Untitled record

full description

Sister Ra'a wallpaper

The present invention relates to a computer simulation of hydrocarbon reservoirs in the ground, in particular the simulation of flow patterns through wells in reservoirs.

Well models played an important role in the numerical simulation of the reservoir. Stock models were used to calculate

<p>5 Production rates of oil, water and gas from wells in oil and gas reservoirs. If the production rate of the well is known, it is used to calculate the flow chart along the perforated phase of the well. With the increased capabilities of measuring flow rates along the perforated stages of the well, an adequate numerical model of the well is required to calculate the correct flow chart to fit the measurements in a reservoir simulator.</p>

It is well known that simple well models such as explicit or semi-implied models can

<p>10 It is sufficient if all the reservoir layers are continually communicating with terrestrial wells in a reservoir simulator. For these models, the borehole yield rate is assigned in proportion to the indices of layer productivity (or overall kinetics). Therefore, the calculations are computationally simple and inexpensive. The structure of the resulting coefficient matrix for reservoir unknowns remains unchanged. The coefficients have a regular sparse structure. So, any sparse matrix solving method like this can be used to solve</p>

<p>15th Linear system of lattice mass pressures and saturation states for each time step of the entire stock etc. simulation model.</p>

However, for reservoirs with a high degree of heterogeneity and which have some strata that are not closely connected, the aforementioned well models cannot provide the correct physical solution. Instead, in some cases, it presents incorrect flowcharts, and causes convergence issues in the emulator.

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With the increasing development of reservoir models, the number of land layers has become within several hundred to represent the heterogeneity of reservoirs. Implicit and fully coupled well models, with simultaneous solution of the reservoir and well equations were necessary to correctly simulate the flow patterns through the well and are also necessary for the numerical stability of the reservoir simulation. In order to solve a fully coupled system, the equations are generally removed

<p>5 well first. This creates an unstructured coefficient matrix of storage unknowns to be resolved. Solutions of this type of matrices require solving methods with special preconditions. For wells with many completions and many wells in a simulation model, this method becomes computationally expensive in terms of processor time.</p>

General description of the invention

<p>10 In summary, the present invention presents a new and improved computer-implemented method for solving the well equations as well as the reservoir equations in a reservoir simulation model with formation layers having fluid flow vertical and fluid flow barrier layers having no vertical fluid flow. The computer-implemented method constitutes a horizontal position reduced-well model system as well as multiple bed-wells in a spool simulation model by aggregating in the form of a single flow layer where the flow layers have flow between the flow barriers in</p>

<p>15th Model etc. Store in the vicinity of wells only. For the given well production rate, the method then solves the reduced well model system by calculating the matrices (using a direct sparse solution matrix) for downhole pressure and reservoir unknowns for the mesh blocks the well passes through (reduced well model system). This method is repeated for the well and wells in reservoir simulator The method then solves the full reservoir simulation model by treating each well as having a specific downhole pressure,</p>

<p>20 Based on a steady-state volumetric equilibrium relationship of layer completion rates, formation pressures and scalability</p>

Moving on to determine the completion rates of the well layers or wells for the complete model of the reservoir, determine the overall rate of the well from the completion rates that were determined for the well layers or wells. The method then generates a record of the completion rates that were determined for the layers and the overall rate that was determined for the well and wells. The simulator calculates the pressure distribution of the saturation of a multiphase flow fluid distributed in the reservoir by:

<p>25 Use the calculated hole rates and cache data assigned to the emulator network blocks. And so on</p>

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The simulator is capable of calculating the pressure and saturation distribution inside the reservoir with a specific production and injection rates into the wells at a specific time.

The current invention presents a new and improved system for data processing to make a well model for horizontal wells as well as multiple vertical wells by simulating a subsurface reservoir from a reservoir model with layers.

<p>5 A composition with fluid flow and barrier layers for fluid flow that do not have a fluid flow. The data processing system includes a processor that performs steps to solve in a matrix manner for the model of the reduced downhole pressure well model system or wells and unknown reservoirs around the well or wells and solve the complete reservoir model by treating the well(s) as it has the specified downhole pressure, and based on Steady-state volumetric equilibrium relationship of layer completion rates, formation pressures and transmittance to determine rates</p>

<p>10 Completion for the strata of the well(s) for the complete model of the reservoir. The processor also determines the overall rate of the well(s) from the completion rates that have been set for the stratum(s). The data processing system also includes a memory that creates a record of the completion rates that are defined for the strata and the rate or rates. that have been identified.</p>

The present invention also introduces a new and improved device for storing data in a readable medium

