ТЕОРЕТИЧЕСКИЕ ОСНОВЫ ХИМИЧЕСКОЙ ТЕХНОЛОГИИ, 2013, том 47, № 4, с. 464-472
УДК 66.011
INTEGRATED GAS LIFT SYSTEM OPTIMIZATION © 2013 г. H. Rasouli", F. Rashidi", B. Karimi4
aFaculty of Chemical Engineering, Amirkabir University of Technology, Tehran, Iran
hrasouli@aut.ac.ir rashidi@aut.ac.ir
bFaculty of Industrial Engineering, Amirkabir University of Technology, Tehran, Iran
b.karimi@aut.ac.ir Received 22.08.2011
An intelligent genetic algorithm has been developed to simultaneously optimize all effective factors, namely, gas injection rate, injection depth and tubing diameter towards the maximum oil production rate with the water cut and injection pressure as the restrictions. The results were field tested in three wells in three different fields located in southern Iran. The field data verified the accuracy of the used model. There was a notable production increment compared to the master development plan of the fields.
DOI: 10.7868/S0040357113040106
INTRODUCTION
In many wells the natural energy associated with oil will not produce a sufficient pressure differential between the reservoir and the wellbore to cause the well to flow into the production facilities at the surface. In some wells also, natural energy will not drive oil to the surface in sufficient volume. The reservoir's natural energy must then be supplemented by some form of artificial lift. There are four basic ways of producing an oil well by artificial lift. These are gas lift, sucker rod pumping, electric submersible pumping and subsurface hydraulic pumping [1]. Gas lift is a widely used method among artificial lift methods, in which gas is injected into the producing well providing energy to the flow. Continuous gas lift being cost effective, easy to implement, very effective in a wide range of operating conditions and requiring less maintenance in comparison to the other alternatives, is one of the most typical forms of artificial lift in oil production [2].
It is a usual technique where there are enough natural gas resources [3]. The basic principle is decreasing the pressure gradient in the liquid by means of the injected gas. The resulting mixture becomes less heavy than the original oil so that it eventually starts flowing (see Fig. 1 [4]).
In gas lift operations, three problems are the most important ones. The first one is finding the optimal position for injection point and the other is estimating the optimal gas injection rate. These parameters are interrelated, the more the rate of gas injection the deeper could be the injection point. In other words, the deeper the injection point the more gas volumes would be needed. The third one is finding the optimal tubing (string) size. The major problem in gas lift design is the optimization. In the present study a new method is devised for optimization of continuous gas
lift with an unlimited supply subject to gas injection pressure and water cut.
GAS LIFT OPTIMIZATION
Gas being of a limited or unlimited supply completely changes the optimum gas lift system design and operation.
Gas lift optimization with limited gas supply
(GOPLGS). The limited supply problem where the gas allocation is the focal point has been the subject of many researches [5—18]. In such a study the researcher is needless of the physics of the well and the reser-
Gas intel
Unloading valves
Operating valve
Ш
о о
Ш
щ
о
с
о
о о
о
Ô-Q3
►Production
Fig. 1. Schematic of a valve position in gas lift well.
voir, and the solution is obtained through several mathematical approaches.
Gas lift optimization with unlimited gas supply (GOPULGS). In the present study an unlimited gas supply problem is considered and this optimization is done with three variables and two restrictions. Conventionally, the oil production rate is optimized based on the sensitivity analysis which is also the only standard method in use. This sole approach suffers from the following shortcomings.
1. Fundamentally this method does not perform optimization and runs a sensitivity analysis in fact. Sensitivity analysis is the next step to optimization and should not be used instead.
2. Sensitivity analysis also is run in a single variable fashion and not multi-variable. This means that when one variable is being varied the others are kept constant and are in the queue for being analyzed for sensitivity.
3. In this method, the constraints cannot be considered and therefore the obtained results are not of acceptable accuracy.
GOPUGS complexity. An essential question may bear in mind about the reason why this optimization problem has not been yet attacked though there have been the three aforementioned weaknesses. And the answer lies in the complexity of multiphase flow problem. The core of nodal analysis is based on the inflow performance relationship (IPR) that formulates the reservoir response and tubing performance curve (TPC) that defines well performance, the intersection being the operation point as shown in Fig. 2.
PROBLEM FORMULATION AND MODELING
In this study it is needed to model the reservoir performance and also the well performance that is done by nodal analysis. These should then be coupled with the appropriate optimization algorithm that is the genetic algorithm here. These subjects are discussed in the next section.
