Oil production optimization of several wells subject to choke degradation

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1 Proceedings of the 3rd IFAC Workshop on Atomatic Control in Offshore Oil and Gas Prodction, Esbjerg, Denmark, May 30 - Jne 1, 2018 We_A_Reglar_Talk.1 Oil prodction optimization of several wells sbject to choke degradation Adriaen Verheyleweghen, Johannes Jäschke Department of Chemical Engineering, Norwegian Univ. of Science and Technology, Trondheim, NO-7491 ( verheyle@ntn.no, jaschke@ntn.no). Abstract: Unplanned maintenance interventions of sbsea oil and gas prodction systems are very expensive, which leads to strict reqirements to eqipment reliability. Withot a systematic way to ensre reliable operation however, a very conservative operational strategy is often chosen, which can lead to sb-optimal operation and the loss of large potential profits. We propose to integrate condition monitoring and prognostics into the prodction planning problem to redce conservativeness by actively steering plant degradation and preventing violation of health-critical constraints. We achieve this by combining eqipment degradation models with reglar process models and solving a shrinking horizon real-time optimization problem ntil the next planned maintenance horizon. A network of oil and gas prodcing wells with artificial gas lift, sbject to particle indced choke erosion is sed as a case example. Keywords: Health-aware prodction optimization, condition-based control 1. INTRODUCTION In this paper we consider an oil and gas prodction network consisting of mltiple wells. The wells are connected to a common manifold, from which the combined flow goes throgh a riser to a topside receiving facility. As the field matres, the reservoir pressre decreases. Eventally, the pressre might drop to sch low levels that flids can no longer overcome the resistance in the riser, and prodction comes to a stop. Artifical gas lift can be sed to redce the pressre drop and increase the flow, prolonging the lifetime of the field. However, increased volme flows (and conseqently velocities), in addition to the decreased density, may lead to accelerated degradation of vlnerable parts of the system. In particlar, erosion of chokes and bends may be a problem, especially if the sand prodction from the reservoir is high. Particle erosion can severely limit the remaining sefl life of exposed eqipment. In rare cases, sand erosion has been known to erode away critical components sch as chokes in as little as a few hors (Hagen et al., 1995). Choke replacement freqencies of 3-4 months, thogh having significant costs associated with them, are not nheard of in the sbsea indstry. Sand prodction generally tends to increase as the field matres and reservoir pressre decreases, thogh it can also pose problems in some green fields. It is conseqently vital to consider potential sand erosion when deciding on a prodction strategy, in order to prevent breakdowns which reqire costly nplanned maintenance intervention. Common indstrial practice is to define an acceptable sand rate (ASR) above which operation is not permitted. The ASR is often conservatively defined in order to accont We acknowledge financial spport by SUBPRO center for research based innovation, and DNV-GL for worst-case erosion scenarios. The operational degrees of freedom for prodction optimization are conseqently severely constrained, leading to sb-optimal operation. The conservativeness can be redced by monitoring the rate of erosion on critical components real time and adjsting operation to reflect eqipment integrity. Monitoring sally involves periodic inspection of weight loss copons. Real-time erosion monitoring systems, sch as ABBs IN- SIGHT (ABB, 2010), exist, bt are not yet widespread in indstry. These systems are sally not integrated with the control system. Set-points of the control system mst still be manally adjsted by the operator. This dependency on the operator can lead to delays, manal overrides and overall redced efficiency of the prodction system. In this paper, we se a health-aware real-time optimization (RTO) approach, in which health monitoring and prognostics is inclded in the decision making process to find the optimal operational strategy withot jeopardizing eqipment health (Verheyleweghen and Jäschke, 2017a). Specifically, we formlate the problem of optimal operation as a dynamic optimization problem