(185aa) Development of Artificial Lift Infrastructure Plan Under Endogenous and Exogenous Uncertainties

Development of
Artificial Lift Infrastructure Plan under Endogenous and Exogenous
Uncertainties

Zuo Zeng,
Selen Cremaschi

Department of Chemical Engineering,
Auburn University, Auburn, AL 36849, USA

selen-cremaschi@auburn.edu

Shale
gas has become a significant source of natural gas in the United States. The
U.S. Energy Information Administration (EIA) estimates that in 2017, shale gas
provided over 60% of U.S. dry natural gas production compared to its 1% share
in 2000 [1]. Because large amounts of fluids are injected to the shale
formation during the fracturing process, shale gas wells often require deliquification to unload the well relatively quickly,
generally within their first or second year of production [2]. Artificial lift
methods (ALMs) are used in horizontal shale-gas-producing wells to lift the
accumulated fluids in the well and to help sustain well performance. Artificial lift methods can
be divided into two types: passive and active. Passive systems, such as
velocity strings, plunger lift and foam lift, mainly naturally carry and remove
liquid from the wellbore because sufficient energy remains in the reservoir.
The active systems, such as sucker rod pump, well head compressors and gas lift,
add energy to the system, and are generally implemented once the reservoir
pressure drops below the wellhead pressure [3].

The
artificial lift infrastructure plan (ALIP) includes which ALM should be
installed, when exactly the selected ALM should be installed and how long the
installed ALM should be operated to maximize the net present value (NPV) of the
well. Selecting
an appropriate ALM for gas well deliquification
mainly depends on the well geometry, operating conditions, and well
performance. Constructing an artificial
lift infrastructure plan is complicated due to uncertainties in economic
factors, such as natural gas price, and in production rates of the well.

In this work, we present a
multistage stochastic programming model to develop artificial
lift infrastructure plans (ALIPs) for shale-gas producing horizontal wells. The model discretize the planning horizon into
equal time periods (corresponding to one month) t = 1, 2, 3…T, where period t
starts at time t-1 and ends at time t. The decision variables are w_i,p,s and z_i,t,s, which track the installation (p ϵ T) and removal t ϵ T time periods of ALM i ϵ I under scenario s ϵ S, respectively. One more binary
variable, y_i,t,p,s,
is introduced, which is equal to one if ALM i is installed on period p and uninstalled on period t in scenario s. The sequencing constraints ensure that each ALM is installed and uninstalled at most once,
only one ALM is installed and uninstalled at any given month, and each ALM is uninstalled
only after its installation time.  Each ALM has defined design and operational limitations such as the ones
specified in the Artificial Lift R&D Council guidelines [5] and in typical
attribute tables [6]. These limitations are incorporated as technical limitation
constraints in the model.

The model incorporates
the impact of exogenous natural gas price uncertainty, which is independent of
decisions, and of endogenous uncertainty associated with the production rate of
the well, which depends on the selected ALM. We assume that natural gas price follows a multiplicative binomial process over
discrete periods [7], and that its rate of change (ROC) has two possible
outcomes {H^P, L^P} with equal probabilities. Figure 1 represents the
scenario tree for natural gas prices. The natural gas price at initial stage is
given by the parameter P₁. We assume that the price uncertainty is
realized every four months, resulting in a total of st = T/4 stages for the exogenous uncertain parameter realizations,
where T is length of the planning
horizon in months. Further, we assume that the two outcomes of ROC H^P
and L^P are constant throughout the planning horizon and
equal to each other. We define ϴ_st as the random variable associated with
natural gas price at stage st ϵ T^’=
{1,2,…,T/4}.

Figure 1: Natural gas price scenario tree

The production rate of a horizontal well is described using a hyperbolic
curve [5]. At first, the well is producing naturally, represented with the
solid curve in Figure 2. After liquid loading, the production from the well
becomes unstable, and is halted (t = p –
1) unless an appropriate ALM is installed to stabilize it. Dashed line in
Figure 2 represents a potential production rate after ALM i is installed at time p. We define the ratio of the production
rate at time p (with ALM i installed) to
the production rate at p-1 (the
production right before ALM i installation) as the flowrate change ratio, Qrc_i,
of ALM i.

Figure 2. Production decline curve when ALM i is installed.