<p>15th By computer Computer-operable instructions to make the data processor create a well model for horizontal as well as multiple vertical wells by simulating a subterranean aquifer reservoir from a reservoir model with formation layers that have fluid flow and barrier layers for fluid flow that do not have fluid flow to implement the steps of the solution in a matrix manner for a system model Well model reducing the pressure of the bottom of the well or wells and unknowns of the reservoir The solution of the complete model of the reservoir by treating the well(s) assuming that it has a specific pressure of the bottom</p>

<p>20 The well, based on a steady-state volumetric equilibrium relationship of layer completion rates, formation pressures and transmittance to determine the completion rates of the well layers (wells) for the full model of the reservoir. The instructions stored in the data storage device also include instructions that make the data processor determine the total rate of the well (l^). bar) from the completion rates determined for the strata of the well(s) or wells, and creates a record of the completion rates set for the strata and the overall rate determined for the well(s).</p>

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Brief explanation of the drawings

Figures 1a and 1b are schematics of a well model in a reservoir simulation of multiple strata aquifers above and below a flow barrier in a reservoir consisting of single layers according to the present invention.

Figures 2a and 2b are schematics of a well model in a multi-layered reservoir simulation

<p>5 Above and below several spaced flow barriers arranged in a single-layer reservoir according to the present invention.</p>

Figure 3 is a schematic diagram of a simulated well model based on an explicit model approach illustrated in Diagonal Geometry.

Figure 4 is a schematic diagram of a simulated well model based on an implicit and paired model approach

<p>10 fully.</p>

Figure 5 is a schematic diagram of a well model to simulate a reservoir with a comparison of flow diagrams obtained from models of Figures 3 and 4.

Figure 6 is a schematic diagram of a specific band network system for well models according to Figures 3 and 4.

Figure 7a and 7b are schematics showing the well model reservoir layers for the well stratum model

<p>15th Unmodified conventional and well bed model according to the present invention, in order.</p>

Figures 8A and 8B are flowchart diagrams that show comparisons between Figure 7A models

and 7b, respectively.

Figure 9 is a schematic diagram of a well layer model with two faulted layers with diagonal coordinates.

Figure 10 is a functional box diagram or flow chart of the data processing steps of a . method

<p>20 A fully implicit well model system that is fully coupled to the simultaneous numerical solution of the reservoir simulation.</p>

Figure 11 is a functional box diagram or flow diagram of the data processing steps of a method and system for a fully implicit sequential well model for reservoir simulation according to the present invention.

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Figure 12 is a schematic diagram of a linear system of equations using a three-diagonal coefficient matrix of an explicit well model of a one-dimensional reservoir simulator with an RCI well.

Figure 13 is a schematic diagram of a linear system of equations using a three-diameter coefficient matrix for a fully implicit well model of a one-dimensional reservoir simulator with an RCI well.

<p>5 Figure 14 is a schematic diagram of a linear system of equations using a three-diameter coefficient matrix of a fixed-well bottom pressure model for a one-dimensional reservoir simulator with a treatment RC well according to the present invention.</p>

Figure 15 is a functional box diagram or a step-by-step flowchart illustrating the analytical method for stock simulation according to the present invention.

<p>10 Figure 16 is a computer network schematic of a fully implicit sequential well model for reservoir simulation according to the present invention.</p>

Figure 17 is a schematic diagram of a three-diagonal coefficient matrix.

Figure 18 is a schematic diagram of a linear system of equations using a three-diagonal coefficient matrix.

<p>15th Figure 19 is a schematic diagram of a specific difference grid system for a horizontal well model oriented in the direction of the y axis according to the present invention.</p>

Figures 20a and 20b are schematics of horizontal well models in a reservoir simulator of multiple subsurface formation layers in a flow barrier area in a reservoir, before and after its formation in a reduced horizontal well model according to the present invention.

<p>20 Figure 20c is a schematic diagram of a linear system of equations for a reduced horizontal well model according to Fig. 20b.</p>

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Figures 21 and 22 are functional box diagrams or flow charts of the data processing steps of a method and system for a reduced horizontal well model according to the present invention.

Figure 23 is a schematic diagram of a specific difference grid system for a reservoir model with multiple wells according to the present invention.

<p>5 Figures 24a and 24b are schematic diagrams showing the network designation symbols in the multiple borehole model according to Figures 19 and 23.</p>

Figures 25a, 25b, 25c and 25d are schematic diagrams showing the network numbering of a 3D storage model.

Figure 26 is a functional box diagram or flow chart of the data processing steps for a method and system 10 to modify the box diagram from Figure 11 for multiple wells in a reservoir with a fully implied well model

It is perfectly combined with the simultaneous numerical solution to simulate the store.

