Brage Rugstad Knudsen

Shut-in based production optimization of shale-gas systems

Abstract This paper presents a novel operational scheme for enhanced utilization of late-life shale multi-well systems. These systems are characterized by a large number of geographically spread wells and pads, where a substantial number of the wells are producing at low erratic rates due to reservoir pressure depletion and well liquid loading. By applying a cyclic shut-in and production strategy, the scheme avoids well liquid loading and optimizes the production from a set of late-life wells at a shared production pad. The scheduling of well shut-ins is formulated as a generalized disjunctive program (GDP), using a novel shale-gas well and reservoir proxy model. The GDP formulation lends itself both to a complete MILP reformulation and reduced size MINLP reformulations; a computational study indicates in favor of the MILP formulation. We include numerical examples to demonstrate the potential benefit of applying the proposed cyclic scheme compared to a non-optimized approach.

Lagrangian relaxation based decomposition for well scheduling in shale-gas systems

Suppressing the e ects of liquid loading is a key issue for e cient utilization of mid and late-life wells in shale-gas systems. This state of the wells can be prevented by performing short shut-ins when the gas rate falls below the minimum rate needed to avoid liquid loading. In this paper, we present a Lagrangian relaxation based scheme for shut-in scheduling of distributed shale multiwell systems. The scheme optimizes shut-in times and a reference rate for each multi-well pad, such that the total produced rate tracks a given short-term gas demand for the field. By using simple, frequency-tuned well proxy models, we obtain a compact mixed integer formulation which by Lagrangian relaxation renders a decomposable structure. A set of computational tests demonstrates the merits of the proposed scheme. This study indicates that the method is capable of solving large field-wide scheduling problems by producing good solutions in reasonable computation times.

Target-rate Tracking for Shale-gas Multi-well Pads by Scheduled Shut-ins ?

Abstract The recent success of shale-gas production relies on drilling of long horizontal wells and stimulation with multistage hydraulic fracturing. This practice normally leads to an initial peak production with a subsequent rate decline, followed by low and erratic production rates caused by water accumulation in the wells. Shale-gas recovery requires a large number of wells in order to maintain a sustainable total gas supply. To reduce the surface area disturbances caused by this extensive drilling and to share available surface infrastructure, the use of multi-well pads is a key driver in shale-gas developments. Furthermore, the inherent rate decline of shale-gas wells, the water accumulation in them and the large number of wells, leads to severe operational challenges for well operators. The fact that shut-ins may be used as a means to prevent liquid loading and boost late-life production rates from shale-gas wells, suggests scheduling of shut-ins to perform maintenance and clean-up of the wells, and to track a target rate for the multi-well pad. In this paper we propose an optimization scheme for shale-gas multi-well pads to schedule shut-ins and to track a target rate. The optimization problem is formulated as a discrete time mixed integer linear program (MILP) with binary variables defining at which times the well is either shut-in or producing. A reservoir proxy model and a well model for each well is designed and tuned against a realistic multi-fractured reservoir model. We demonstrate the benefits and the potential of the proposed methodology through a one-month production planning problem for an eight-well shale-gas pad.

On MINLP Heuristics for Solving Shale-well Scheduling Problems

Abstract This paper describes mixed integer nonlinear programming (MINLP) heuristics for solving dynamic scheduling problems in complex petroleum production systems with a network topology. We modify the Feasibility Pump heuristic for convex MINLPs [Bonami and Goncalves, 2010] by formulating a multiobjective problem, in which we aim at balancing the two goals of quickly obtaining a feasible solution and preserving solution quality with respect to the objective value. We further present a simple linearization-based heuristic, only aimed at quickly generating feasible solutions. The MINLP heuristics are applied to a dynamic multi-pipeline shale well and compressor scheduling problem, targeted on application in decision-support tools for improving operations in large shale-gas systems. Developing efficient and robust heuristics are important for the applicability of these tools, in the sense that low computation times are often more important than global optima. A computational study shows that the proposed objective-oriented Feasibility Pump is competitive both in terms of solution quality and computation time compared to other heuristics and the branch-and-bound method.