where the objective is to maximize the overall profit of the plant, withot violating constraints on the maximm allowable choke erosion. We also show how ncertainties in the model parameters can be taken into accont by formlating the problem of optimal operation as a worst-case / min-max optimization problem or a mlti-stage stochastic optimization problem. We implement both methods and solve the problem repeatedly in a shrinking-horizon, RTO-like fashion. The remainder of the paper is strctred as follows: In Section 2 we give a process description for the gas lifted well network. In Section 3 we formlate the optimization problem and explain how ncertainty is treated. Simlation reslts are presented and discssed in Section 4. Copyright 2018, IFAC 1

2 Gas lift valves Prodction choke facility ṁ pg = ṁ rg + ṁ lg (1) ṁ pl = ṁ rw + ṁ ro (2) ṁ p = ṁ pg + ṁ pl, (3) where ṁ lg is the flow rate of lift gas throgh the annls, ṁ rg is the flow rate of gas from the reservoir, and ṁ pg and ṁ pl are the flow rates of prodced gas and liqid respectively. The liqid flow ṁ rl is the sm of the flow of water ṁ rw and the flow of oil ṁ ro from the reservoir. Finally, the total flow rate throgh the prodction choke is ṁ p. Adjsting the gas lift rate and the total flow throgh the prodction choke is achieved by opening and closing the valves. The flow rates can then be expressed in terms of the valve eqation: Fig. 1. Illstration of the oil and gas network with artificial gas lift. Finally, conclding remarks are given and ftre work is described in Section PROCESS DESCRIPTION The model for the oil and gas prodction system sed in this work is based on the model by Krishnamoorthy et al. (2016). An illstration of the process is given in Fig. 1. A fll description of the model is given there, bt for the sake of completeness, we provide a smmary below. The model was modified slightly in the following ways: (1) The model ses a larger time horizon since or aim is to do health-aware RTO, which reqires the time horizon to captre the degradation dynamics. We therefore assme that changes in mass flow rates are instantaneos, reslting in constant mass hold ps. The dynamics in or work are instead dictated by gradal choke degradation and slow decline of reservoir pressre. (2) The model considers a three-phase system consisting of oil, gas and water. (3) The model is extended to inclde three wells and a riser Gas injection at the bottom of the well lowers the average flid density, thereby redcing the hydrostatic pressre drop in the well. As a reslt, the bottom hole pressre and conseqently the flow from the reservoir increases, ntil a certain point. Too large gas injection rates reslt in increased frictional pressre drop de to increased velocities. We define the short term optimal gas injection rate (with respect to oil and gas prodction), as the point at which the marginal frictional pressre drop is balanced by the marginal hydrostatic pressre drop. As we shall see later, the increased velocities lead to more rapid degradation, which might force s to operate at lowerthan-short-term-optimal gas injection rates. 2.1 Process model The steady-state mass balances in each well are ṁ p = C pc ρw (p wh p m ) (4) ṁ lg = C lg ρa (p a p wi ). (5) Here, C pc and C lg are the valve coefficients of the prodction choke and the lift gas valve respectively, and ρ w and ρ a are the flid densities in the well tbing and in the annls. Pressres p driving the flow are denoted by wh for wellhead, m for manifold, a for annls and wi for well injection point. Assming that the ideal gas law can be applied here, we express the density of the gas in the annls as ρ a = Mp a (6) T a R m a = (A 2 a A 2, (7) w) L a where M is the molar mass of the lift gas, T a is the temperatre in the annls and R is the niversal gas constant. The average density in the well tbing is ρ w = m gt + m lt ρ l L r A r L w A w (8) ρ l = WC ρ w + (1 WC )ρ o. (9) In the above expressions m a, m gt and m lt are the holdps of gas in the annls, and holdps of gas and liqid in the tbing, L r and A r are the length and cross-sectional area of the tbing above the gas injection point, and L w and A w are the length and cross-sectional area of the tbing below the gas injection point. The flow from the reservoir is given by ṁ rl = PI (p r p bh ) (10) WC = ṁrw (11) ṁ rl ṁ rg = GOR ṁ ro, (12) where p r = m rgrt. (13) V r Above, PI is the prodctivity index, WC is the water ct, GOR is the gas-oil-ratio, and p r is the reservoir pressre. These are well-specific parameters. Finally, the well pressres are decreasing as the reservoir is slowly depleting. We model the reservoir as a storage tank, yielding dm rg = ṁ rg (14) dt Copyright 2018, IFAC 2

