We present hybrid derivative free algorithm methods that maximize NPV while solving the problem of placement of hydraulic fracturing stages and horizontal wellbore trajectory in a tight heterogeneous gas condensate reservoir. These parameters are important in reservoir management and field development optimization as they determine the interaction of the wellbore with the reservoir. Thus, they have a large impact on production performance of the field and the cost of field development.
We couple a tight heterogeneous gas condensate reservoir model to an optimization algorithm that determines the parameters that maximize the economic value of the field. The optimization algorithm proposed in this paper exploits the advantage of stochastic global search (particle swarm optimization) and local pattern search (hill climber) techniques to find the optimized parameters. The optimization process starts with the particle swarm optimization (PSO) algorithm, which is executed with an initial guess based on engineering experience until the objective function (in this study NPV) fails to improve in the next couple of iterations. This is followed by the hill climber (HC) algorithm that improves the objective function.
Observations from our investigation show that an optimal field development plan (FDP) is essential to optimize the placement of hydraulic fracturing stages along a horizontal wellbore and to optimize the wellbore trajectory inside the reservoir. However, these parameters would have to be optimized simultaneously in a non-systematic manner. We integrate reservoir engineering experience and economics knowledge into the optimization algorithm by embedding practical constraints into the problem formulation.
The algorithm is executed in a reasonable amount of computation time, considering the complexity of the problem. The optimization process evaluates various possible field development plans involving different hydraulic fracturing stages and well placement trajectories. The investigation demonstrates how these parameters impact the economic value of the field, how to optimize the placement of hydraulic fracture stages along a horizontal wellbore, and how to optimize the wellbore trajectory inside the reservoir.
The methodology presented in this work should allow industry professionals working with unconventional reservoirs to improve the economic value of a field in a shorter timeframe while considering all possible field development plans, a task that would be time consuming and tedious if carried out manually.
This study presents a new geostatistics modeling methodology for the purpose of achieving the following three objectives. (1) Connecting geostatistics and machine learning methodologies, (2) Using non-linear topological mapping to reduce the original high dimensional data space to low dimensional subspace, as well as clustering for identifying and extracting meaningful patterns for both visualization and efficiency purposes, and (3) Using unsupervised learning algorithms to bypass potential problems encountered while using supervised learning algorithms.
Past observations have indicated that due to lack of labeled input data, artificial neural network (ANN) architecture, based on feedforward and backpropagation supervised learning, is difficult to apply.
To eliminate this difficulty and accomplish the 3 aforementioned objectives we introduce in this paper TopoSim, a neural topology-preserving based geostatistical simulation algorithm, which integrates (1) Self-Organizing Map (SOM) and its updated version, Growing Self-Organizing Map (GSOM), and (2) ANN with an unsupervised competitive learning structure. The proposed simulation integrates in a single step dimensionality reduction and extraction of input data structure pattern. Connectivity between geostatistical simulation problems and machine learning tasks are explained and constructed for the first time.
We perform TopoSim unconditioned geostatistical realizations, which show improvements in continuity and pattern reproduction when compared with previously developed single normal equation simulation (SNESIM) algorithms.
We conclude that the geostatistical simulation task is essentially a machine learning problem, i.e., getting the model to learn from available data and subsequently using the model for prediction purposes.
The average reservoir pressure is a key parameter in material balance calculations, but its determination is challenging when dealing with shales because of their low and ultra-low permeabilities. This paper presents an easy-to-reproduce methodology for calculating the average reservoir pressure from flowing data, and its use in a new Material Balance Equation (MBE) that considers the simultaneous contribution of free, adsorbed and dissolved gas.
The procedure developed in this paper uses a modified gas compressibility factor (Z') introduced in the new MBE. Since
In conventional reservoirs, a well is shut-in and the average reservoir pressure is determined from the corresponding pressure build-up test. But, for the case of unconventional shale gas reservoirs, shutting the wells in is unacceptable due to the long time it would require for estimating average reservoir pressure. The methodology developed in this paper for shale gas reservoirs circumvents this problem by using dynamic data.
Production data from multi-stage hydraulically fractured horizontal wells completed in a Canadian shale gas reservoir are used for testing the effectiveness of the new methodology. Comparison of typical well spacing values vs. the drainage area calculated with the new methodology leads to the conclusion that, probably, only 40% of the gas is being drained efficiently.
The novelty of this work relies on the development of a methodology for calculating average reservoir pressure, OGIP, drainage area, and optimum well spacing in shale reservoirs through the combination of dynamic data and a new MBE that considers simultaneously the effects of free, adsorbed and dissolved gas.
A hybrid hydraulic fracture (HHF) model composed of (1) complex discrete fracture networks (DFN) and (2) planar fractures is proposed for modeling the stimulated reservoir volume (SRV). Modeling the SRV is complex and requires a synergetic approach between geophysics, petrophysics, and reservoir engineering. The objective of this paper is to characterize and evaluate the SRV considering the initial hydraulic fracturing efficiency, fracture network complexity, mechanics, and microseismicity distribution along 145 stimulated stages in a multilateral horizontal well on the Muskwa, Otter Park and Evie Formations in the Horn River Shale in Canada.
