Optimal Drilling Planning by Considering the Subsurface Dynamics

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Optimal Drilling Planning by Considering the Subsurface Dynamics – Combing the Flexibilities of Modeling and a Reservoir Simulator Mohammad Sadegh Tavallali, Farnoosh Bakhtazma, Ali Meymandpour, and Iftekhar A Karimi Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00800 • Publication Date (Web): 07 Nov 2018 Downloaded from http://pubs.acs.org on November 8, 2018

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Industrial & Engineering Chemistry Research

Optimal Drilling Planning by Considering the Subsurface Dynamics – Combing the Flexibilities of Modeling and a Reservoir Simulator

M.S. Tavallali,a* F. Bakhtazma,a,b A. Meymandpour,a I.A. Karimic a

Department of Chemical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran 71987-74731 Department of Chemical, Petroleum and Gas Engineering, Shiraz University of Technology, Shiraz, Iran 71557-13876 c Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117585 b

Abstract Many drilling and oil companies are facing tight budgets and a promising option for survival is to optimally revisit the drilling plans and production operations. Although there are some options for this task in the current reservoir simulators, more in-depth analysis is indeed required. Hence, in this study we borrow the flexibilities and capabilities of both modeling and a reservoir simulator to spatiotemporally plan the drillings of new injector and/or producer wells, determine the total number of new wells, and schedule the production/injection from all wells. The entire approach is both mathematically enriched and simple to use in the industry. We show that our methodology outperforms the decisions of an industrially accepted reservoir simulator in two separate examples by 4.4% and 2.4% respectively. Keywords: Drilling planning, well placement, reservoir simulator, MINLP, evolutionary method Submission Status: Revision submitted to IECR on 28 September 2018

*

Corresponding author: E-mail [email protected]

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Introduction

The financial situations of many countries either directly or indirectly rely on the petroleum production. Hence, there has been considerable investments in the hardware sector of this industry. Amongst others, well drilling activities play a major role with long-lasting economic impacts and therefore have absorbed many investments and expenses. However, this industry is facing a very challenging situation. From one hand, as can be seen in Figure 1-a, the statistics suggest an increase in the global demand for both natural gas and oil, and consequently higher production levels of these commodities1. On the other hand, the same statistics show that as the global market experienced a decrease in oil price, the number of active rigs and completed wells also started to decline (Figure 1-b). These two conditions imply that both production and drilling activities should be planned, and executed in the most efficient way to fulfil the market demand and face the decline in oil price. Any petroleum field experiences five distinct stages in its life, i.e. exploration (0-10 years), appraisal (1-5 years), development (1-5 years), production (3-30 years) and abandonment (1-2 years)2. Well drilling might happen during the first to the forth stages with different purposes, including exploration, reservoir core sampling, oil/gas production and water/gas injection. Drilling is a preliminary/complementary action for production and its planning has attracted many researchers in the recent years. Probably we can categorize the existing studies into two main groups based on the approach they have utilized, i.e. black or gray box (heuristic/evolutionary and adjoint based methods) versus mathematical programming (equation based). In addition to these two, the reservoir simulators also provide some specific options, let us take them as the third group.


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In the first group, the focus has mostly been on the well placement by coupling reservoir simulators with external optimization algorithms, without further modeling attempt. For instance, Hamida et al. utilized a problem specific and modified version of genetic algorithm for well placement 3; Wang et al.4 used multilevel coordinate search to address joint problem of well placement and well control, and Naderi and Khamechi

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employed metaheuristic bat algorithm

for well placement. Volkov and Bellout used adjoint-based gradient approximation method in a forward-backward simulation format for deviated well placement 6. Although practical, one of the shortcomings of such approach is its considerable computational expenses due to the high simulation time. Hence, Chen et al.

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coupled a numerical simulator with so-called cat swarm

optimization algorithm and attempted to reduce the simulation time by defining a specific analytical formula-based objective function. Similarly Pouladi et al.8 used volumetric pressure approximation data provided by fast marching method as a proxy for reducing the computational cost. In fact proxies have attracted many researchers with the hope of reducing the simulation and hence the optimization time 8, 9. However, the second group uses the mathematical programming technique 10-12. An example is a series of studies by Tavallali, Karimi and their coworkers; they tackled the static13 and later the dynamic well placement problem14, 15 and formulated these problems through a framework for mixed integer nonlinear programming (MINLP) problems. Their model included rigorous reservoir dynamics, as well as many logical decisions implemented in GAMS optimization package. Not only their approach addressed well placement, but also it considered production planning and well-to-manifold allocations. Finally, some industrial reservoir simulators, such as ECLIPSE16 also offer some options, we take it as the third group. These options are for timing of well openings (e.g., qdrill) which can 3 ACS Paragon Plus Environment


