John Killough

Beyond dual-porosity modeling for the simulation of complex flow mechanisms in shale reservoirs

The state of the art of modeling fluid flow in shale reservoirs is dominated by dual-porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive micro- and nano-pore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual-porosity models and Darcy’s law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of the complex flow mechanisms occurring in these reservoirs. This paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three porosity systems: inorganic matter, organic matter (mainly kerogen), and natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nano-pores and micro-pores in kerogen are incorporated into the simulator. The multiple-porosity model is built upon a unique tool for simulating general multiple-porosity systems in which several porosity systems may be tied to each other through arbitrary connectivities. This new model allows us to better understand complex flow mechanisms and eventually is extended into the reservoir scale through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual-porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple-porosity simulation.

Computed tomography imaging of air sparging in porous media

This paper describes the use of an X ray computerized tomography scanner for noninvasive, three-dimensional, high-resolution imaging of air distribution patterns during air sparging in water-saturated sandpacks. Experiments were performed in Plexiglas cylindrical cells using well-defined Ottawa sands. The reconstructed images provide detailed porosity and air saturation distributions previously unavailable. Two classes of behavior were observed. In high-permeability (106 darcy) uniform sandpacks a relatively few, discrete, and tortuous air pathways were formed. Steady state was rapidly attained, and the intrachannel air saturations were low (0.10). In contrast, low-permeability (3 darcy) sandpacks increased the breadth of air contact, delayed attainment of steady state, and displayed high air saturations (0.50). The concept of a hydrodynamic stagnation saturation and standard one-dimensional fractional flow theory proved useful in explaining the experiments. Numerical simulation confirms the explanations, even when capillary pressure and compressibility effects are included.

Ninth SPE Comparative Solution Project: A Reexamination of Black-Oil Simulation

The ninth SPE Comparative Solution Project presented in the following paper provides a reexamination of black-oil simulation based on a model of moderate size (9,000 cells) and with a high degree of heterogeneity provided by a geostatistically-based permeability field. Nine participants provided data for the comparison which is based on a dipping reservoir with twenty-five somewhat randomly placed producers and a single water injector. Results showed that significant agreement could be achieved for this problem on the basis of total production rates, saturations, and reservoir pressures. On the other hand, rates for some individual wells did show variations of as much as bottomhole pressures. All participants were able to simulate the study in fewer than sixty time steps with an average of 4-5 Newton iterations per step. In addition, the results showed that this moderate-sized problem could be simulated in only a few minutes in a workstation environment for the two plus years of data.

Compositional Modeling of Tight Oil Using Dynamic Nanopore Properties

A typical tight oil reservoir such as the Bakken has matrix pore sizes ranging from 10 nm to 50 nm. At such small scales the confined hydrocarbon phase behavior deviates from bulk measurements due to the effect of capillary pressure. In addition, compaction of pore space can bring about order of magnitude changes for tight oil formation properties during pressure depletion further exacerbating these deviations. Without considering these facts a conventional reservoir simulator will likely not be able to explain the inconsistent produced GOR observed in the field compared to simulated results. The effect of these inaccuracies on ultimate recovery estimation can be devastating to the underlying economics. This paper presents a compositional tight oil simulator that rigorously models pressure dependent nanopore-impacted rock and fluid properties, such as suppression of bubble point pressure, decrease of liquid density, and reduction of oil viscosity as well as their interactions with pore space compaction. The cubic Peng-Robinson equation of state is used for phase behavior calculations. Capillary pressure is evaluated by standard Leverett J-function for porous media. Modifications to the stability test and two-phase split flash calculation algorithms are provided to consider the capillarity effect on vaporliquid equilibrium. The simulator can capture the pressure-dependent impact of the nanopore structure on rock and fluid properties. As a result, the problem of inconsistent GOR is resolved and the history matching process is greatly facilitated. It is shown that inclusion of these enhanced physics in the simulation will lead to significant improvements in field operation decisionmaking and greatly enhance the reliability of recovery predictions. Introduction The recent advances in massive hydraulic fracturing techniques have enabled the oil industry to economically extract hydrocarbon from ultra-tight, unconventional resources, such as shale gas, liquid rich shale and tight oil. The success in North America has stimulated the development of unconventional plays worldwide. For example, a marine shale play in southern China has showed large potential and attracted great attention (Wei et al. 2012; 2013a, b). However, despite the great success and potential, the understanding of fluid flow mechanism in shale and properties in confined pore space is still poor. The flow mechanism in the shale matrix is complicated by organic and inorganic portions of the matrix with distinct wettabilities. Yan et al. (2013 a, b, c, d) proposed a micro-model to model single-phase gas and two-phase gas-water flow in shale matrix blocks by considering different flow mechanisms in organic and inorganic nanopores. Yan’s work also upscaled the single-phase gas flow to well-scale modeling via the apparent permeability approach. On the other hand, the fluid properties in the confined nanopore space deviate from the corresponding bulk measurements in which zero vapor-liquid interface curvature is assumed. This assumption is generally held when the vapor-liquid equilibrium takes place in PVT cells. But, when the fluid is confined in pore spaces of nano-size, the significant interfacial curvature may cause a large capillary pressure difference between liquid and vapor phases. The effect of capillary pressure on vapor-liquid equilibrium is not new to the oil industry. A number of researchers have conducted both experimental and theoretical investigations with general conclusions that capillarity effect on vapor-liquid equilibrium is negligible for conventional reservoirs (Leverett 1941; Sigmund et al. 1973, 1982; Shapiro and Stenby 1997; Shaprio et al. 2000). Perhaps due to this reason, essentially all the current commercial simulators assume no pressure difference between vapor and liquid phases during flash calculations. However, ignoring capillarity in vapor-liquid equilibrium might not be a valid assumption for unconventional reservoirs. A typical tight oil reservoir such as the Bakken has matrix pore size ranging from 10 nm to 50 nm. At such small scales, the confined hydrocarbon phase behavior is believed to deviate from bulk measurements due to the extra capillarity effect. Rock wettability is another factor to consider when dealing with capillary pressures. Wang et al. (2012) performed a wettability