3 2.2 Choke degradation model Choke erosion rates depend on a nmber of different factors, sch as physical properties of the flid and the impacting particle. In addition, erosion rates are heavily dependent on the choke geometry, as this will inflence the flow patterns. It is therefore a challenging task to predict the erosion rates for a given choke, withot expensive comptational flid dynamics (CFD) simlations. DNV- GL (2015) give an overview over some erosion prediction models for simple choke geometries, based on which they recommend ASRs. We se the erosion model presented in DNV-GL (2015), which is a variation of the model presented in Hagen et al. (1995). The erosion rate is given as de dt = K F (α) U p n G C 1 GF ṁ sand C nit (15) ρ t A t where de dt is the erosion rate in mm/yr., K, n, C 1, GF and C nit are varios constants. ṁ sand is the sand prodction rate and G is defined as G = d p β (1.88 log (A) 6.04) D pipe (16) where d p is the particle diameter, and D p is the pipe diameter. β and A are dimensionless parameters A = Re tan (α) β (17) β = ρ p ρ f (18) where Re is the Reynolds nmber of the flow, ρ p is the paricle density and ρ f is the flid density. The sand prodction rate ṁ sand is assmed to be proportional to the overall mass flow rate from the reservoir: ṁ sand = SR ṁ r, (19) where SR is the sand rate parameter. Frthermore, in Eqation 15, F is the dctility of the choke gallery material, which is F = 0.6 [sin(α) ( sin(α) sin 2 (α) )] 0.6 (20) [1 exp( 20α)] for dctile materials. Here, α is the particle impact angle, which is given as ( ) 1 α = arctan, (21) 2R with R being the radis of the choke gallery. U p is the particle impact velocity, which is determined by U p = 3 Q = 3 Q 4 A g 8 H D, (22) where Q is the actal volmetric flow rate, A g is the effective gallery area, H is the effective height of the gallery and D is the gap between the choke cage and choke body. 3. OPTIMIZING ECONOMIC PERFORMANCE SUBJECT TO HEALTH CONSTRAINTS By combining the process model and the health degradation model described in Section 2, the combined DAE model can be sed to formlate an optimization problem in which the economic performance is maximized sbject to constraints on the maximm allowable health degradation. In previos work (Verheyleweghen and Jäschke, 2017b), we have shown that failing to inclde the constraints on health degradation will lead to nreliable operation, since this constraint always will be active in the optimal soltion for the operation strategy. The health state of the plant is assmed to be known at any given time, meaning that real-time erosion monitoring systems are installed and working. The optimization problem which is solved at each RTO iteration can be written as: min t f t 0 φ (x, z,, p) dt (23a) s.t. f(x, z,, p) 0 (23b) g(x, z,, p) = 0 (23c) where φ is the objective fnction which is to be minimized, and f and g are the ineqality constraints and eqality constraints. The variables x, z and denote the differential states, algebraic states and inpts, respectively. p is sed to denote the ncertain parameters. The dynamic problem (23) is discretized and solved with orthogonal collocation with three collocation points for each finite element (Biegler, 1984). The discretized problem can be written as min N φ (x k, z k, k, p k ) (24a) s.t. f(x k, z k, k, p k ) 0 k = 1...N (24b) g(x k, z k, k, p k ) = 0 k = 1...N (24c) where N denotes the horizon length. 3.1 Uncertainty handling To accont for plant-model mismatch / parametric ncertainty, or intrinsic stochasticity of the system, we consider some of the variables (denoted p in (23)) to be stochastic. In particlar, it is assmed that the sand prodction rate SR and the prodctivity index PI in each of the three wells are stochastic. For simplicity, we assme that the nine ncertain variables are independent and normally distribted, p k N (µ k, σ k ). Varios approaches for optimization nder ncertainty are fond in literatre. Two of the most poplar approaches are worst-case optimization and scenario-based optimization. Worst-case optimization; stochasticity is acknowledged by sbstitting in the worst-case realizations in the ncertain parameters. If constraints are satisfied for the worstcase realization, they shold also hold for other parameter realizations, for most cases. Thogh it can be shown that the worst-case soltion may be infeasible for other parameter realizations, this approach has been sccessflly demonstrated for a nmber of practical applications. Scenario-based optimization; in which the probability distribtion of the ncertain parameters is discretized into Copyright 2018, IFAC 3