Figure 27 is a schematic diagram of a simplified linear system of equations for two wells, and a three-dimensional reservoir model.

Detailed description:

To illustrate, the present invention presents a fully implicit sequential well model for reservoir simulation. Stock simulation 15 is the process of making a mathematical model of stock geometry. Describes the flow of fluids inside an oil or gas storage

(Porosity media) by a set of PDEs. These equations describe the pressure (energy) distribution, oil and water distribution, gas velocity distribution, and fault volumes (saturation) of oil, gas and water at any point in the reservoir at any time during the life of the reservoir producing the oil. The flow of fluids within a reservoir is described by tracing the movement of a component in a mixture.

<p>20 Amounts of components such as methane, ethane, CO2, nitrogen, H2S and water either in units of mass or moles.</p>

Since these equations and the laws of thermodynamics and related physical laws describing fluid flow are complex, they can only be solved with digital computers to obtain the pressure distribution,

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The distribution of velocity, liquid saturation, the amount of mass component, or the distribution of moles inside the tank at any time and at any moment. This can only be done by solving these equations numerically, not analytically. The numerical solution requires that the storage is divided into arithmetic elements (cells or grid blocks) in the area, and the vertical direction (z, y, x - that is, three-dimensional spaces) and time is divided into periods of days or months.

<p>5 For each component, the unknowns (pressure, velocity, fault size, etc.) are determined by solving complex mathematical equations.</p>

In fact, a reservoir simulation model can be thought of as an assembly of rectangular prisms (such as bricks in a building wall). Changes in pressure and velocity fields occur due to oil, water and gas production in wells distributed in reservoirs. The simulation is performed over time (t). Generally, production rate or

<p>10 The injection is known to each well during the production date of the stockpile. However, since wells pass through several layers of reservoir (elements), the contribution of each reservoir component (wellbore) to production is calculated by different methods. The present invention deals with calculating the contribution of each wellbore to the total well production. Considering that these calculations can be costly and with the need for boundary conditions that are very important for the simulation, the proposed method indicates that there is a practical way to correctly calculate</p>

<p>15th for flow path diagram through a well. As will be described, it can be shown that some of the other methods used will lead to an incorrect flow diagram which causes problems in obtaining the correct numerical solution and can be computationally very expensive.</p>

conventions

Δz, Δy, Δx = Grid dimension in X, Y and Z directions

<p>20 KZ, KY, KX = Permeability in X, Y and Z directions</p>

p = pressure

ρ = density of fluid (oil)

g = gravitational constant

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z = AR from a given depth

ro = radius of method Δx 0.2 = Peaceman

rw = radius of the wellbore

Tz, Ty, Tx = Transmissibility of rocks in x, y and z directions

<p>5 The equations that explain a general model for simulating a reservoir and determine the conditions of the well of interest with respect to the current invention are shown below in equation (1):</p>

np np np np

Δx∑TxρijλjΔΦj+Δy∑TyρijλjΔΦj+Δz∑TzρijλjΔΦj+∑ qij= ^tnij=1 j =1 j=1 j=1 Δ^t

i=1,..n_c.. )1(

where Tz, Ty, Tx is the mobility of the rocks in the y, x and z directions as defined in the equation below), i is the number of phases of the fluid, np is the total number of phase of the fluid, which is usually 3

<p>10 (oil, water and gas), Σ is the collective term, ρi,j is the density of the i component of the j fluid phase, λj is the j phase kinetics (Equation 6), Φj is the fluid potential (corrected reference pressure) for the fluid phase j, and similarly Δx is the operator The difference in the x direction, Δy is the differential factor in the y direction, Δz is the differential factor in the z direction of the reservoir, and qi,j is the volumetric well limit (source or sink) of the i component of the grid mass (cell) located at (x, y, z) (, and Δt is the differential factor in the range</p>

<p>15th time, n is the total number of moles of component i, and nc is the total number of components in the fluid system (methane, ethane, propane, CO2, etc.).</p>

Equation (1) is a set of paired nonlinear partial differential equations that describe the flow of fluids in a reservoir. In the above set of equations ni represents the i component of fluids. nc is the total number of hydrocarbon and water components flowing into the reservoir. Here, a component expression means methane

<p>20 Ethane, propane, H2S, CO2, water, etc. The number of components depends on the water system -</p>

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Hydrocarbons available for storage are of interest. Usually, the number of components can range from 3 to 10. Equation (1) combines the continuum and momentum equations.

