Article pubs.acs.org/IECR
Integrated Oil-Field Management: From Well Placement and Planning to Production Scheduling M. Sadegh Tavallali†,‡ and Iftekhar A. Karimi*,† †
Department of Chemical & Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117585 Department of Chemical Engineering, Shiraz Branch, Islamic Azad University, Shiraz, Iran 71987-74731
‡
S Supporting Information *
ABSTRACT: Integrated management can benefit oil-field development and exploitation tremendously. It involves holistic decisions on the order, placement, timing, capacities, and allocations of new well drillings and surface facilities such as manifolds, surface centers, and their interconnections, along with well production/injection profiles. These decisions have profound longterm impacts on field productivity; however, the dynamic nature of oil reservoirs makes them strongly intertwined and highly complex. Hence, a dynamic, holistic, and integrated approach is necessary. Most existing well placement studies ignore surface effects and drilling-rig availability and assume that all wells are opened simultaneously at the beginning of the production horizon. In this work, we extend our previous study [Tavallali et al. Ind. Eng. Chem. Res. 2014, 53 (27), 11033] and develop a mixed integer nonlinear programming (MINLP) approach for addressing such limiting assumptions. We develop a revised outerapproximation algorithm involving two multiperiod, nonconvex MINLPs and several local search strategies. Numerical results for a literature example show significant improvement in the net present value for oil-field development.
1. INTRODUCTION Oil and gas are major energy resources for the modern world and will continue to be so for the near future. They are typically produced by drilling production wells in huge petroleum fields with several reservoirs. Well drilling can account for up to 60% of the total capital expenditure (CAPEX) required for a field. On average, 1829 drilling rigs were active in 2002, which doubled to almost 3518 rigs in 2012.2 Additionally, according to the International Association of Drilling Contractors (IADC), nearly 572.334 million man-hours were spent on 74% of the worldwide oil and gas well drilling-rig fleets3 in 2012. Clearly, the overall profitability of an oil-field exploitation project depends greatly on the cost effectiveness and efficiency with which the field is developed and operated over its lifetime. Wells are the only access to a subsurface pay zone, but surface facilities are necessary for processing the extracted fluids to obtain the valued oil. Naturally, surface-facility installations and retrofitting follow most drilling activities. The best fielddevelopment strategies involve many critical technoeconomic decisions, including (but not limited to) locating the best drilling sites, determining their numbers and capacities, identifying the best surface-facility installations, performing continual retrofitting and scheduling, and making the best production decisions. These strategies must consider numerous subsurface and surface factors and conditions, as well as market and economy constraints. 1.1. Planning and Scheduling of Field Development. Figure 1 shows a schematic of a multireservoir oil field and its surface infrastructure. The subsurface fluids (oil, gas, and water) are usually distributed anisotropically in the underground porous media. Wells connect the subsurface reservoirs with various surface facilities. The subsurface pressure drives oil production through what are known as producer wells. This driving force is often boosted by injecting a fluid such as water © 2015 American Chemical Society
through what are known as injection wells. The multiphase oil flow from a producer well traverses through the well tubing to a manifold and then a surface center. A series of valves regulates the flow along this path. A similar surface infrastructure exists for the injection network, where water flows from water processing centers through manifolds to injection wells. Petroleum fields are spatiotemporally dynamic subsurface systems with nonlinear, complex, and intertwined interactions with production, injection, and processing networks at the surface. Manifolds and/or centers are usually shared among multiple wells and fields, and the variations in the operation of one element can significantly affect the performance of the others. In fact, activities such as drilling and installation affect the field dynamics dramatically. Satisfactory and profitable exploitation of a field requires that one consider the entire system dynamics over long periods using an integrated approach. Trapp field in Russell and Barton counties of Kansas illustrates this point very well. This field spans 56960 acres and was explored in 1929.4 Figure 2 shows the history of its oil production and active wells. As is evident, oil production expectedly declined over the years, and the declines had to be arrested periodically by well-planned and scheduled development activities. Since 1929, 3979 wells have been drilled in this field, but only a fraction of these wells are active now. A typical well can undergo many transformations before being abandoned for good. It might begin as a producer well, then it might be shut in for a while, and then it might be reworked and started again. Some producer wells can be converted to injector or enhanced oil recovery (EOR) wells. In all of these Received: Revised: Accepted: Published: 978
September 7, 2015 December 16, 2015 December 22, 2015 December 22, 2015 DOI: 10.1021/acs.iecr.5b03326 Ind. Eng. Chem. Res. 2016, 55, 978−994
Article
Industrial & Engineering Chemistry Research
Figure 1. Schematic of a hydrocarbon field with multiple reservoirs and associated production infrastructure. The wells (producers or injectors) connect the subsurface reservoirs to the surface facilities. The production manifolds gather oil from the wells for the oil separation centers to process and supply downstream. The injector manifolds take water from the water processing centers for the injector wells. Adapted from http://www. software.slb.com/.
