Deterministic tools to predict gas assisted gravity drainage recovery factor

Naturally fractured rocks contain most of the world's petroleum reserves.This significant amount of oil can be recovered efficiently by gas assisted gravity drainage(GAGD).Although,GAGD is known as one of the most effective recovery methods in reservoir engineering,the lack of available simulation and mathematical models is considerable in these kinds of reservoirs.The main goal of this study is to provide efficient and accurate methods for predicting the GAGD recovery factor using data driven techniques.The proposed models are developed to relate GAGD recovery factor to the various parameters including model height,matrix porosity and permeability,fracture porosity and permeability,dip angle,viscosity and density of wet and non-wet phases,injection rate,and production time.In this investigation,by considering the effective parameters on GAGD recovery factor,three different efficient,smart,and fast models including artificial neural network(ANN),least square support vector machine(LSSVM),and multi-gene genetic programming(MGGP)are developed and compared in both fractured and homogenous porous media.Buckinghamπtheorem is also used to generate dimensionless numbers to reduce the number of input and output parameters.The efficiency of the proposed models is examined through statistical analysis of R-squared,RMSE,MSE,ARE,and AARE.Moreover,the performance of the generated MGGP correlation is compared to the traditional models.Results demonstrate that the ANN model predicts the GAGD recovery factor more accurately than the LSSVM and MGGP models.The maximum R^(2)of 0.9677 and minimum RMSE of 0.0520 values are obtained by the ANN model.Although the MGGP model has the lowest performance among the other used models(the R2 of 0.896 and the RMSE of 0.0846),the proposed MGGP correlation can predict the GAGD recovery factor in fractured and homogenous reservoirs with high accuracy and reliability compared to the traditional models.Results reveal that the employed models can easily predict GAGD recovery factor without requiring complicate governing equations or running complex and time-consuming simulation models.The approach of this research work improves our understanding about the most significant parameters on GAGD recovery and helps to optimize the stages of the process,and make appropriate economic decisions.

Fuel optimal low thrust rendezvous with outer planets via gravity assist

Low thrust propulsion and gravity assist (GA) are among the most promising techniques for deep space explorations.In this paper the two techniques are combined and treated comprehensively,both on modeling and numerical techniques.Fuel optimal orbit rendezvous via multiple GA is first formulated as optimal guidance with multiple interior constraints and then the optimal necessary conditions,various transversality conditions and stationary conditions are derived by Pontryagin's Maximum Principle (PMP).Finally the initial orbit rendezvous problem is transformed into a multiple point boundary value problem (MPBVP).Homotopic technique combined with random searching globally and Particle Swarm Optimization (PSO),is adopted to handle the numerical difficulty in solving the above MPBVP by single shooting method.Two scenarios in the end show the merits of the present approach.

Solar sailing trajectory optimization with planetary gravity assist

Significant propellant mass saving can be obtained with the use of complex multiple intermediate flyby maneuvers for conventional propulsion systems,and trip time also decreases for a portion of the proper solar sail missions.This paper discusses the performance of gravity assist(GA)in the time-optimal control problem of solar sailing with respect to sail lightness number and the energy difference between the initial and final orbit in the rendezvous problem in a two-body model,in which the GA is modeled as a substantial change in the velocity of the sailcraft at the GA time.In addition,this paper presents a method to solve the time-optimal problem of solar sailing with GA in a full ephemeris model,which introduces the third body’s gravity in a dynamic equation.This study builds a set of inner constraints that can describe the GA process accurately.Finally,this study presents an example for evaluating the accuracy and rationality of the two-body model’s simplification of GA by comparison with the full ephemeris model.

Low-thrust trajectory optimization of asteroid sample return mission with multiple revolutions and moon gravity assists

Near-Earth asteroids have gained a lot of interest and the development in low-thrust propulsion technology makes complex deep space exploration missions possible. A mission from low-Earth orbit using low-thrust electric propulsion system to rendezvous with near-Earth asteroid and bring sample back is investigated. By dividing the mission into five segments, the complex mission is solved separately. Then different methods are used to find optimal trajectories for every segment. Multiple revolutions around the Earth and multiple Moon gravity assists are used to decrease the fuel consumption to escape from the Earth. To avoid possible numerical difficulty of indirect methods, a direct method to parameterize the switching moment and direction of thrust vector is proposed. To maximize the mass of sample, optimal control theory and homotopic approach are applied to find the optimal trajectory. Direct methods of finding proper time to brake the spacecraft using Moon gravity assist are also proposed. Practical techniques including both direct and indirect methods are investigated to optimize trajectories for different segments and they can be easily extended to other missions and more precise dynamic model.