In Equation (1) qi,j is the rate of well perforation at position x,y,z of component i and z,y,x is the number of the center of mass of the grid (cell). Again, compute this limit of specific production rates at

<p>5 Wellhead is the subject of the current invention.</p>

In addition to the differential equations in Equation (1), the pore size constraint at which point (element) in the reservoir must be satisfied:

(p (x, y, z))= ∑^{^}₌₁ )2(

where Vp is the pore size of the mesh mass, P (x, y, z) is the fluid pressure at the point x, y, z, Nj 10 is the total number of moles in the fluid phase j, and ρj is the fluid phase density j.

There are 1 . equations ^nc + In equations (1) and (2), the unknowns are 1 ^nc +. And these equations are solved at the same time using the thermodynamic phase constraints for each component i by means of equation No. (3):

<p>)3( _^( ^; 1, 2, ... , P, T) = _^ ( ^ ; 1, 2, ... , P, T)</p>

<p>15th where fi is the component escape, the upper letter V represents the vapor phase, L represents the fluid phase, n is the total number of moles of the component i, and P is the pressure and T represents the temperature.</p>

In a reservoir fluid system there are typically three phases of the fluid: an oil phase, a gas phase and a water phase. Each fluid phase can contain different amounts of the components described above based on the reservoir pressure and temperature. The phases of the fluid are described by the symbol j. The j symbol has a maximum value of 3

<p>20 (oil, water and gas phases). The symbol is the maximum number of phases (sometimes it can be 1 (oil); 2 (oil and gas or oil and water); or 3 (oil, water and gas). The number of phases varies depending on the storage pressure) P) and its temperature (T). Symbol _^ It is the number of moles of component i in the fluid system. The symbol nc is the maximum number of components in a fluid system. The number of phases and the proportion of each component are determined in</p>

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every phase _,^ In addition to the phase density ^ρj And^ρi,j From Equation No. (3). In Equation No. (3), V represents the vapor phase (gas) and L means the liquid phase (oil or water).

The total number of moles in a fluid phase is determined by the equation:

)4( ,^ 1=^{^}^∑ =

<p>5 The total moles of the component are determined by equation (5).</p>

<p>)5( ^ ,^ ₁₌^{^}_^∑ =</p>

Phase kinetics in equation No. (1), the relationship between phases, the definition of fluid potential and differential symbols are defined in equations (6) to (9).

(6) λj = kr,j/μj

<p>10 In equation (6), the numerator determines the relative phase permeability and the denominator is phase viscosity</p>

The capillary pressure between phases is defined by equation (7) for phase pressures:

₎₇₍ Pc(sj,sj′)=Pj - P~j′

The j-phase fluid potential is determined by the following equation:

₎₈₍ Φj = Pj-gρjz

<p>15th The separate differential influences in the y, x, and z directions are defined by the following equations:</p>

^Δx^{U = U}x+Δx ^-Ux^{, Δ}y ^=Uy+Δy ^-Uy^{, Δ}z+Δz ^=Uz+Δz ^-Uz

)9( ^{Δt = Ut+Δt - Ut ,}

where Δ is defined as the discrete differential symbol and U is any variable.

Equation (1), along with the constraints and definitions in equations (3) through (9), is written for each network block (cell) in a stock simulator using a specific differential method for volume control (which may include

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Some blocks of the network are wells). The resulting equations are solved at the same time. This is done to find the distribution of ni (i.e., x, y, x, t), and P (i.e. z, y, x, and t) for certain well production rates qT for each well being Including calculating the component rates in Equation No. (1) according to the current invention using the new well model formula. In order to solve equations (1) and (2), the reservoir limits are entered in the blank (z, y, x), and the distribution of

<p>5 The lithological property K(x, y, z), rock porosity distribution, fluid properties and saturation-dependent data were included in the simulation.</p>

According to the present invention and as will be explained later, a reduced well model system is formed that gives the same determination of the calculated bottom pressure as the previous complex computationally time-consuming full-coupled well models.

<p>10 According to the present invention, it is determined that for the network blocks through which the path of the well passes when a number of . are connected</p>

Formation Layers Arranged, connected layers for processing can be combined into a single layer, as shown schematically in Figures 1 and 2 of the well model. This is done by identifying the floor flow barriers in the reservoir for the well cells, and integrating the layers above and below the different flow barriers for the well cells. Therefore, the entire well model system is reduced by using many layers for inclusion in a process well model.

<p>15th As shown in Figure 1, the L-well model represents in a simplified schematic form the blocks (cells) of a complex aquifer network where the well that passes through it consists of seven separate layers of the formation 10, each of which is connected by flow in the vertical direction with the layers Adjacent 10. The L model contains another set of ten formation layers around well 12, each of which communicates by flow in the vertical direction with adjacent layers 12. Groups of formation layers 10 are connected</p>

<p>20 and 12 by flowing with similar adjacent layers in the L model and separated as shown in</p>

Figure 1 with a fluid impermeable barrier layer 14 which is a barrier to the vertical flow of the fluid.