An exact penalty-function approach to proactive fault-tolerant economic MPC

This paper presents a fault-tolerant economic model predictive control scheme for proactive handling of incipient actuator faults. The scheme applies an ℓ1 exact penalty function with a set of switching rules in order to steer the system by a minimum-time approach inside a controlled invariant set where stability of the system can be preserved during loss of actuation from the faulty actuator. We consider the approach for linear control systems, thereby allowing computation of a lower bound for the penalty parameter to ensure exactness of the penalty function. We prove nominal asymptotic stability of the modes of the proposed model predictive control scheme, and illustrate the approach by a numerical example.

Reducing the risk of another Aliso Canyon

![Figure][1] In 2015, residents had to be evacuated from the Porter Ranch area of Los Angeles due to the natural gas leak from the Aliso Canyon storage facility. PHOTO: SCOTT L./WIKIMEDIA COMMONS In their Report “Methane emissions from the 2015 Aliso Canyon blowout in Los Angeles, CA” (

Towards an objective feasibility pump for convex MINLPs

This paper describes a heuristic algorithm for finding good feasible solutions of convex mixed-integer nonlinear programs (MINLPs). The algorithm we propose is a modification of the feasibility pump heuristic, in which we aim at balancing the two goals of quickly obtaining a feasible solution and preserving quality of the solution with respect to the original objective. The effectiveness and merits of the proposed algorithm are assessed by evaluation of extensive computational results from a set of 146 convex MINLP test problems. We also show how a set of user-defined parameters may be selected to strike a balance between low computation time and high solution quality.

Lagrangian Relaxation Based Production Optimization of Tight-Formation Wells

Abstract Dry and semi-dry tight formation gas wells normally share the characteristic production profile defined by an initial high production, with an early steep decline and subsequent low pseudo steady-state gas rates. Small volumes of co-produced liquids will, even for dry gas wells, eventually bring the wells into the state of liquid loading, causing erratic unpredictable production rates deteriorating the performance of the wells. This state of the wells can be prevented by performing short shut-ins when the gas rate falls below the minimum rate needed to avoid liquid loading. Multi-well shut-ins may however lead to very high and low peak rates, possibly causing problems for the capacity of shared surface systems or lower and upper bounds on the total rate in a production plan. This paper presents a Lagrangian relaxation based scheme for scheduling of shut-in times for late-life tight formation gas wells with a shared gathering system. The proposed scheme includes a QP formulation for solving the Lagrangian dual, together with an aggregated construction and improvement heuristic for generating primal feasible solutions from the solution of the Lagrangian. We include several test examples to demonstrate the efficiency of the proposed decomposable scheme.

Petroleum production optimization – A static or dynamic problem?

Abstract This paper considers the upstream oil and gas domain, or more precisely the daily production optimization problem in which production engineers aim to utilize the production systems as efficiently as possible by for instance maximizing the revenue stream. This is done by adjusting control inputs like choke valves, artificial lift parameters and routing of well streams. It is well known that the daily production optimization problem is well suited for mathematical optimization. The contribution of this paper is a discussion on appropriate formulations, in particular the use of static models vs. dynamic models. We argue that many important problems can indeed be solved by repetitive use of static models while some problems, in particular related to shale gas systems, require dynamic models to capture key process characteristics. The reason for this is how reservoir dynamics interacts with the dynamics of the production system.

Global Optimisation of Multi-Plant Manganese Alloy Production

Abstract This paper studies the problem of multi-plant manganese alloy production. The problem consists of finding the optimal furnace feed of ores, fluxes, coke, and slag that yields output products which meet customer specifications, and to optimally decide the volume, composition, and allocation of the slag. To solve the problem, a nonlinear pooling problem formulation is presented upon which the bilinear terms are reformulated using the Multiparametric Disaggregation Technique (MDT). This enables global optimisation by means of commercial software for mixed integer linear programs. We demonstrate the model and solution approach through case studies from a Norwegian manganese alloy producer. The computational study shows that the model and proposed optimisation approach can solve problem sizes of up to ten furnaces to a small optimality gap, that global optimization approach with MDT scales well with larger, real problem instances, and that the model outperforms the current operational practice.