Reservoir performance calculation. By reservoir performance we mean the ability to transfer fluids from the bearing rock to the wellbore given a pressure gradient. This ability is shown by the productivity index (PI). PI (J) is equal to the ratio of oil production rate and pressure difference between the reservoir and the bottom hole flowing pressure:
Pwf, МРа
j==
Qo
Qo = J(Pr - Pwf )•
(1)
A
R, m3/h
Fig. 2. Relation between (1) IPR and (2) TPC (nodal analysis): A — operating point.
2. Two phase flow (PR < Pb). The most commonly used equation in this case is the Vogel's equation [19]:
Qo
= 1 - 0.2pwf - 0.81 pwf
Pr
Pr
(3)
Ap Pr - Pwf Whether the flow in the reservoir is single phase or two-phase the above equation is expanded as one of the following.
1. Single phase flow (PR> Pb). In this case, we have 1866.37k0h , x
q° = »—f, / / u 1 (PR - Pwf). (2)
BoV-o [ln(rc/rw) + s] This equation is obtained from the Darcy's law and is for the steady state conditions.
q = 1866.31k0hpR [1 - 0.2(pwf/pR] - 0.8(pwf ¡pR)
0 BoV0 [In(rjrw) + s]
The above equations are based on the Darcy's law and as indicated in them the reservoir potential depends on many parameters most of which are intrinsically invariant. The only parameter that can be altered is the bottom-hole flowing pressure (pwf). As pvlf is decreased the pressure difference between the reservoir and the well-bore increases and the oil production rate is enhanced. In gas lift operation pf decreases and the oil production rate increases as a result. The curve that is obtained from these equations is known as the IPR and a typical IPR curve can be seen in Fig. 2.
Well performance calculation. This topic discusses the ability of the well to lift the fluids from bottom hole to the surface facilities. This is also entitled as vertical lift performance or tubing performance curve. This complicates the problem as the flow in the well is multiphase. Multiphase flow can be from the bottom hole or can be developed in the well.
In the multiphase flow problem we are not faced with an explicit and exact function for which a classical approach suits. The variables are some of integer and discrete nature and relationships and restrictions also are nonlinear. Metaheuristic methods are perhaps the best suitable way outs currently available and this superiority comes from their independence up on explicit and derivability of the function.
As the fluid travels upward in the well its pressure drops and the pressure drop for multiphase flows is difficult somehow. The bottom hole flowing pressure is usually unknown and should be guessed. Based on this initial guess and by a selected pressure drop equation
Fig. 3. Procedure to model pressure and temperature distribution in wellbore.
we can obtain a wellhead pressure and compare it with the real value. The initial guess can then be corrected to improve calculations:
Pwh = Pwf = Pwf - z {d^ > (5)
Ap = kPacc + ^Pfric + APhyd. (6)
As indicated in the formula, the pressure drop is composed ofthree terms: acceleration, friction, hydrostatic.
In the present study the Ansari model [20, 21] is used and the following steps are considered:
1. Initially the well is segmented (segment lengths are usually 61 m).
2. The bottom hole pressure is guessed for a given oil rate.
3. The flow regime prediction and pressure drop calculations are started from the lowermost segments.
4. The outlet pressure of the segment is calculated, this pressure is the inlet pressure of the next segment. The same is for temperature.
5. This is repeated for all segments till the uppermost one is reached. The obtained wellhead pressure is compared with its known value and the initial guess is corrected.
6. The above steps are done for 10 oil production rates. These rates are usually taken between 0.05 to
°.95 of Qo max.
The procedure to model pressure and temperature distribution in wellbore is shown in Fig. 3.
Gas lift formulation. Gas lift modeling is the same as for natural flow condition with this difference that
from a given depth upwards the gas—oil ratio (GOR) increases abruptly. This lowers the oil density and the oil column weight. The pressure drop equations will change to the followings:
Pwh = Pwf - Ap = Pwf - z fj^j =
= Vp - ( - g z -.
dp j
dZj Zn
(7)
7
1Щ
For calculation of injection pressure that is one of our constraints the Economides equation [22]:
pinj = Pf 0010287y j (8)
Elements and parameters of gas lift system are shown in Fig. 4.
Genetic algorithm structure. A genetic algorithm (GA) is a search technique used in computing to find exact or approximate solutions to optimization and search problems
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