According to the present invention, the L-well model for the purpose of treatment is shortened to a reduced-well model or

Simplified R (Fig. 1a) by aggregating or combining, for the purpose of determination of effortΦ and completion rates, layers 10 of the well model L over the flow barrier 14 as a composite layer 10a in the reduced model R.

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Similarly, layers 12 of the L-well model below the flow barrier 14 are combined as a composite layer 12a in the reduced-well model R.

Similarly, as illustrated by Figure 2, the 1-L septic model consists of five separate upper formation layers20, each of which is connected by a vertical flow with adjacent layers.

<p>5 20. The 1-L model contains another set of seven layers for composition 22, each of which has a</p>

Connection by ground flow with adjacent layers 22. Groups of formation layers 20 and 22 that are in contact by flow with other similar adjacent layers are separated in Model 1-L as shown in Figure 2 by a fluid impermeable barrier 24 which is a barrier. For fluid flow Arca. Another set of nine layers to configure 25 in contact is separated from

<p>10 By flowing together from the layers 22 below a fluid barrier layer 26 which is a barrier to the flow of the fluid is arranged as shown in Model 1-L. A final bottom set of nine layers of composition 27 in contact by flowing together is placed under a fluid flow buffer layer 28 in the model.</p>

.L-1

According to the present invention, the 1-L well model for treatment purpose is reduced to the reduced or . model

<p>15th Simplified 1- R (Fig. 2a) by aggregation or merging, for the purpose of determining well bed effortΦ and completion rates, layers 20 of Model 1-L above the flow barrier 24 to a composite layer 20a of the reduced model R. Similarly, other layers are combined 22, 25, and 27 for Form 1-L below the flow baffles 24, 26 and 28 in composite layers 22a, 25a, and 27a in reduced Form 1-R.</p>

Well model systems or reduced well models are solved according to the present invention to determine the value of unknowns

<p>20 etc. Balance and downhole pressure. After that, the wells are processed in a fully simulated reservoir model system</p>

Such as downhole pressure and is implicitly solved to determine the value of the unknowns etc. The diagonal elements of the coefficient matrix and the right side vector of the stock model are the only components that are modified in the processing according to the current invention, and this modification is just a minor modification. Then the technique or methodology of an ordinary sporadic solving method is used to solve the unknowns of the Khazine. Puncture rates are calculated using

<p>25 Reservoir unknowns (pressures and saturation states). These rates are added to calculate the total rate </p>

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for the well. The error between the total well rate determined according to the present invention and the input well rate will decrease with a nonlinear Newton simulator for each time step.

The calculated flow rates according to the present invention also converge with the calculated flow rates with the full-coupled asynchronous solution for the entire reservoir simulation model that includes several wells. and see n sister ra'a

<p>5 The current solution requires a small well system model, the solution cost is low. It turns out that the present invention approach converges if the reduced well system is constructed correctly, using the magnification correctly when merging the contact layers.</p>

It is well known that simple vertical well models, such as explicit or semi-implied models, are

Generally suitable if all layers of the stock are contacted ARCA. As shown in Figure 3,

10

An explicit well model E consisting of an Nz number of 30 storage layers in contact with the vertical flow, for each

permeability layer ^x,i (here i represents layer number, not component) and thickness ^zi And the rate of the qi hole layer identifier

As shown in Figure 3. The total production rate qT of the explicit model E is the sum of the discrete production rates qi of the Nz layers of the explicit model as shown in equation (3) in the same figure.

<p>15th For explicit models, the borehole production rate is assigned in proportion to production factors</p>

Layer (or aggregate kinematics). Therefore, the calculations are simpler. The matrix of emerging coefficients for unknowns remains the same, i.e. maintains a regular reserve formula, as shown in the matrix formula in Figure 12. Therefore, any method of solving the reserves matrix can be used to solve the linear system for network mass pressures and saturation states for each time step.