Figure 2. Number of wells and oil production levels for the past 46 years in Trapp field, Kansas.
1.2. Literature Review. A typical petroleum field might operate over a few decades. Its state changes continually, and hence, strictly speaking, rigorous subsurface models are required to capture its complex dynamics. However, many studies in the literature have severely approximated the subsurface behavior while claiming to place wells optimally. Such studies can be classified as surface infrastructure planning studies (see ref 6). They involve planning of the installation/ operation of manifolds, processing centers, and their allocations and interconnections. These studies typically postulate a predetermined list of potential locations for various installations, and address well selection, drilling, production planning, and capacity expansion. Beckner and Song7 reported high computational costs for sequencing drilling operations and suggested reformulation to exploit model structure rather than directly using commercial solvers. Iyer et al.8 developed a mixed integer linear programming (MILP) model with several simplifying assumptions. They assumed a uniform reservoir pressure, noninteracting wells, linear pressure drops with flows,
cases, planning and scheduling are crucial and must consider subsurface dynamics to yield maximum benefit. Thus, field development must continue throughout a field’s life span, and the identification, sequencing, and scheduling of various drilling, installation, and operation activities have a huge impact on maximizing the oil recovery from a field. Furthermore, these decisions must be made with limited resources, as budgets, new drilling rigs, and workover rigs are always limited and usually far fewer than the targeted wells. In addition, the petrophysical data on a field’s subsurface formations represent a major source of uncertainty for these decisions. The huge reservoir dimensions and costly and limited samplings limit data accuracy significantly. Although the uncertainty decreases as oil production progresses, much depends on the initial and continual development activities, which must be planned and executed well over the project life. Tavallali et al.5 have written an in-depth review and overview of the challenges in the optimal exploitation of oil fields. 979
DOI: 10.1021/acs.iecr.5b03326 Ind. Eng. Chem. Res. 2016, 55, 978−994
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Industrial & Engineering Chemistry Research
poral nonconvex MINLP models and developed an effective modification of the outer approximation algorithm for its solution. However, in both works, we assumed all wells to open production at time zero. From the above discussion, the current major gaps in the literature are as follows: (1) The subsurface dynamics and often the multiphase flow to the surface are either ignored or severely approximated in most studies. As a result, their predictions of water/oil fronts are not accurate. (2) When the subsurface dynamics is considered using a simulation−optimization approach, the orders of drilling and/or installations are not addressed, or the interactions between the subsurface and surface network are not considered. (3) Some studies use a predetermined list of potential locations/connections and then try to determine the orders of drillings/installations. However, such a list is based on either heuristics7,21 or severe approximations.12 In this study, we extend our previous work1 to include the scheduling of drillings, surface network installations, and capacity expansions. Specifically, we consider the placement, capacity, allocation, and timings of network elements such as wells, manifolds, processing centers, and connecting transfer lines. This study offers several advances compared to our previous work as follows: (1) Our previous study1 assumed that all drillings and installations occurred at time zero. In this work, we allow them to occur at any time and also schedule them. (2) We allow the possibility of outsourcing oil from other fields when the field under study cannot meet the market demand and/or production target. (3) As drilling rigs are generally far fewer than drilling targets, rig availability is an important constraint, which we consider in this work. (4) In contrast to our previous study,1 the use of an existing producing element can be discontinued or a shut-in well can be reopened for production. (5) We present another enhanced version of our modified outer approximation/equality relaxation/augmented penalty (OA/ER/AP) algorithm,1 and we again demonstrate the effectiveness of local searches. We begin with a precise problem statement, followed by our model. Then, we develop a solution strategy and evaluate its performance with a case study.