4 a finite nmber of scenarios and incorporated into the optimization problem in the form of a scenario tree. An illstration of a scenario with for scenarios is shown in Fig. 2. By optimizing for all scenarios simltaneosly, it is ensred that the obtained soltion is not only feasible for the worst-case realization or expected realization, bt for all possible realizations in the scenario tree. Frthermore, the degree of sb-optimality of the soltion can be redced by weighing the individal scenarios with their respective probabilities. This leads to a soltion that is, on average, less conservative than the worst-case approach. Possibility of ftre recorse is inclded in the optimization by design of the scenario tree, which makes this method well sited to RTO problems nder ncertainty. The drawback of the this method compared to the two others is the increased problem size and conseqent comptation time, de to the need for additional variables for each scenario. Worst-case and scenario-based RTO maybe classified nder the mbrella-term of robst optimization, in which parameter realizations are assmed to occr within bonded ncertainty sets. These approaches are perhaps the easiest to grasp conceptally, bt other ways to handle ncertainty (sch as chance constrained optimization, dynamic programming, and fzzy programming) exist in literatre. We will however only consider worst-case and scenario optimization in this work. 3.2 Worst-case optimization The worst-case optimization problem can be written as N min φ (x k, z k, k, p k) (25a) s.t. p k = arg max f(x k, z k, k, p k ) p k k = 1...N (25b) g(x k, z k, k, p k ) = 0 k = 1...N (25c) where p k is the worst-case parameter realization, i.e. the scenario which leads to the largest constraint violation. De to the two nested optimization problems, this approach is also known as min-max optimization. These problems are generally difficlt to solve or even intractable (Ben-Tal et al., 2009). In general, we mst reqire p k to be bonded for the inner problem to have a soltion. In some cases, sch as the one considered in this work, the worst case parameter realization p k can be known a priori. This significantly simplifies the problem since the second optimization problem disappears. 3.3 Scenario-based optimization In scenario-based optimization, we discretize the continos distribtion fnction into a finite nmber of discrete scenarios, and optimize the following objective min S i=1 p i N sbject to the following constraints φ (x i,k, z i,k, i,k, p i,k ) (26a) x 1,0 x 2,0 x 3,0 p + 1,0 2,0 x 1,1 x 4,0 p 3,0 4,0 x3,1 t 0 (present) p + 1,1 x 1,2... x 1,20 x 2,1 p 1,1 x 2,2... x 2,20 p + 2,1 x 3,2... x 3,20 x 4,1 p 2,1 x 4,2... x 4,20... t 1 t 2 t 20 Robst horizon Prediction horizon Fig. 2. Scenario tree with N = 20 and S = 4. s.t. f(x i,k, z i,k, i,k, p i,k ) 0 i = 1...S, k = 1...N g(x i,k, z i,k, i,k, p i,k ) = 0 (26b) i = 1...S, k = 1...N (26c) S A i,k i,k = 0 k = 1...N (26d) i=1 where S is sed to denote the nmber of scenarios, and p i denotes the probability of realizing scenario i. (26d) are the so-called non-anticipativity constraints, which are needed to enforce non-anticipativity, i.e. making sre that the optimal soltion does not depend on yet nrevealed information. The scenario tree shown in Fig. 2 has N = 20 and S = 4, for example. For the kind of scenario trees encontered in RTO problems, each branching represents the different parameter realizations de to ncertainty. One might expect that the branches from each node shold be identical to the branches from its parent node. Alternatively, if the nknown parameters are estimated between each RTO iteration, this information can be inclded in the scenario tree by propagating the probability distribtion into the ftre from each node and adjsting the parameter realizations of the child nodes according to the propagated probability distribtion. In any case, this wold lead to exponential growth of the scenario tree, with