A New Approach for the Simulation of Fluid Flow In Unconventional Reservoirs Through Multiple Permeability Modeling

Shale reservoirs are characterized by ultra-low permeability, multiple porosity types, and complex fluid storage and flow mechanisms. Consequentially the feasibility of performing simulations using conventional Dual Porosity Models based on Darcy flow has been frequently challenged. Additionally, tracking of water in shale continues to be controversial and mysterious. In organic-rich shale, kerogen is generally dispersed in the inorganic matter. Kerogen is different from any other shale constituents because it tends to be hydrocarbon-wet, abundant in nanopores, fairly porous and capable of adsorbing gas. However, the inorganic matter is usually water wet with low porosity such that capillary pressure becomes the dominant driving mechanism for water flow, especially during hydraulic fracturing operations. This work presents a technique of subdividing shale matrices and capturing different mechanisms including Darcy flow, gas diffusion and desorption, and capillary pressure. The extension of this technique forms a solid and comprehensive basis for a specially-designed simulator for fractured shale reservoirs at the micro-scale. Through the use of this unique simulator, this paper presents a micro-scale two-phase flow model which covers three continua (organic matter, inorganic matter and natural fractures) and considers the complex dynamics in shale. In the model, TOC is an indispensable parameter to characterize the kerogen in the shale. A unique tool for general multiple porosity systems is used so that several porosity systems can be tied to each other through arbitrary connections. The new model allows us to better understand the complex flow mechanisms and to observe the water transfer behavior between shale matrices and fractures under a microscopic view. Sensitivity analysis studies on the contributions of different flow mechanisms, kerogen properties, water saturation and capillary pressure are also presented. Introduction In recent years, unconventional resources have played a significant part to balance between the increasing energy demand and the shortage of production from the conventional reservoirs in the United States (Wei et al. 2013). Hydrocarbon from organic rich shale is one of the most significant unconventional resources. The successful development of shale reservoirs is greatly attributed to horizontal well drilling and hydraulic fracturing operations. In industry, effective hydraulic fracturing for shale wells is performed mainly through injecting slickwater under high pressure. However, generally the recovery of fracturing fluid is quite low. King (2012) suggested that the water might be trapped in the small pores and the micro-fractures of shale. Besides, evidence shows that there is a high concentration of chloride salts in the flowback fluid, while it cannot be explained either from the composition of fracturing fluid (mostly fresh water) or from the constituents of shale and the salinity of formation brine (King 2012). Wang and Reed (2009) propose that there exist four pore systems in the organic-rich shale: inorganic matter, organic matter (kerogen), natural fractures and hydraulic fractures. It is also suggested that the organic matter is oil wet and that single oil or gas phase flow without residual water is dominated in kerogen fragments. However, the inorganic matrix is mostly considered as water-wet (Kalakkadu et al. 2013). Through the approach of Molecular Dynamics Simulation and with the initial condition of water and NaCl, Hu et al. (2013) suggested that water could be filled in the larger pores in the kerogen through capillary condensation but no water enters the smaller 0.9 nm kerogen pores. Water exists in the inorganic MgO pores in the liquid phase; meanwhile, there is a much higher ionic concentration in the inorganic matter than that in the kerogen. In shale gas reservoirs, the source of shale gas can be thermogenic, biogenic or combined source (Darishchev et al. 2013). Natural gas is usually considered to exist in three forms: compressed gas in pores and fissures, adsorbed gas in the organic and inorganic matter, and dissolved gas in the kerogen (Javadpour 2009; Zhang et al. 2012). Usually it might be reasonable