a constant productivity index for each well throughout the planning horizon, and no injection operations. They expressed reservoir pressure and gas-to-oil ratio (GOR) as functions of cumulative oil production and used piecewise linear approximations for their profiles. Such an approach ignores the effects of spatial well placements. Several subsequent studies simply built on the work of Iyer et al.8 Aseeri et al.9 extended its deterministic model to a stochastic model; however, they faced serious dimensionality issues, which they resolved by using a sampling average algorithm for stochastic parameters such as oil price and productivity index. van den Heever and Grossmann10 fitted an exponential function to describe reservoir pressure versus cumulative oil flow rate and quadratic functions to describe cumulative gas production and GOR versus cumulative oil flow rates. Cavalho and Pinto11 assumed a linear pressure decline with oil removal to define a maximum flow rate for each well and devised a multiperiod MILP model. They used the algorithm of Iyer et al.8 and addressed well-platform assignments in the master problem and assignment timings in the subproblems. Such two-stage approaches can be seen elsewhere as well. Barnes et al.12 suggested an MILP followed by an mixed integer nonlinear programming (MINLP) to address the design and operation of oil and gas fields. Whereas the MILP makes the design decisions (locations and capacities of platforms and drilling centers), the MINLP makes the well operation decisions. Similarly to Iyer et al.,8 they assumed noninteracting wells with constant productivity indices. In a subsequent study, Gupta and Grossman13 developed a nonconvex MINLP model for a deterministic multifield problem and later reformulated it as an MILP. Following previous works,8,10 they employed regression models to capture the field dynamics related to the maximum oil flow rate, water-to-oil ratio (WOR), and GOR versus fractional oil recovery. Although an extensive, detailed, and important contribution, it involved limiting assumptions such as identical well performances in each reservoir. Another class of studies comes mostly from the petroleum engineering community. They typically simulate the subsurface using a reservoir simulator by assuming that all wells are drilled and begin production at the start of the planning horizon.14−18 We19,20 previously reviewed these studies. ECLIPSE,21 a commercial reservoir simulator, provides an option of “drilling queue”, which is a list of predefined wells to be deployed sequentially based on some priority. The drilling is activated whenever a production target is not met. Güyagüler22 suggested solving an ordering problem for this queue whenever the queue is called. He viewed this ordering problem as a traveling salesperson problem and solved it with a genetic algorithm. He also reported high computational costs despite ignoring surface network connections and changes. In a recent study,23 we showed that an advanced optimization-based approach can outperform a predefined drilling list. In our recent studies, we have attempted to change the existing paradigm, by combining the two aforementioned categories of work, and have made some progress toward integrated reservoir management. In ref 19, we addressed well placement and production planning in a single reservoir with a rectangular shape and employed a rigorous reservoir model with multiphase flow up to the wellheads. In ref 1, we extended this approach to multireservoir oil fields with irregular shapes and completed the connection to surface facilities by addressing surface-element installations and allocations. We formulated these inherently dynamic optimization problems as spatiotem-
2. PROBLEM STATEMENT Consider a new/existing oil and gas field (Figure 1) with multiple reservoirs driven by water injection and/or primary expansion. Each reservoir has three fluid phases: oil, water, and gas. The field has elements such as producer wells, injector wells, shared oil manifolds, shared water manifolds, central oil processing centers, and central water processing units. We would like to boost the production in such a field through some or all of the following tasks: (1) drilling new vertical producer wells, (2) installing new manifolds and/or processing centers along with appropriate new connections, (3) shutting down or starting up existing field elements (4) managing all throughputs (wells, manifolds, transfer lines, and processing centers) during the planning horizon, and (5) expanding surface center capacities. Here, we consider “drilling” as “installation” of a well. In addition to the field under study, the oil company has 980
DOI: 10.1021/acs.iecr.5b03326 Ind. Eng. Chem. Res. 2016, 55, 978−994
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Figure 3. Schematic diagram of a hydrocarbon field, where r1, r2, and r3 are three different reservoirs in the same field (with possibly different production mechanisms). The thick blue and black lines depict the injector and producer wells, respectively.