each scenario tree having n N r scenarios, where n r is the nmber of discrete realizations of the probability distribtion. To avoid this explosive growth of scenarios, a robsthorizon N robst < N, i.e. the stage ntil which branching occrs, is commonly defined (Lcia et al., 2013a). By choosing a robst horizon shorter than the RTO horizon, we disregard the possibility of ftre recorse, and are conseqently expected to get a sb-optimal soltion. However, the loss is expected to be small, since the later stages of the RTO typically do not effect the objective mch. A robst horizon longer than N robst = 1 or N robst = 2 is rarely sed, since the marginal improvement of the soltion in practice rarely jstifies the increased dimensionality of the Copyright 2018, IFAC 4

5 Table 1. Possible realizations considered for the ncertain parameters in the scenario-based approach. Variable PI, SR wells wells Lower [-] [-] Mean [-] [-] Upper [-] [-] Table 2. Bond constraints Variable Lower Upper Unit bond bond Choke opening, wells [ ] Gas lift rate, wells [kg/s] Total gas lift rate [kg/s] Choke erosion, wells [mm] NLP. In this work, we only branch once, so N robst = 1, which yields a two-stage stochastic program. We frther redce the nmber of scenarios by limiting n r, the nmber of discrete realizations sed to approximate the continos probability fnction. We generate the scenario tree similarly to what is proposed by Lcia et al. (2013b), i.e. by sing all possible combinations of the maximm and minimm ncertain parameter realizations, in addition to a scenario for the expected and nominal ncertain parameter realizations, for a total of n r = S = 65 scenarios. The possible scenario realizations are given in Table Smmary of scenario-based problem formlation The objective is to maximize the profit, i.e. maximizing the oil and gas prodction and minimizing the cost of prodced water and the cost of gas. S=65 min p i x i,k,z i,k, i,k i=1 where φ = 3 well=1 N NPV (φ (x i,k, z i,k, i,k )) c g ṁ rg + c o ṁ ro + c lg ṁ lg. (27a) (27b) Here, NPV is the net present vale with a discont factor r = 0.1 and c g, c o and c lg are the gas price, oil price and gas injection cost, respectively. We assme c g = 3 USD/MMBt, c o = 44 USD/bbl, c lg = 1.3 USD/MMBt. Bond constraints for the variables are given in Table 2. In addition come the non-anticipativity constraints and the model constraints explained in (26) for the scenariobased approach. For the worst-case method, we have that (25) and (26) are identical when S = 1 and the worstcase scenario p k is bonded and known a priori. For this particlar problem, we have that the worst case scenario occrs when both PI and SR are high in all three wells. 4. RESULTS We implemented the model in MATLAB sing Casadi (Andersson, 2013) and solved the NLP from the discretized problem with IPOPT (Wächter and Biegler, 2006). Both ncertainty handling strategies, i.e. worst-case RTO and scenario-based RTO, were implemented. Fig. 3. Three snapshots of the open-loop soltions of the scenario-based RTO at t = 0, t = 2 and t = 4 years. The red, ble and yellow scenarios are for the first, second and third wells, respectively. The dashed lines show the past states, while the solid lines show the predicted states for each of the 65 scenarios. 4.1 Problem (27) is solved repeatedly in a shrinking horizon fashion, starting with N = 18. After finding the optimal soltion, only the first inpt is implemented on the actal plant, before the model is re-optimized. This process is illstrated in Figre 3, which shows the open-loop soltion of the scenario-based optimization problem at three selected times t = 0, t = 2 and t = 4 years. The predicted states for the 65 scenarios are shown in solid lines, while past states are shown as dashed lines. It can be seen that the first inpts are identical for all scenarios de to the non-anticipativity constraints. Red, ble and yellow color distingish the first well, second well and third well, respectively. Figre 4 shows the closed-loop soltion of the scenariobased method (solid line with circlar markers) compared with the worst-case method (dotted line with cross markers). The total profit of the two operational strategies, in terms of (27a), is 6.91 bn. USD for the scenario approach and 6.75 bn. USD for the worst-case approach. Althogh the actal nmbers shold be taken with a pinch of salt, the relative difference of approx. 2.5% is significant. Copyright 2018, IFAC 5