Hydraulic fracturing jobs in shale reservoirs are designed with a view to achieve economic production by exploiting fracture network complexity. The task involves significant challenges in modeling and forecasting, which complicates the examination of operations to enhance their performance, including refracturing or infill drilling.
In this study, an HHF is run in a numerical simulation model to evaluate the SRV performance in planar and complex fracture networks using microseismicity data collected during 75 stages of hydraulic fracturing in the Horn River shale. Post-fracturing production is appraised with Rate Transient Analysis (RTA) for determining effective permeability under flowing conditions, compare to the numerical simulation and the hydraulic fracturing design.
Fracturing stages with larger fracture patch sizes, associated with the microseismic events in a fixed stress drop, correspond to higher stimulated areas, fracture conductivity, and gas production. Several microseismic events are observed in the heel of the laterals that are aligned to the far field NE stresses, indicated a loss of efficiency along the wellbore lateral during hydraulic fracturing. The hydraulic propagation modeling revealed increment of the leak-off coefficient, related to the natural fractures and communication with other stages. The production performance is evaluated in the numerical model, to measure interference between stages.
The SRV, modeled with HHF networks, is able to match the post-fracturing production history. Fracture mechanics is important in order to understand the flowing performance of the reservoir.
The inclusion of propagating models and RTA allowed to characterize possible fracture geometries in the reservoir and to observe limitations inherent to large dispersion and uncertainty of the microseismicity cloud. Also, to observe areas where the stimulation may have propped natural fractures totally or partially, which will benefit the production of gas.
This study presents a better understanding and characterization of the SRV in shale gas reservoirs, especially in those cases where microseismicity dispersion is problematic and where the SRV is not easily delimited.
The objective of this study is to present methods for calculating organic and inorganic porosities in shale oil reservoirs. This is achieved by combining density, neutron and NMR logs as well as laboratory geochemical and synthetic geochemical properties of organic matter. The study also presents methods for calculating these porosities when all the above data are not available. This is important as data scarcity is a common problem in most shale reservoirs.
Shales are generally composed by clays, inorganic matrix, organic matter and natural fractures. In this study, responses of density, neutron, and NMR logs are written in terms of properties of each shale component including clays, solid and porous volume for both inorganic (including natural fractures) and organic matter. Different analytical models are built depending on available input data and the approach used to convert weight total organic carbon (TOC) to TOC volume percentage. However, as is usually the case, the availability of different sources of information including geochemical data, routine and/or special core analysis will enhance the validity of the interpretation.
Models developed in this study indicate that organic porosity results (intrinsic and scaled to total volume) are very consistent with values measured in the laboratory and values reported in the literature. There are three approaches for converting weight TOC to percent volume TOC. Our results show that these three approaches have to be used carefully. Their indiscriminate use can lead to errors as the organic porosity is very sensitive to the TOC transformation. The organic porosity is also very sensitive to properties assumed for each component of the reservoir rock.
Depending on petrophysical and reservoir engineering needs, the organic porosity can be easily scaled to the volume of only the organic matter (intrinsic organic porosity) or to the bulk volume (total organic porosity) of the total system. In addition to organic porosity, the models developed in this study also allow calculating kerogen volume and its respective solid portion, allowing thus an estimate of solid kerogen and porosity within the kerogen material. Furthermore, the models also allow calculating inorganic porosity (matrix plus natural fractures).
Unlike current models that use separately conventional logs or NMR logs to calculate the porosity associated with organic matter, this study integrates all these logs as well as laboratory and synthetic geochemical properties of organic matter to develop new methods for estimating rigorously-scaled organic porosity.
The objective of this paper is to estimate the long-term energy mix – i.e. the combination of resources including solids, liquids and gases that will satisfy energy demand to the year 2040 – with a Global Energy Market model (GEM). The GEM provides a close match of the historical energy mix dating back to the year 1850 and is then used to make forecasts for the future. Originally developed in 2007, the GEM was used to project the energy mix to the year 2030. In the present paper, the validity of the original projection is tested against the most recently available data.
The GEM estimates the fractional contribution of different primary energy sources to the global market. In total, there are six parameters that allow the GEM equation to give the best possible match of the historical energy mix. Using the estimated parameter values, the model can then be extended into the future, providing a reference case and alternative scenarios of the energy mix based on evolving unconventional, conventional and renewable resource quantities, costs, technologies, economic growth, population and policies.
The original GEM findings from 2007 forecasted a "2030 1/3 forecast", indicating that solids, liquids and gases would each occupy a third of the energy market in the year 2030. After further disaggregating the categories, it was found that liquids, mostly, oil would experience a declining market share by 2030 while natural gas would see a rapid rise. The share solids, mostly coal, was relatively flat by that time. Our new results show continued penetration of natural gas in the energy mix – a result consistent with efforts to reduce carbon emissions.