Simulation of Compositional Reservoir Phenomena on a Distributed-Memory Parallel Computer

Distributed-memory parallel computer architectures appear to offer high performance at moderate cost for reservoir simulation applications. In particular, the simulation of compositional reservoir phenomena shows great promise for parallel applications because of the large parallel content of the compositional formulations. This paper focuses on the application of a distributed-memory parallel computer, the iPSC/860, to the solution of two compositional simulations: one based on the Third SPE Comparative Solution problem and another based on a real production compositional model. An improved linear equation solution technique based on multi-grid and domain decomposition methods is compared with other techniques in serial and parallel environments.

How to Improve our Understanding of Gas and Oil Production Mechanisms in Liquid-rich Shale

Three phase oil, gas, and water flow in liquid-rich shale plays is investigated in this paper, using a state-of-the-art technique of dividing shale matrix into different sub-media. Shale reservoirs always present numerous challenges to modeling and understanding, from unintuitive, heterogeneous, and difficult to characterize rock properties, to limited understanding of the governing flow equations, lack of fundamental knowledge on related desorption mechanisms, and nearly impermeable formations with pores on the order of magnitude as the mean free path of gas molecules. This work proposes a partitioning scheme to divide porous media in shale into three different sub-media (porosity systems) with distinctive characteristics: inorganic matter and kerogen (in the shale matrix), along with fracture network (natural or hydraulic). The current model gives us the capability of better analyzing the complex nature of mass transfer in shale. Relative permeabilities in our model are accounted for by employing the functions specifically presented for shale reservoirs. Our model can also handle various flow and storage mechanisms corresponding with shales such as molecule/wall interactions and slippage of the gas phase, multicomponent desorption, and capillarities. Simulation results show that hydrocarbon production from shale reservoirs exhibits complicated dynamics that are controlled by a number of different factors. Because of very high capillary pressure in shale, water is observed to imbibe into the water-wet inorganic matter during the late production period. On the contrary, mass flow in the oil-wet kerogen is mostly limited to two-phase oil and gas flow. Although kerogen is considered to be a rich source of hydrocarbon, relatively high capillary pressure and very low rock permeability hinder oil production in organic-rich shale. We might be able to address such problems by employing an appropriate production enhancement technique compatible with the ultra-tight nature of such reservoirs.

Beyond Dual-Porosity Modeling for the Simulation of Complex Flow Mechanisms in Shale Reservoirs