<p>20 Well Models: An approach to several ground-well models for reservoir simulation is presented, also based on the simplicity of the fluid system in the form of a flow from a slightly compressible single-phase oil flow into the reservoir. However, it should be understood that the present invention is generally applicable to reservoirs, and can be used in a number of wells and fluid phases in a typical reservoir simulation model.</p>

Δz, Δy, Δx = Grid dimensions in z, y, x . directions

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Figure 6 illustrates the fixed-difference network G used in this description of the Arce well model. As we have shown, a well is located at the center of the central cell in the vertical directions. The models shown below consider that the well is completed in the vertical Nz directions, and the voltages in the cells Neighboring:

Φ _BW , _BE , _BNE , _BS

<p>5 They are fixed and known magnitudes of the simulation range (previous time step or repetition value). Here, the bottom symbol B denotes the “boundary”, W denotes the western abutment, E denotes the eastern neighborhood, and N and S denotes the northern and southern neighborhoods, respectively. Other Φ describes fluid stresses (corrected reference pressure). As can be seen in Figure 6, a number of reservoir layers penetrate into the well in the vertical direction represented by the parameter I, and for Nz ... i = 1, 2, 3, with Nz which is total</p>

<p>10 The number of layers in the stock model. For each layer i, there are four neighboring cells in the same areal plane (x, y). These adjacent cells are in the east-west direction (x direction) and north-south direction (y direction). The voltage Φ of the eastern, western, northern and southern neighborhoods is known from Simulator time step calculations, and those efforts are assigned that can be considered to be unchanged by the simulation time step.</p>

<p>15th neighborhoods that can change in the vertical direction but are assumed to be known. The volume equilibrium equation in the regular state of cell (i) in Figure 6 is as follows:</p>

Twi(ΦBw-Φi)+TEi(ΦBE-Φi)+TNi(ΦBN-Φi)+TSi(ΦBS-Φi)+ ^TUp,i^(Φi-1^-Φi^)+TDown,i^(Φi+1^-Φi^)-qi^=0.

)10(

In equation (10), T represents the mobility between cells. The suffixes N, E, W, and S denote west, east, south and north directions, and (i) represent the cell parameter.

20 The ability to move between cells in three directions is defined by the following equation (11):

Twi = kx,i-1 / 2

Δy_i Δz_i0.5(Δx +Δx )

)11(

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Twi = kx,i-1 / 2

Δy_i Δz_i0.5(Δx +Δx )

^TNi ^{= k}y,i-1/2

Δx Δz

0.5(Δyi-1 +Δyi)

_,^ = ^

_{^ ^}

^{,^+1}2 0.5( ^+1 + ^)

Δx_iΔy_i

Up,iz,i-1/ 2 _{0.5(Δz +Δz )}

TDown,i = kz,i+1 / 2

Δx_i Δy_i

0.5(Δz +Δz )

In the above equations (11), Δxi is the size of the network block (cell size) in the x direction of the i number of the network block (cell). Similarly, Δyi is the network block size (cell size) in the y direction of the i number of the network block (cell), The Δzi is the mesh mass size (cell size) or the mesh layer thickness in the z direction of the i number of the mesh mass (cell). 1/2-Kz,i is the cap permeability at the interface of i and 1-i cells.

10 Similarly, 1/2+Kz,i is the ground permeability at the interface of i and 1+i cells. As can be seen in Figure (6), cell i is in the center, and is 1/2 + i interface between cells i and 1 + i. For convenience, the upper letter j is lowered when expressing east-west flow. Similarly (j - 1, i ) is in the north neighborhood of the central cell (i,j). Hence, the symbol (j - 1/2,i) is the interface between the central cell and the north axle in the y direction.

15th The same notation is implemented for the south adjacency: (j + 1/2,i) which denotes the interface between the central cell (i,j) and the south adjacency (j+1,i), in the y direction. For convenience in the above equations, lower The uppercase i is when expressing the y (or j) direction. As is clear, the mobility is defined in Equation (11) in a similar way.

In Figure 14, the diagonal terms c,i . are defined^̃ With Equation (17a) below, the transferability between 20 cells of the three directions is as defined in Equations 11, as shown above.

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The term in Figure 14 (right side) is expressed by equation (17b) in the text. It is extracted here as follows:

~

^bi ^=-(PIi^Φw^+Twi^ΦBw^+TEi^ΦBE^+TNi^ΦBNE ^+TSi^ΦBS⁾

where Nz ... ,2, 1 = i, with Nz again being the total number of networks in the vertical directions,

<p>5 and the number of family classes. In this extraction of equation (17b), the throughput of the layer PIi is defined by equation (17) and the limits of voltage ΦB are the known boundary voltages at the boundaries of neighboring cells to the west, east, north, and south of the central cell. Traditionally, these terms use the cell and the grid mass. mutually.</p>

Generally speaking, conventional well models can be divided into three groups: (a) the outright well model; (b)

<p>10 Well model dedicated to downhole pressure; And the model of the well is completely implicit. (Aziz K, Setari A,</p>

Oil Storage Simulation, Applied Science Publishing Ltd., London 1979). For a better understanding of the invention

Present, a quick overview of each well model is presented.