other oil fields that can supply oil at some fixed price. Although we do account for drilling-rig availability, we do not address rig routing and scheduling. Then, our problem can be stated as follows: Given. (1) Geological and petrophysical data (e.g., permeability, porosity, field structure, compressibility factors, viscosity, initial saturation, and pressure maps) of the field under study and the maximum oil outsourcing capacity from other fields (2) Structural data (e.g., surface connections, well diameters, lengths, and roughness) (3) Operational data and their limits (allowable limits on manifold or bottom hole pressures, inlet pressures at the separation centers, maximum water cut, processing capacities of the manifolds and centers, production horizon, oil demand forecast) (4) Economic data (e.g., fluid production/injection costs, drilling and installation expenses, and costs of outsourcing oil from other fields), Determine. (1) Numbers, locations, times, and order of installation of new elements (with required flow lines and valves) and their throughputs (2) New surface connections (well-to-manifold, well-tosurface-center, and manifold-to-surface-center), along with their order and schedule (3) Incremental capacity installations/expansions of new/old centers and, hence, the total processing capacity of the field (4) Operational status of all field elements
(5) Dynamic pressure and throughput profiles at all network elements (6) Dynamic pressure and saturation profiles (waterfront locations) for each reservoir (7) Oil outsourcing plans (if any) Maximizing. Net present value (NPV) of the oil/gas exploitation project over the planning horizon. Assuming. (1) All reservoirs are horizontal and planar, but disconnected (2) All reservoirs are undersaturated (i.e., pressure exceeds bubble-point pressure) (3) All reservoirs give the same fluid product, and all three phases (oil, water, and gas) are compressible (capillary pressure is negligible in all reservoirs) (4) All wells (producer and injection) are vertical (although a well can pass through multiple reservoirs, it can access only one reservoir at a time) (5) Manifold capacities remain constant over time (6) Installation of an element takes no longer than one time period defined in our multiperiod model (7) No element can be installed in the last period of the planning horizon (8) Each well (existing or potential) is preallocated to some manifolds/centers (existing or potential) based on some criteria such as distance, from which the best allocations will be selected (this condition can be relaxed, but will increase computation time8) Allowing. (1) A producer wellhead can be connected to one or more manifolds or oil processing centers 981
DOI: 10.1021/acs.iecr.5b03326 Ind. Eng. Chem. Res. 2016, 55, 978−994
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Industrial & Engineering Chemistry Research (2) Central water processing units can supply water to injector wellheads directly or by shared manifolds (3) Existing manifolds and centers can make/receive new connections (4) Processing center capacities can vary with time, as more separators can be installed (5) Reservoirs can have arbitrary shapes, and their surface elevations can vary from point to point; thus, they can overlap vertically (6) Any network connection (well-to-manifold and manifold-to-center) can be discontinued or revived at any time (7) Any well can be shut-in or reopened at any time Respecting. (1) Once a well hits the water-cut limit, it is shut in
