CC BY
1
основной раздел
УДК 1082
Niyazova N.
Assistant Ozbekistan, Namangan Namangan Engineering-Pedagogical Institute CREATION OF MATHEMATICAL MODELS FOR THE MANAGEMENT OF DEVELOPMENT OF GAS FIELDS IN THE WATER PRESSURE
ABSTRACT
This article discusses the management of complex processes, gas and water filtration process as the object of the research and development of gas fields of management systems of technological processes.
The boundary layers of gas with water bodies, water filtration properties are studied and the general appearance of the mathematical model of gas pressure is given.
Keywords: oil, gas, mining, filtration, process, water, optimal management, well.
INTRODUCTION
For theoretical analyzing the development of oil and gas fields and using in practice, solving the issue with the appropriate boundary conditions and the solution of parabolic differential equations are sufficient. To check the created model and algorithm of solving, the single measured filter problems should be done, results taken and it must be analyzed.
In fact, the filter processes in the layer of producing gas fields take place in three dimensional (3D) Euclid space. But to consider the three dimensional filtration process we need to have extremely huge geological-physical data. In order to solve the tasks of 3D filtration in taking available information concerning geological-geophysical sights cause complex problems. During conducting research filtration problems were solved for one and two D cases, checked according to special testing and also numerical results are appropriate in terms of physics were systematically analyzed. In experiment 2D cases are often applied. But today using the modern computers to solve this kind of problems enable people who are working in this field.
Optimum management of developing process of oil and gas fields is based on mathematic models of expressing the hydro-dynamic process in the following layer. Therefore methods of optimum management depend on improving calculating methods and analyses. Giving the concrete mathematical decision of the studying object and solving task of optimum management can create advantage in optimizing the work of technological object in a higher level and all recourses of a managing system. A criterion for the selection of the system dealing with the complex issues and the complexity of solutions requires
research. Currently, the process for the management of a very large number of mathematical models, methods, algorithms and software, which are among the many objects, including oil and gas deposits are in use. The choice of mathematical models for the management of the process there are a lot of requirements, as follows.
The chosen model must represent all of the same features of the object of investigation: The distribution of pressure in the amount of gas production, gas-water boundary conditions, the level of gas saturation and so on. The selected model should have, from the mathematical point of view, to be correct and should have a clear physical meaning. The model parameters and functional relationships should not be related to the model.
Processes involved in the management of the mathematical model of the physical process, parameters should not be abandoned. Practice shows how complex the system, the process for the selected model will satisfy all the requirements of the above complex.
The staff working in this field should take the following information into consideration:
> The theory of the development of oil and gas deposits
> Layer physics
> Hydrodynamics
> Geology and geophysics
> Mathematical modeling
> New modern computer technologies
> Organization and management of development
Gas facilities design and management process for mathematical modeling of modern methods that could constitute, without full knowledge of all the properties of the object that is not enough and does not give effective results on the basis of false information.
In practical terms the only way to determine the successes and shortcomings of the voluntary development technology is the mathematical modeling and computational experiment. And this saves too much time and material savings, and can be the basis for the impossible economically experiments.
Putting the issue forward: For example, having a height h, area G = G1+G2 must be bounded by the contour of ri. G1 sphere t = 0 in the starting time is bounded with the continuous curve line G1, starting is saturated with dynamic viscosity coefficient bodily fluid extraction. From the layer (Xi YJ), with the help of coordinated wells Qi (t) volume debit amount of gas must be mined. The process of development of the gas field under the water pressure must be managed in such a way that Qi (t)due to choosing the debits and managing some of the parameters, all ri border must be provided close to the wells in a flat slip.
/о о о о О О о
о о о о /, к;о о о о
V___
S - borderline of the wells; l3 - Г2 - limit of normal; ri - move of borderline of gas and water;
r2 - outer line of aqueous layer; ri0 - initial position of the gas
dp0 and water borderline.
■ 2 = 0
Figure 1.5. Sceme for the 2-dimensional task of moving gas-water borderline.
Mathematical model of gas-water filtration technology process satisfies the following derivative differential equations in the parabolic type: in the gas sphere
8_
dx
ki(x,y)hl(x,y) 5Pl
2 Л
Mi
dx
+ ■
8_
dy
k(x,y)h(x,y) dPi
2
Mi
dy
dP
= 25(x, y)^i (x, y)hi (x, y) • —1 + Fi (x, y, t)
dt
( x y)e Gi
in the water sphere
A
dx
/k2(x,y)h2(x,y) dP2 ^ d r
M2
dx
+ ■
dy
k 2 ( x, y)h2( x y) ш dP
M2 dy
dP
= P (x,y)h2(x,y) •—^ + F2(x,y,t) dt
expresses by the following initial
Pi(x,y,0|t=o = P(x,y) e G1
P2(X, ^ t) t=0 = P2(X, y) e G2 ,
(x, y) e G2
(1)
(2)
boundary conditions.