Multi-objective interplanetary trajectory optimization combining low-thrust propulsion and gravity-assist maneuvers

To expand mission capabilities needed without a proportional increase in cost or risk for exploration of the solar system,the multiple objective trajectory using low-thrust propulsion and gravity-assist technique is considered.However,low-thrust,gravity-assist trajectories pose significant optimization challenges because of their large design space.Here,the planets are selected as primal scientific mission goals,while the asteroids are selected as secondary scientific mission goals,and a global trajectory optimization problem is introduced and formulated.This multi-objective decision making process is transformed into a bi-level programming problem,where the targets like planets with small subsamples but high weight are optimized in up level,and targets like asteroids with large subsamples but low weight are optimized in down level.Then,the selected solutions for bi-level programming are optimized thanks to a cooperative Differential Evolution(DE) algorithm that is developed from the original DE algorithm;in addition,an sequential quadratic programming(SQP) method is used in low-thrust optimization.This solution approach is successfully applied to the simulation case of the multi-objective trajectory design problem.The results obtained are presented and discussed.

Optimal design of near-Earth asteroid sample-return trajectories in the Sun–Earth–Moon system

In the 6th edition of the Chinese Space Trajectory Design Competition held in 2014, a near-Earth asteroid sample-return trajectory design problem was released, in which the motion of the spacecraft is modeled in multi-body dynamics, considering the gravitational forces of the Sun, Earth, and Moon. It is proposed that an electric-propulsion spacecraft initially parking in a circular 200-kin-altitude low Earth orbit is expected to rendezvous with an asteroid and carry as much sample as possible back to the Earth in a 10-year time frame. The team from the Technology and Engineering Center for Space Utilization, Chinese Academy of Sciences has reported a solution with an asteroid sample mass of 328 tons, which is ranked first in the competition. In this article, we will present our design and optimization methods, primarily including overall analysis, target selection, escape from and capture by the Earth-Moon system, and optimization of impulsive and low-thrust trajectories that are modeled in multi-body dynamics. The orbital resonance concept and lunar gravity assists are considered key techniques employed for trajectory design. The reported solution, preliminarily revealing the feasibility of returning a hundreds-of-tons asteroid or asteroid sample, envisions future space missions relating to near-Earth asteroid exploration.

Hybrid method for accurate multi-gravity-assist trajectory design using pseudostate theory and deep neural networks

This paper presents a novel hybrid method to design the continuous and accurate multi-gravity-assist trajectory for a high-fidelity dynamics.The gravitational perturbation of the primary body is considered during the gravity assistance.The pseudostate technique is applied to approximate the gravity-assisted trajectory,where the optimal sweepback duration is solved using a trained deep neural network.The major factors that affect the optimal sweepback duration of the approach and departure segments are investigated.The results show that the optimal sweepback duration of the approach segment only relies on the shape of the approach trajectory and is independent of the flight time.Then,a gravity-assisted trajectory patched strategy and a hybrid algorithm combining the particle swarm optimization and the sequential quadratic programming are developed to optimize the multi-gravity-assist trajectory.The proposed hybrid method is applied to the Europa orbiter mission.In comparison with the traditional patched conic method,this method demonstrates outstanding performance on accuracy and significantly reduces the computational time and complexity of the trajectory correction with the high-fidelity dynamics.

Design of MGA trajectories for main belt asteroid

Asteroid exploration is one of the most sophisticated missions currently being investigated. Gravity-assist trajectories have proven valuable in interplanetary missions such as the Pioneer, Voyager and Galileo. In this paper, we design interplanetary trajectory for main belt asteroid exploration mission with the Mars gravity-assist (MGA) using “pork chop” plots and patched-conic theory and give some initial valuable trajectory parameters on main belt asteroid exploration mission with MGA.

Low-thrust trajectory optimization in a full ephemeris model

The low-thrust trajectory optimization with complicated constraints must be considered in practical engineering. In most literature, this problem is simplified into a two-body model in which the spacecraft is subject to the gravitational force at the center of mass and the spacecraft＇s own electric propulsion only, and the gravity assist （GA） is modeled as an instantaneous velocity increment. This paper presents a method to solve the fuel-optimal problem of low-thrust trajectory with complicated constraints in a full ephemeris model, which is closer to practical engineering conditions. First, it introduces various perturbations, including a third body＇s gravity, the nonspherical perturbation and the solar radiation pressure in a dynamic equation. Second, it builds two types of equivalent inner constraints to describe the GA. At the same time, the present paper applies a series of techniques, such as a homotopic approach, to enhance the possibility of convergence of the global optimal solution.