The flowrate change ratio is the endogenous uncertain parameter of the
model. Let ξ_i represent the
random variable associated with the endogenous uncertain parameter Qrc_i.
We assume that the random variable ξ_i has two outcomes with equal
probabilities, i.e., Ω_i = {H^Qcr, L^Qcr}. The full scenario set for the MSSP model is constructed
using the Cartesian product of outcomes of endogenous and exogenous uncertain
parameters, and it is defined as S:={×_{st ϵ
T’}ϴ_st}×{×_iϵIξ_i}.

We apply the proposed MSSP
model to develop ALIPs for two wells in Woodford shale field. Well I has high average production conditions with a gas rate of
800 thousand standard cubic feet per day (Mscf/D) and
a liquid rate of 520 BPD. Well II has a low liquid flowrate and a gas
production rate of 200 Mscf/D. We consider 12, 16, 20,
and 24-month planning horizons for both wells. We first solve the deterministic
versions of the problems constructed using the expected values of all uncertain
parameters. The optimal solution of Well I recommends Sucker Rod Pump (SRP)
method for all planning horizons. For Well II, which has a low liquid flowrate,
the optimal ALM is SRP if the planning horizon is 12, 16 and 20 months, and Well
Head Compression (WHC) for the planning horizon of 24 months. The optimal
solutions to the deterministic problems reveal that different ALMs may be installed
for different planning horizons indicating a trade-off between flowrate change
ratios and low operating costs among ALMs. The MSSP models have 64, 128, 256
and 516 scenarios for 12, 16, 20, and 24-month planning horizons. The
deterministic equivalent of the MSSP models (which are mixed integer linear
programming models) cannot be solved to optimality for planning horizon longer
than 12 months within 36000 CPUs. In 12-month planning horizon, the optimal
solution for Well I recommends to install SRP at the beginning and install the
Electrical Submersible Pump (ESP) at month 7 for all scenarios. To obtain
feasible solutions for all instances, we apply the generalized knapsack problem based decomposition algorithm (GKDA) [9]. The GKDA
decomposes both time periods and scenarios of the original MSSP into a series
of knapsack sub-problems and solves these problems at appropriate decision
points of the planning horizon. The GKDA yields feasible
solutions within 60 CPUs for all instances. For example, for the 12-month
planning horizon, the GKDA selects SRP at initial time period and selects ESP
at month 7, which is the optimal solution of the MSSP.

References

1.      
https://www.eia.gov/tools/faqs/faq.php?id=907&t=8.

2.      
Bondurant, A. B., Dotson, B. D., and Oyewole, P. O. (2007). “Getting the Last Gasp: Deliquification of Challenging Gas Wells,” SPE paper 11651
presented at The International Petroleum Technology Conference, Dubai.

3.      
Oyewole, P.
O., Lea, J. F. (2008). Artificial-lift selection strategy for the life of a gas
well with some liquid production. SPE Annual Technical Conference and
Exhibition held in Denver

4.      
Zeng, Z., & Cremaschi,
S. (2017). Artificial lift infrastructure planning for shale gas producing
horizontal wells. Proceedings of the FOCAPO/CPC, Tuscan, AZ, USA, 8-12.

5.      
http://beta.alrdc.com/recommendations/gas%20well%20deliquification/artificial%20lift%20selection%20---%20new%20version.htm

6.      
Weatherford. (2013). Introduction to Artificial
Lift Systems.
<http://www.alrdc.com/recommendations/Gas%20Well%20Deliquification/artifi...
(accessed 10 April 2018.)

7.      
Cox, J. C., Ross, S. A., & Rubinstein, M.
(1979). Option pricing: A simplified approach. Journal of financial Economics,
7(3), 229-263.

8.      
M. J. Fetkovich, E.
J. Fetkovich, and M. D. Fetkovich,
1996, Useful Concepts for Decline Curve Forecasting, Reserve Estimation, and
Analysis. Society of Petroleum Engineers 11(01): 13-22.

9.      
Zeng, Z., & Cremaschi,
S. (2018). A generalized knapsack-problem based decomposition heuristic for
solving multistage stochastic programs with endogenous and/or exogenous
uncertainties.  Industrial & Engineering Chemistry Research (In
review).