Our proposed paper is novel in that it uses the most recent statistics of the last 10 years on consumption of different energy sources to verify the accuracy of the original GEM projections carried out in 2007. Once the results are proven reasonable, new scenarios are developed with an extended time horizon to the year 2040.
A post stack seismic inversion has been applied to 2D and 3D seismic data in order to obtain a quantitative assessment of rock properties including density, compressional velocities and porosity in a tight gas sandstone. To achieve this objective, the study develops a new relationship between Acoustic Impedance (AI) and porosity.
This study focuses on a post stack seismic inversion through a band limit technique that involves three major steps: 1) Derive a low frequency velocity model using sonic logs, 2) Invert the seismic traces using a recursive inversion procedure giving as a result the middle frequency model band of the AI, and 3) Combine the previous models in order to obtain the full band limit inversion product.
The methodology is demonstrated using data from a tight gas reservoir formation chracterized with low porosity and permeability located at approximately 2, 000 meters (TVDSS) in the study area. From the model inversion, the acoustic impedance (AI) is compared with variations in porosity resulting in a reasonable correlation for the stratigraphic interval studied.
The methodology can probably be extended to other regions around the world, which possess tight gas formations with similar characteristics to the ones described in this work.
This paper presents a new simplified method for forecasting oil and gas production during transient and boundary dominated flow (BDF), which does not require the use of complex analytical or numerical modeling tools. The method is based on the behaviour of the beta derivative (β), where two approximate straight lines are obtained during transient flow and BDF with slopes m_t and m_b, respectively.
The method is applicable not only to vertical wells in conventional reservoirs producing during BDF but also to hydraulically fractured vertical/multifractured horizontal wells in unconventional reservoirs with prevailing transient (linear) flow. Upon selection of an appropriate β_BDF (which mainly depends upon the type of flow regime, i.e., radial or linear) and using the proposed equations, type curves can be generated that provide a convenient method for obtaining the slopes of beta derivatives for transient flow (m_t) and BDF (m_b) through a type curve matching process. The method is validated by comparing results against oil and gas numerical simulations of vertical and hydraulically fracture vertical wells.
The developed method is not biased toward any flow regime or presence of skin. Flow regime and skin effects are embedded in the β_BDF and m_t parameters. Transient and BDF flow are accounted for through the slopes m_t and m_b, respectively. Corroborated with the use of numerical simulation, the proposed method provides reliable production rate forecasting while staying away from the complexities of analytical or numerical modeling.
Analysis of production data from tight and shale petroleum (oil and gas) reservoirs requires the use of complex models for which some of the input data are rarely known with a high level of accuracy. On the other hand, simplified decline
production analyses are generally weak from the point of view of the physics of petroleum reservoirs and many times rely on the adjustment of empirical exponents. Under these circumstances, the degree of forecasting uncertainty is
In this work, we introduce a rigorous physics-based method that utilizes continuous succession of pseudo-steady states (SPSS) to perform production data analysis. Very little input data are required, while at the same time rigorous physics and engineering concepts are used. The method is shown to be accurate during the transient as well as the boundary dominated flow periods.
This method consists of a combination of three easy to use well-known equations: material balance, distance of investigation and boundary dominated flow. It uses a capacitance-resistance methodology (CRM) in which the material balance
equation over the investigated region represents the capacitance, and the boundary dominated flow equation represents the resistance.
The capacitance and resistance are used in a stepwise procedure to calculate the depletion and the new rates or flowing pressures. The method is compared for both radial and linear flow geometries against analytical solutions for liquids and numerical simulations for gas reservoirs, both of which exhibit transient and boundary dominated flow. Excellent agreement is obtained, thus corroborating the validity of the new method. The proposed methodology is easy to implement
in a spreadsheet and is demonstrated using real production data.
It is concluded that complex systems with complicated mathematical solutions (e.g. Laplace space solutions) can be represented adequately using simple yet accurate concepts, as demonstrated in this study.
In Alberta and British Columbia, a huge amount of tight gas is trapped inrelatively low-permeability rock formations. Physical fracturing of theseformations could enhance the overall formation permeability and thus improvetight gas extraction. One of the outstanding issues in rock fracturing is todetermine the magnitude of applied effective stress. The generaleffective-stress law is defined as seff =sc - asp, where sc andsp are total confining stress and fluid pore pressure,respectively. Each physical quantity of rock responds to total stress and porepressure in a different way, and thus each quantity has its own unique Biot'seffective-stress coefficient. The main objective of this study is toexperimentally determine the Biot's coefficient for permeability of Nikanassinsandstone. A series of permeability measurements was conducted on Nikanassinsandstone core samples from the Lick Creek region in British Columbia undervarious combinations of confining stress and pore pressure. In addition,permeability values were measured both along and across bedding planes toinvestigate any anisotropy in the Biot's coefficient.