Search Space Pruning Based on Image Tools for Preliminary Interplanetary Trajectory Design

A novel gravity assist space pruning(GASP)algorithm based on image tools is proposed for solving interplanetary trajectory optimization problem.Compared with traditional GASP algorithm,the concept of image is introduced to avoid missing interesting solutions with appropriate number of function evaluations.Image tools allow us to evaluate the objective function in regions in place of points and provide an effective way to evaluate the forward and backward constraints for the multi-gravity assist trajectory optimization problem.Since the interesting solutions of the interplanetary trajectory optimization problem are often clustered in a small portion of the search space rather than being overall evenly distributed,the regionwise evaluations with image tools make the little large interval with the proper Lipschitzian tolerances sampling effective.The detailed steps of the proposed method are presented and two examples including Earth Venus Mars(EVM)transfer and Earth Venus Venus Earth Jupiter Saturn(EVVEJS)transfer are given.Finally,a comparison with solutions given by the literature demonstrates the effectiveness of the proposed method.

直井-水平井辅助重力泄油数值模拟原理及应用

蒸汽辅助重力泄油(steam assisted gravity draining,SAGD)技术是稠油开采的重要方法之一。目前SAGD驱油过程,在热质传递机理、油藏动态特性、影响机制及开采效果等方面,还有很多问题描述分析不够精准,需要进一步研究。基于热力学、传热传质学、油藏工程和渗流力学等多学科交叉方法,对SAGD驱油过程进行了描述分析,给出了热质传递过程的能量和质量动态方程。根据相似理论,提出了SAGD驱油过程的两个主要无量纲数:与驱油过程流动、热质传递特性相关的无量纲参数,与时间有关的无量纲数。基于直井-水平井SAGD驱油模式,对其热质传递过程进行了分析,给出了不同阶段热质传递的计算式。利用改进的STARS软件,对直井-水平井SAGD驱油进行了模拟分析,分析了注汽速度、蒸汽干度和水平渗透对驱油过程影响,进而对各参数给出了一些优选范围。研究结果为SAGD驱油优化设计和运行等提供了理论依据和技术参考。

Oil production rate predictions for steam assisted gravity drainage based on high-pressure experiments

Dual-well steam assisted gravity drainage(SAGD) has significant potential for extra-heavy oil recovery.China is conducting two dual-well SAGD pilot projects in the Fengcheng extra-heavy oil reservoir.Quick,direct predictions of the oil production rate by algebraic models rather than complex numerical models are of great importance for designing and adjusting the SAGD operations.A low-pressure scaled physical simulation was previously used to develop two separate theoretical models corresponding to the two different growth stages observed in the SAGD steam chambers,which are the steam chamber rising stage and the steam chamber spreading stage.A high-pressure scaled model experiment is presented here for one dual-well SAGD pattern to further improve the prediction models to reasonably predict oil production rates for full production.Parameters that significantly affect the oil recovery during SAGD were scaled for the model size based on the reservoir characteristics of the Fengcheng reservoir in China.Experimental results show the relationship between the evolution of the steam chamber and the oil production rate during the entire production stage.High-pressure scaled model test was used to improve the gravity drainage models by modifying empirical factors for the rising model and the depletion model.A new division of the SAGD production regime was developed based on the relationship between the oil production rate and the evolution of steam chamber.A method was developed to couple the rising and depletion models to predict oil production rates during the SAGD production,especially during the transition period.The method was validated with experiment data and field data from the literature.The model was then used to predict the oil production rate in the Fengcheng reservoir in China and the Athabasca reservoir in Canada.

Predicting the performance of steam assisted gravity drainage (SAGD) method utilizing artificial neural network (ANN)

As the price of oil decreases,it is becoming increasingly important for oil companies to operate in the most costeffective manner.This problem is especially apparent in Western Canada,where most oil production is dependent on costly enhanced oil recovery(EOR)techniques such as steam-assisted gravity drainage(SAGD).Therefore,the goal of this study is to create an artificial neural network(ANN)that is capable of accurately predicting the ultimate recovery factor of oil reservoirs by steam-assisted gravity drainage(SAGD).The developed ANN model featured over 250 unique entries for oil viscosity,steam injection rate,horizontal permeability,permeability ratio,porosity,reservoir thickness,and steam injection pressure collected from literature.The collected data set was entered through a feed-forward back-propagation neural network to train,validate,and test the model to predict the recovery factor of SAGD method as accurate as possible.Results from this study revealed that the neural network was able to accurately predict recovery factors of selected projects with less than 10%error.When the neural network was exposed to a new simulation data set of 64 points,the predictions were found to have an accuracy of 82%as measured by linear regression.Finally,the feasibility of ANN to predict the recovery performance of one of the most complicated enhanced heavy oil recovery techniques with reasonable accuracy was confirmed.