6 are not exceeded dring operation, which means that the risk of costly nforeseen maintenance interventions is minimized. We also show that parametric ncertainty in the model shold be handled with a scenario-based stochastic optimization approach, as this leads to better economic performance than the conservative min-max formlation that is commonly sed. The objective of the paper is to showcase the efficacy of or framework, rather than providing reslts which correspond 1:1 with real field data. We have therefore sed a simple choke degradation model and reservoir model. It is nderstood that accrate models mst be developed for the specific eqipment in qestion before real-world implementation. These degradation models will have to be developed by CFD simlations and/or in collaboration with eqipment manfactrers. Frthermore, ftre work will address the isse of overall plant reliability vs. single component reliability, as correlation between failre modes may significantly impact the overall plant reliability. ACKNOWLEDGEMENTS This work is fnded by the SUBPRO center for research based innovation, and DNV-GL. REFERENCES Fig. 4. Closed-loop soltions for the compared approaches. The solid line with circlar markers shows the scenario-based RTO, while the dotted line with cross markers shows the worst-case RTO. The red, ble and yellow scenarios are for the first, second and third wells, respectively. 4.2 Discssion In this work, we have assmed fll state feedback, meaning that the initial vales for the states are perfectly known. To simlate plant model-mismatch, the ncertain parameters are pertrbed with random noise between each RTO iteration. Since NPV of prodction is maximized, we see that early prodction is higher than late prodction. De to depleting reservoir pressre, we also see the need for more lift gas as the field matres. However, de to the decreased density and conseqent higher erosion rates, overall prodction mst be throttled down to prevent choke failre, as only so mch prodction can be permitted over the lifetime of the field. 5. CONCLUSION AND FUTURE WORK Or health-aware RTO framework combined diagnostics, prognostics and prodction optimization of a sbsea gaslifted oil and gas prodction network sbject to sand particle indced choke erosion. We show that by combining a prognostic model for the choke erosion in the prodction optimization, we can make sre that critical erosion levels ABB (2010). Condition Monitoring and Prodction Optimization Insight - Erosion Management System. e.abb.com/pblic/a19574f541925d b004ba78b/ TP002 Insight erosion management system.pdf. Andersson, J. (2013). A General-Prpose Software Framework for Dynamic Optimization. Ph.D. thesis, Arenberg Doctoral School, KU Leven. Ben-Tal, A., El Ghaoi, L., and Nemirovski, A. (2009). Robst Optimization. Princeton University Press. Biegler, L.T. (1984). Soltion of dynamic optimization problems by sccessive qadratic programming and orthogonal collocation. Compters & chemical engineering, 8(3-4), DNV-GL (2015). Recommended practice RP-O501: Managing sand prodction and erosion. dnvgl/rp/ /dnvgl-rp-o501.pdf. Hagen, K., Kvernvold, O., Ronold, A., and Sandberg, R. (1995). Sand Erosion of Wear-Resistant Materials: Erosion in Choke Valves. Wear, 186, Krishnamoorthy, D., Foss, B., and Skogestad, S. (2016). Real-Time Optimization nder Uncertainty Applied to a Gas Lifted Well Network. Processes, 4(4), 52. Lcia, S., Finkler, T., and Engell, S. (2013a). Mlti-Stage Nonlinear Model Predictive Control Applied to a Semi-Batch Polymerization Reactor nder Uncertainty. Jornal of Process Control, 23(9), Lcia, S., Sbramanian, S., and Engell, S. (2013b). Non-Conservative Robst Nonlinear Model Predictive Control via Scenario Decomposition. In Control Applications (CCA), 2013 IEEE International Conference on, IEEE. Verheyleweghen, A. and Jäschke, J. (2017a). Framework for Combined Diagnostics, Prognostics and Optimal Operation of a Sbsea Gas Compression System. In 2017 IFAC World Conference, volme 50, Verheyleweghen, A. and Jäschke, J. (2017b). Health-Aware Operation of a Sbsea Gas Compression System nder Uncertainty. In Fondations of Compter Aided Process Operations / Chemical Process Control FOCAPO/CPC. Wächter, A. and Biegler, L.T. (2006). On the Implementation of an Interior-Point Filter Line-Search Algorithm for Large-Scale Nonlinear Programming. Mathematical programming, 106(1), Copyright 2018, IFAC 6