The state of the art of modeling fluid flow in shale reservoirs is dominated by dual porosity models which divide the reservoirs into matrix blocks that significantly contribute to fluid storage and fracture networks which principally control flow capacity. However, recent extensive microscopic studies reveal that there exist massive microand nanopore systems in shale matrices. Because of this, the actual flow mechanisms in shale reservoirs are considerably more complex than can be simulated by the conventional dual porosity models and Darcy’s Law. Therefore, a model capturing multiple pore scales and flow can provide a better understanding of complex flow mechanisms occurring in these reservoirs. Through the use of a unique simulator this paper presents a micro-scale multiple-porosity model for fluid flow in shale reservoirs by capturing the dynamics occurring in three separate porosity systems: organic matter (mainly kerogen), inorganic matter, natural fractures. Inorganic and organic portions of shale matrix are treated as sub-blocks with different attributes, such as wettability and pore structures. In the organic matter or kerogen, gas desorption and diffusion are the dominant physics. Since the flow regimes are sensitive to pore size, the effects of nanopores and vugs in kerogen are incorporated into the simulator. The separate inorganic sub-blocks mainly contribute to the ability to better model dynamic water behavior. The multiple porosity model is built upon a unique tool for simulating general multiple porosity systems in which several porosity systems may be tied to each other through arbitrary transfer functions and connectivities. This new model allows us to better understand complex flow mechanisms and in turn is extended into the reservoir scale considering hydraulic fractures through upscaling techniques. Sensitivity studies on the contributions of the different flow mechanisms and kerogen properties give some insight as to their importance. Results also include a comparison of the conventional dual porosity treatment and show that significant differences in fluid distributions and dynamics are obtained with the improved multiple porosity simulation. Finally a case for reservoir-scale model covering organic matter, inorganic matter, natural fractures and hydraulic fractures is presented and will allow operators to better predict ultimate recovery from shale reservoirs. Introduction The development of unconventional resource plays in North America has achieved great success towards satisfy the growing energy demand. The organic shale formations which provide the basis of unconventional oil and gas production continue as an enigma as far as understanding production characteristics are concerned. Because of this many investigators have been inspired to establish suitable models to characterize fluid flow in shale encountering great challenges along the way. Shale is referred to as extraordinarily fine-grained sediments commonly showing fissility (Javadpour, 2009). Loucks et al. (2012) systematically classified nanometer to micrometer sized pores in the shale matrix into interparticle pores and intraparticle pores associated with mineral particles and organic-matter pores within kerogen. The organic matter has different physical properties from common rock constituents and could significantly affect gas storage and flow in shale. Curtis et al. (2010) found that mostly kerogen is scattered in inorganic minerals, and pores within it are basically round in cross-section interestingly with numerous small pores residing on the interior walls of larger pores. Due to forming during the process of hydrocarbon generation, the pore networks in the organic matter in shale are mainly considered to be oilor gas-wet (Wang et al., 2009; Odusina et al., 2011). Experiments on Barnett Shale demonstrated that the both adsorbed gas and free gas stored in the shale matrix are linearly increased with TOC content (Jarvie, 2004), and Javadpour (2009) also theoretically proposed that beside free gas storage in shale, gas could also be adsorbed on the surface of kerogen and dissolved within it. Hill et al. (2000)

A New Approach To Load Balance for Parallel Compositional Simulation Based on Reservoir Model Over-Decomposition

The quest for efficient and scalable parallel reservoir simulators has been evolving with the advancement of high performance computing architectures. Among the various challenges of efficiency and scalability, load imbalance is a major obstacle that has not been fully addressed and solved. The reasons that cause load imbalance in parallel reservoir simulation are both static and dynamic. Robust graph partitioning algorithms are capable of handling static load imbalance by decomposing the underlying reservoir geometry to distribute a roughly equal load to each processor. However, these loads determined by a static load balancer seldom remain unchanged as the simulation proceeds in time. This so called dynamic imbalance can be further exacerbated in parallel compositional simulations. The flash calculations for equations of state in complex compositional simulations not only can consume over half of the total execution time but also are difficult to balance merely by a static load balancer. The computational cost of flash calculations in each grid block heavily depends on the dynamic data such as pressure, temperature, and hydrocarbon composition. Thus, any static assignment of grid blocks may lead to dynamic load imbalance in unpredictable manners. A dynamic load balancer can often provide solutions for this difficulty. However, traditional techniques are inflexible and tedious to implement in legacy reservoir simulators. In this paper, we present a new approach to address dynamic load imbalance in parallel compositional simulation. It overdecomposes the reservoir model to assign each processor a bundle of subdomains. Processors treat these bundles of subdomains as virtual processes or user-level migratable threads which can be dynamically migrated across processors in the run-time system. This technique is shown to be capable of achieving better overlap between computation and communication for cache efficiency. We employ this approach in a legacy reservoir simulator and demonstrate reduction in the execution time of parallel compositional simulations while requiring minimal changes to the source code. Finally, it is shown that domain over-decomposition together with a load balancer can improve speedup from 29.27 to 62.38 on 64 physical processors for a realistic simulation problem.

Parallel Linear Solvers for Reservoir Simulation: A Generic Approach for Existing and Emerging Computer Architectures

Recent architectural advances in the computer industry focus on the numerical solution of intensive flows, such as in oil reservoirs, on several processors simultaneously. Different computer architectures evolved from connection of these processors: shared memory with a few processors, distributed memory with up to a few hundred processors, and massively parallel with several thousand processors. Oil industry researchers are developing efficient techniques to improve hydrocarbon recovery in reservoirs by use of these computers. In this work, a generic approach is developed to solve the large system of sparse linear equations that arises in reservoir simulation. This approach uses a combination of domain decomposition and multigrid techniques that results in efficient and robust algorithms for sequential computers with one processor and for parallel computers with few to several tens of processors. The efficiency and robustness of these methods is comparable with widely used sequential solvers for problems of practical interest, which include implicit wells and faults. In parallel, these methods prove to be an order of magnitude faster on a 32-node iPSC/860 hypercube.