robust because bubble generation depends only on two unknown parameter.
- North America > United States > Texas (0.93)
- Asia (0.68)
- Research Report > New Finding (0.74)
- Research Report > Experimental Study (0.74)