Study of reservoir properties and operational parameters influencing in the steam assisted gravity drainage process in heavy oil reservoirs by numerical simulation

This study was originally aimed at suggesting a two-dimensional program for the Steam Assisted Gravity Drainage(SAGD)process based on the correlations proposed by Heidari and Pooladi,using the MATLAB software.In fact,the work presented by Chung and Butler was used as the basis for this study.Since the steam chamber development process and the SAGD production performance are functions of reservoir properties and operational parameters,the new model is capable of analyzing the effects of parameters such as height variation at constant length,length variation at constant height,permeability variation,thermal diffusivity coefficient variation and well location on the production rate and the oil recovery among which,the most important one is the thermal diffusivity coefficient analysis.To investigate the accuracy and authenticity of the model outcomes,they were compared with the results obtained by Chung and Butler.The privilege of this method over that proposed by Heidari and Pooladi lies in its ability to investigate the effect of thermal diffusivity coefficient on recovery and analyzing the effect of temperature distribution changes on thickness diffusivity.Based on the observations,results reveal that the proposed model gives more accurate predictions compared to the old model proposed by Chung&Butler.

Capacity of Sun-driven lunar swingby sequences and their application in asteroid retrieval

For deep-space mission design,the gravity of the Sun and the Moon can be first considered and utilized.Their gravity can provide the energy change for launching spacecraft and retrieving spacecraft as well as asteroids.Regarding an asteroid retrieval mission,it can lead to the mitigation of asteroid hazards and an easy exploration and exploitation of the asteroid.This paper discusses the application of the Sun-driven lunar swingby sequence for asteroid missions.Characterizing the capacity of this technique is not only interesting in terms of the dynamic insights but also non-trivial for trajectory design.The capacity of a Sun-driven lunar swingby sequence is elucidated in this paper with the help of the“Swingby-Jacobi”graph.The capacity can be represented by a range of the Jacobi integral that encloses around 660 asteroids currently cataloged.To facilitate trajectory design,a database of Sun-perturbed Moon-to-Moon transfers,including multi-revolution cases,is generated and employed.Massive trajectory options for spacecraft launch and asteroid capture can then be explored and optimized.Finally,a number of asteroid flyby,rendezvous,sample-return,and retrieval mission options enabled by the proposed technique are obtained.

Jupiter system exploration trajectory design: Summary of the winning solution at CTOC10

This paper presents the methods and results submitted by the winning team from Harbin Institute of Technology of the 10th China Trajectory Optimization Competition(CTOC10).The problem posed by CTOC10 requires exploring the Jupiter system using a combined spacecraft.The exploration mission consists of the detection of Jupiter’s magnetic field and an exploration of the Galilean moons.The mission is completed through three steps:problem analysis,orbital design process,and data processing.The orbital design process is mainly divided into four parts,namely,repeating groundtrack orbit design,gravity-assisted orbit design,initial orbit parameter selection,and local optimization adjustment.The designed orbit is then evaluated using a heuristic optimization algorithm applied during the data processing.Finally,six full-coverage observations of Jupiter’s magnetic field are realized under the constraints of fuel and time.The final index of the submitted result is 357.8067.

Data-driven model for predicting production periods in the SAGD process

Many studies have analyzed the cumulative production performance in the SAGD(steam assisted gravity drainage)process by data-driven models but a study based on these models for a dynamic analysis of a SAGD production period is still rare.It is important for engineers to define the production period in a SAGD process as it has a stable and high oil production rate and engineers need to reset operational conditions after the production period starts.In this paper,a series of SAGD models were constructed with selected ranges of reservoir properties and operational conditions.Three SAGD production period parameters,including the start date,end date,and duration,are collected based on the simulated production performances.artificial neural network,extreme gradient boosting,light gradient boosting machine,and catboost were constructed to reveal the hidden relationships between twelve input parameters and three output parameters.The data-driven models were trained,tested,and evaluated.The results showed that compared with the other output parameters,the R^(2) of the end date is the highest and it becomes higher with a larger training data set.The extreme gradient boosting algorithm is a better choice to predict the Start date while the artificial neural network generates better prediction for the other two output parameters.This study shows a significant potential in the use of data-driven models for the SAGD production dynamic analysis.The results also serve to support the utilization of the datadriven models as efficient tools for predicting a SAGD production period.