Implicit Well Model

For the implied well model, the source term qi is defined in Equation No. (10) according to Equation No.

<p>15th (12) as follows:</p>

k_x,iΔz_i

^qi ⁼ i=Nz ^{, q}T

∑ k_x,iΔz_i

)12( ⁱ⁼¹

where qi is the production rate of cell i (the mass of the mesh) through which the well passes and pierces it. Substituting equation (12) into equation (10) for cell i we get

^TUpi^Φi-1^+TC,i^Φi^+TDown,i^Φi+1^=bi (13)

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where

^Tc,i ^=-(TUp,i^+Tdown,i^+TWi^+TEi^+TNi^+TSi⁾

And:

^bi ^{= -} i=Nz^{x, q}T ^{- (T}Wi^Φ BW ^+TEi^ΦBE ^+TNi^ΦBNE ^+TSi^ΦBS⁾

∑k_x,iΔz_i

¹⁼14( ⁱNS(

<p>5 By writing equation (13) for all cells 1 = i, Nz around the well for all cells of the well only leads to a linear system of equations using a three-diameter coefficient matrix of the type shown in Figure 12, which can be written as a vector matrix as follows:</p>

^

^ARR ^ΦR ^=bR (15)

In Equation (15), ARR is a three-dimensional matrix (Nz × Nz), and ΦR and bR are

<p>10 vectors (1 x Nz). Equation (15) is solved by computing the masses of the network of unknown voltages of the reservoir ΦR through which the well passes using a solution method for a linear three-diameter system such as the algorithm</p>

.Thomas

Three-Diameter Matrices and Systems

Three-diagonal matrices are matrices with only three diagonals in the middle, with a real number or 15 as the entries in the diagonals. These diameters are called "bottom diameter", "central diameter" and "diameter .".

top.” The remaining elements or entries of the triple-diagonal array are zeros. For example, Figure 17 shows a 3-diagonal matrix with the dimensions of a matrix of 8x8 (or order 8 = n). In Figure 17, the elements of A; and the ith element of A, i.e. 8 ,1 = i, ai, a3, a2, a1, representing the bottom diameter, bi, b3, b2, b1, the central diameter, and ci, c3, c2, c1, the top 20 diameter elements.

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An example of a three-diagonal system of equations is shown in Fig. 18. The solution to a linear system of equations using a three-diagonal matrix such as defined above and shown in Fig. 18 is easily solved by Gaussian elimination. An example of solving equations in this way is given in:

.<a href="https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm">https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm</a>

5 Thus, the solution of xi was implemented as shown below and in Figure 18 by solving the matrix relationships from equations (16) to (16e) as follows:

<img file="SA8656B1_D0001.tif" />

<a name="caption1"></a>

so-*•

2: - 94 - :41 ; ί~ ?1,7^-Aΐ — 2,...,1. (6 ah)

Well model for downhole pressure

φw is the uniform effort along the length of the open wellbore for production using conventional techniques according to the techniques

Annotated in references, such as the book: “Muskat” Physical Principles of Oil Production

"The Flow of Homogeneous Fluids and McGraw-Hill Book Co.". (1949) 15

For Prototyping .Through Porous Media”, McGraw-Hill Book Co. (1937)

In the present context, the frictional pressure loss along the length of the well has been neglected. Assuming that φw is known (or defined), the rate of oil from the hole is calculated by equation (17) as follows:

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qi = PIi (Φi -ΦW)

(Φi -ΦW)

2πk_x,iΔz_iln(r_o,i / r_w)

)17(

where

PIi

is the layer productivity coefficient, and^Φw is the assigned downhole effort (reference pressure

corrected(, and ^Φi It is the pressure of the storage network mass through which the well passes for the mass of the network (cell), and it is called ⁱ ،

^o,i Peaceman method for the well block radius of the mesh block and i was defined as ^{w 0.2Δx} ,

5 is the radius of the well.

The variable quantities are explained in Equation No. (17) in the previous section of Conventions. Substituting Equation (17) into Equation (10) and summing the terms for cell i, we get the following result:

₎₁₈₍^TUpi^Φi-1^+TC,i^Φi^+TDown,i^Φi+1W ^=bi

let's make

^Tci^=-(TUp,i^+Tdown,i^+TWi^+TEi^+TNi^++TSi^+PIi⁾_{(10) 18a}

b_i = -(PI_iΦ_W + T_WiΦ _BW + T_EiΦ _BE + T_NiΦ_BNE + T_SiΦ_BS) _(18b)

When writing equation (18) for all grid blocks i = 1, Nz results in the matrix system shown in Figure 14. It can be seen that the matrix of Figure No. 14 for a well model dedicated to downhole pressure is similar to the matrix of Figure No. 12, and by comparison we find that equation No. (18) It is similar to equation number

<p>15th (13). A custom well model for downhole pressure can easily be solved by matrix treatment</p>

By computer using a traditional approach to solve the three-diagonal equation.