be interpreted as the required plan for drillings17. To do so, a preliminary list of wells are introduced to the software before the simulations. In the case of production decline and deviation from the production target the software opens the candidate wells one by one based on the provided order in the aforementioned list. This action seems to be a piecemeal approach and let us refer to that as qdrill in this paper. The abovementioned first group of studies are simple to implement however have mostly ignored the timing of drilling. In contrast, the second set of studies by mathematical programming seems to be cumbersome to implement and very complicated for simple users in the industry, however drilling planning as a logical decision has usually been an integrated part in them. Both approaches should be compared to the outcome of the third group. There are clear rooms for improvement of current situation and the most practical approach can be to simultaneously employ some of the capabilities of both first groups to offer a new and novel approach which addresses some of the existing shortcomings, even the limitations of the third group. To do so, we mix the flexibility of using reservoir simulators (in their simple mode for production simulation, and not for drilling timing) as the central part of our black box from the first category to satisfy the required set of partial differential equations (conservation and constitutive equations), and the strength of mathematical and logical modeling from the second category. We connect them by a heuristic method (genetic algorithm). That is used to determine the combined drilling scheduling, well placement, and well throughputs. Moreover, we utilize the concept of well groups to consider the dependency of operation of each single well on the other wells in the same group. Finally, our hypothesis is that the solution offered by the third group (mainly by qdrill in this study) is suboptimal as there are limitations in setting appropriate objective function for them. Hence one of the targets of this study is to compare the performance 4 ACS Paragon Plus Environment

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of such a solution from the above third group with that of our proposed method. In what follows, we initially introduce this technique by discussing our logical model for dynamic well placement and drilling planning, followed by describing its solution strategy. After that we thoroughly examine and analyze our technique on two different examples and compare that with the qdrill keyword of ECLIPSE.

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Problem Definition

A drilling project over a planning horizon of years in a petroleum field is to be optimally scheduled. Using available (drilled) wells, the field can be in operation while drilling starts. The reservoir can be of any shapes, and the target wells can be of any types. Here, the problem can be summarized as below: Given: a. Production horizon, and operational data for this period including the bottom hole pressure (BHP), tubing head pressure (THP), and production (injection) flow rate limit for each well, well group and the entire field b. Geological data of the reservoir(s) (such as permeability and porosity map), petrophysical and PVT data of the fluids (such as viscosity, density, bubble point pressure) c. Economic forecast and number of available drilling rigs over this horizon. Although unit costs, revenues and drilling budget as well as the number of available drilling rigs can be time variant, it should be scheduled from the very beginning. d. Potential wells’ geometries (for both conventional vs. unconventional) wells), their trajectories (with accessing the data such as location of top and bottom parts, curvature, relative position of possible laterals on the main trunk), locations, types (injector vs. 5 ACS Paragon Plus Environment


producer) and perforation layers are predetermined. However this assumption can be removed at a very high computational cost 18. Assumptions: a. A pre-processing of given well candidates is used to ensure that no potential well intersects another well. b. Each given time period is long enough for drilling one well, and drilling does not take longer than one period. c. All given data and parameters are deterministic. For instance, although there are many uncertainties in geological data, we assume the given reservoir realization matches the underground formation. d. The production mechanism can be with/without water injection. e. Although wells can penetrate and pass through several geological grid blocks, each well is perforated only in one layer, and each grid block hosts only one candidate well. Policies: a. If water-cut limit is violated in any time periods, the well is shut-in for that given period. b. In order to ensure the return of initial investment, no drilling is permitted in the last period of time horizon. Determine: a. The drilling schedule (where, when and what to drill). b. Wellhead flow rates and BHP profiles over production time.


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Targeting to maximize the net present value (NPV) of the overall drilling and production projects.

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Modeling

Sets Consider the reservoir to be enclosed in the tightest possible cuboid and then let the spatial domain be discretized in a Cartesian system into , and number of cuboid grid blocks in , and directions with lengths of , and Δ ( = 1,2, … , ; = 1,2, . . , and = 1,2,3, … , ). For brevity of the model presentation, we combine the spatial indices into a single index (with = + − 1 + − 1, = 1, 2, 3, … , × × ). To better characterize the model we further define the below sets: = [|interior grid blocks, inside the reservoir domain ] 3 ∈ = [|candidate or existing injector wells, identified by perforation location at grid block ] 3 ∈ = [|candidate or existing producer wells, identified by perforation location at grid block ]

Optimal Drilling Planning by Considering the Subsurface Dynamics

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