Cm = {c|manifold m is or can be connected to center c} 1 ≤ r ≤ R , n ∈ IPr
We use t = 0 to refer to the state before time zero. In what follows, we assume that, unless stated otherwise, all variables and constraints indexed by t, r, m, and c are to be written for all their valid values: 1 ≤ t ≤ T, 1 ≤ r < R, 1 ≤ m < M, and 1 ≤ c < C. 3.1. Dynamics. We discussed and modeled the multiphase flow in the subsurface porous media of a reservoir and through the wells, pipes, manifolds and centers in our previous work.1 The model equations can be represented as follows:
g t(Xt , Y t , Bt ) = 0
(1)
ht (Xt , Y t , Bt ) ≤ 0
(2)
t
where X denotes various continuous variables (including saturation, pressure, and phase mobilities at each reservoir cell; pressure at well bore, wellhead, manifold, and center; flow rate through each element), Yt represents various binary variables, and Bt denotes the various geological, operational, thermodynamic, and economic parameters. Because the details of gt and ht are in our recent article,1 we avoid their repetition here. However, to keep this article self-sufficient, we include their final mathematical expressions in the Appendix. In the remaining sections, we discuss the new and modified equations. For the notation, please refer to the Nomenclature section. The reader might wish to review the Appendix before continuing further. 3.2. Installation and Operation Decisions. We define a binary variable to decide whether an element should be used in a period t (1 ≤ t ≤ T)
3. FIELD MODELING Figure 3 presents a schematic of a field. Assume that the field has R reservoirs (r = 1, 2, ..., R), C existing/potential processing centers (c = 1, 2, ..., C), and M existing/potential manifolds (m = 1, 2, ..., M). Of these, we let the first Ce processing centers (1 ≤ c ≤ Ce) and the first Me manifolds (1 ≤ m ≤ Me) exist already at time zero. Following Tavallali et al.,19 we discretize both the time and space coordinates. We divide the planning horizon H into T periods of arbitrary lengths Δht (t = 1, 2, ..., T) and use t = 0 to denote the zero time. We bound each reservoir r using the tightest possible rectangle made up of Ir cells of arbitrary lengths Δxir (i = 1, 2, ..., Ir) in the x direction and Jr cells of arbitrary lengths Δyjr (j = 1, 2, ..., Jr) in the y direction. Then, we index these Ir × Jr cells in reservoir r by a single-dimension index n = i + (j − 1)Ir and define the following sets: Interior Cells:
⎧1, if center c is in use during period t ustc = ⎨ ⎩ 0, otherwise
(3)
⎧1, if manifold m is in use during period t zstm = ⎨ ⎩ 0, otherwise
(4)
⎪
⎪
IPr = {n|cell n is inside reservoir r }
⎪
Interior Cells in the x Direction:
⎪
IX r = {n|n ∈ IPr , (n + 1) ∈ IPr , and i < Ir }
Interior Cells in the y Direction:
zustmc
IYr = {n|n ∈ IPr , (n + Ir ) ∈ IPr , and j < Jr }
⎧1, if the connection between manifold m ⎪ = ⎨ and center c is in use during period t ⎪ ⎩ 0, otherwise
c ∈ Cm (5)
Existing/Potential Wells: ⎧1, if the well at cell n of reservoir r is ⎪ ystnr = ⎨ in use during period t ⎪ ⎩ 0, otherwise
PWr = {n|n ∈ IPr is an existing producer well} IWr = {n|n ∈ IPr is an existing injector well}
n ∈ IPr
NWr = {n|n ∈ IPr is a potential location for a new producer well}
(6)
= IPr − PWr − IWr − {n ∈ IPr |a new producer well is yzstnrm
infeasible at cell n}