(x, y) e Г2
dP I
— \r = 0
dl3
At the same time, the pressure prevailing in the border division and continuity of the flow
X, y, t) r + = P2( x, y, t) r _
Mi dl 2
k 2 dP2
Г+
M2 dl 2
ГГ
and also changing law of the shift of the border
д£2 к2{ху) дР2 _
_ ; i — i dt /л2 т( x, у)[<^( x, у) — &0ст (х, у)] di 2 ' 21t—0 0
2
Laws of the change according to time of the amount of gas mined from the wells
) = r k¿X, yMx, y) P^ d^ ds e S,
V) J Pam di 1 , V , y) !,
are given
Here k - conductivity coefficient, h - layer height? fi* - the aqueous layer of the pitch ratio, m - porosity ratio, /u1, ¡i2 - dynamic viscosity coefficient accordingly of gas and water, t- time, 5 - ratio of saturation with gas, Si -borderline of wells, li, 13 are norms conducted in accordance with the borders of ri and r2, 12 - moving gas-water border, G1, G2 - gas and water sector.
(1.1) - (1.2) taking all the conditions of the issues of the 2-D filtration in the equation into account (initial, border, internal etc.), we develop the algorithms in the next section, check according to the special testing, analyze the results systematically, and use for concrete objects.
According to the methods of the theory of optimal management layer to solve the issues of the development or to clarify the parameters of the algorithm is obtained as a result of compounding. More precisely, along with to find a proper solution for the 2-dimensional issue, it is necessary to find a solution to the limited issue as well. Eventually, this leads to an increase in the time machine, for example, when using thousands of elementary unit of net, it can get into a difficult situation.
Modern methods of optimal management of water pressure are to put the issue of the optimal management of the development of gas fields and allow them solving. At the same time, in many cases, the approximate approach must be felt, there will be no need to resolve the issue.
Mathematical modeling of process management - full form of the mathematical language, all terms are expressed in the form of boundaries (equations and inequalities). Solution for the status of these systems are optional available. Criterion known as the target is expressed in the form of the function. The aim of the solving the issue of optimizing is to mark the maximum or minimum value of the function, which is determined the boundaries of equation system. These mathematical methods allow putting the issue of optimal management in a simple form and solving them. Suppose, in order to solve the mathematical model of gas and liquid filtration, all of the information in the describing layer of the process of development of gas fields must be given. In terms of functional minimum, pressure of layer, permeability and porosity ratio must be required to determine.
T m n -, v , /
j(m, к, M,s, T, h)=JXZ ^,■, t)- ni,■, t)
0 >1 »=1
dt
. (1.4)
In this context, ^ and P and accordingly i - actual and calculated pressure in the well situated in r coordinate, n-, i- the number of measurements, calculated in the well.
Restrictions are taken into account in the field of parameters which can be used to improve the accuracy of identification and the concrete layer for changes in their range. Such limitations for deposit, Kern analysis, statistical data, and others are taken into account. As a result, the development of gas fields in the mathematical model of the process to identify the ratio of incoming leads to the issue of conditional optimization.
j(/)= "s j(x) * = (xi,X2,...,Xn )
(1.5)
Here, a sum of x , ^ in general meaning is given on the following system of equations and inequality:
a ^ x ^ b i=1,2,....n R (x )> 0 £ = 1,2,....s.
Q =
R.
s
(1.6)
is the functional limitation or dependencies between parameters.
t 'j i ' Xi — Xo — k, Xo — LL, X * — Xr — h • ¿i t
In our situation 1 ' 2 ' 3 4 ' 5 is that we can
*
accept the condition of the variable values, * is the optimization problems.
The optimal management, designing processes to develop oil and gas fields of research together, ought to give attention to all the variables in the system.
These parameters can be an opportunity to assess the key factors in the process, these factors: a change in pressure in the layer, the amount of gas being used and the number of wells identified, boundary conditions, the intensity of the mining and gas wells. They allow to predict the process at mining use.
References:
1. Konovalov A.N. Tasks problems of filtering multiphase incompressible fluid.-Novosibirsk: Science, 1988.-166 page.
2. Marchuk G.I. Methods of calculus mathematics.-M.: Nedra, 1977.-456 page.
3. Katkovnik V.Y. Nonparametric identification and data smoothing.-M: Science, 1985.-408 page.
4. Jakbarov O.O. Models and optimal algorithm of controlling filtering system: Dus...kand. Tech. science.- Tashkent. AHRUz IK, 2004.-138 page.
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