Existing/Potential Allocations:
⎧1, if the connection between the well at cell n of ⎪ = ⎨ reservoir r and manifold m is in use during period t ⎪ ⎩ 0, otherwise
n ∈ IPr , m ∈ M nr
M nr = {m|cell n of reservoir r is or can be connected to manifold m} 1 ≤ r ≤ R , n ∈ IPr
yustnrc
Cnr = {c|cell n of reservoir r is or can be connected to center c} 1 ≤ r ≤ R , n ∈ IPr
⎧1, if the connection between the well at cell n of ⎪ = ⎨ reservoir r and center c is in use during period t ⎪ ⎩ 0, otherwise
n ∈ IPr , c ∈ Cnr 982
(7)
(8) DOI: 10.1021/acs.iecr.5b03326 Ind. Eng. Chem. Res. 2016, 55, 978−994
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Industrial & Engineering Chemistry Research +1 yu tnrc ≥ yu tnrc −
Because each installation activity requires one period, an element that does not exist at time zero cannot be used in the first period. Therefore, we set us1c = zs1m = zus1mc = ys1nr = yzs1nrm = yus1nrc = 0 for all those elements that do not already exist at time zero. For these potential installations, we define the following 0−1 continuous variable for each period t (1 ≤ t < T) ⎧1, if center c is installed in period t uct = ⎨ ⎩ 0, otherwise ⎧1, if manifold m is installed in period t zmt = ⎨ ⎩ 0, otherwise
us1c
zu tmc
⎧1, if the transfer line from manifold m to ⎪ = ⎨ center c is installed in period t ⎪ ⎩ 0, otherwise
(9)
(10)
c ∈ Cm
yu tnrc
MCmUzstm ≥
c ∈ Cm
ynrt ≥ ystnr+ 1 −
∑ ystnr′
+1 yz tnrm ≥ yz tnrm −
′ ∑ yz tnrm t ′≤ t
(24)
zustmc+ ∑
∑
∑
yustnrc ≥ ustc
r = 1 n ∈ IPr ∋ c ∈ Cnrc
(25)
Flow Management. Equations 22−25 also enforce that, if an element is active (inactive) in a period, then at least one (all) element(s) must be connected to it (inactive) δnrqnrt ≤ qnrt,U ystnr
n ∈ IPr
(26)
QM tm ≤ QM tm,Uzstm
(27)
QCtc ≤ QCtc ,Uustc
(28)
qmctmc ≤ QM tm,Uzustmc
c ∈ Cm
,U qwm tnrm ≤ qwm tnrm yzstnrm
≤
qtnr,
,U qwc tnrc yustnrc
QMtm,
(29)
n ∈ IPr , m ∈ M nr
n ∈ IPr , c ∈ Cnr
(30) (31)
QCtc,
where and are the total liquid (oil + water) flows through the wells, manifolds, and centers, respectively; qmctmc is the total liquid flow between manifold m and center c; and qwmtnrm (qwctnrc) is the total liquid flow between well nr and t,U t,U t,U manifold m (center c). Similarly, qt,U nr , QMm , QCc , qmcmc , t,U t,U qwmnrm , and qwcnrc are their respective upper bounds. Additionally, δnr = −1 for nr ∈ IWr and 1 otherwise. Any productive well should produce at least a minimum cumulative oil flow (qLo,nr). In addition, we demand that the total flow through a newly installed element must exceed some minimum cumulative liquid flow (QMLm and QCLc )
(17)
n ∈ IPr (18)
t ′≤ t
zustmc ≥ zstm
m ∈∋ c ∈ Cm
t t ′= 1
(23)
R
(16)
∑ zustmc′
yzstnrm ≥ zstm
∑
∑
CMW cUustc ≥
t
zu tmc ≥ zustmc+ 1 −
∑
c ∈ Cm
(15)
t ′= 1
n ∈ IPr
c ∈ Cnr
r = 1 n ∈ IPr ∋ m ∈ M nr
qwc tnrc
∑ zstm′
yustnrc ≥ ystnr
∑
R
MW mUzstm ≥
t
zmt ≥ zstm+ 1 −
yzstnrm+
∑
(22)
Equations 9−14 are defined for potential new elements only and not those that already exist at time zero. Because no element can be installed in the last period, the above variables are also not defined for the last period. Now, we can infer them based on when they are used for the first time. For instance, if a new element is used during period (t + 1) for the first time, then it must have been installed in period t and must not have been used during or before period t. Then, for new elements, we combine the above ideas to write (1 ≤ t < T)
t ′= 1
(21)
n ∈ IPr
(14)
∑ ustc′
yus1nrc
1≤t