Fully implicit well model

The total production rate qT of a well according to the implied well model is determined exactly according to Equation (19).

i=Nz

qT -∑PIi(Φi-ΦW) = 0.0

ⁱ⁼¹ )19(

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10

15

The discrete completion rate qi is calculated by equation (17). For the implicit well model, it was assumed that the wellbore effort ^{Φ W} Fixed through the well but unknown.

Substituting equation (19) into equation (10) and summing the terms for cell i into cell (i), we get the following result:

^TUpi^Φi-1^+TC,i^Φi^+TDown,i^Φi+1W^-PIi^ΦW ^=bi

let's make:

^Tci^=-(TUp,i^+Tdown,i^+TWi^+TEi^+TNi^+PIi⁾

(20b) bi = -(TWiΦBW + TEiΦBE + TNiΦBN + TSiΦBS)

By writing equation (20) for all cells, we get a linear system of equations as shown in Figure 13, where the solid line of the upper diameter represents TUp,i as defined in equation (11), and the solid line of the lower diameter explains the elements named TDown,i as previously explained in Equation (11). The central term TC,I is defined by equation (20a) and the right-hand side bi is defined by equation (20b).

The linear system of the matrix (Equation 20) from Figure 13 can be represented in a vector matrix as follows:

^

_ΦΦ_WR

^b_Rb_W

^ARR

A_WR

^ARW

AWW

)21(

In Equation No. (21), ^RR is a triangular matrix^RW (Nz×Nz is a vector (1×Nz) (PI's of the reservoir), ^AWRis a vector (1×PI's) (Nz) and^AWW is a non-vector quantity (1x1). In this example:

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AWW

Nz

∑ PI _NZ

= i=1

Writing it in algebraic form:

^

₎₂₂₍ A_RRΦ_R + A_RwΦ_W = b_R

^

₎₂₃₍ AwRΦR + AwwΦW =bw

Solve ^W From equation (22) it results in:

₎₂₄₍ Φ_W = A^-1ww (b_w - A_wRΦ_R )

Substitution in Equations (21)



₎₂₅₍ ARRΦR +ARw(A^-1ww(bw-AwRΦR))=bR

By summing the terms in equation No. (25), we get:

(A_RR - A_ww^- A_wR A_RWΦ_R =b_R -A_RwA_ww^- b_{w (10)(26 .)}

Transaction matrix ^{(RR - ww wR RW )} In equation (26) it is a complete matrix (Nz×Nz). The resulting matrix of coefficients can be defined as follows:

ARR -Aww^-1AwRARW A^~ =)27(

b~ = b_R - A_RwA_ww^-1b_w

15th Then equation (26) can be written as follows:

~^~

^{AΦR = bR} )28(

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The matrix of Equation (28) can be solved by means of a direct solution by sampling by the Gaussian method or any other conventional solving method suitable for entire matrices.

If the number of Nz layers is large in the implied well model, and the wells are perfectly complemented in all layers, then solving equation (28) becomes costly with respect to the time required for computation. For this reason,

<p>5 Also, if many wells are involved, equation (28) is generally solved by iterative methods.</p>

An example of this is in "Fully Implicit Well Model Fully Coupled to Parallel Mass-Cell Stocker Simulation", Saudi Arabia Sector SPE Technical Symposium, May 14-16, 2005.

Flow diagram I (Fig. 10) illustrates the basic computer-processing sequence for a fully implicit, synchronous solution for a fully-coupled well model for the matrix type shown in Fig. 13. During step

<p>10 100, the simulation begins with a reading of the inventory and production data. Data etc. Store includes engineering information about</p>

Storage, such as volume and range (length) in the z, y, x directions and reservoir properties such as permeability distribution, porosity distribution, layer thickness, relative permeability data, capillary pressure data, fluid properties data such as fluid density tables, modulation volume factor tables, And viscosity tables, wells location, and well bore locations in the reservoir.

<p>15th Production data includes the measured or specified oil, water and gas production rate of ^bar defined in the previous step. The production data also includes the minimum downhole pressure for each well.</p>

In many cases, only oil and water production rates are entered if gas production data is not available. If no water is produced in the field, only oil production data is output.

During step 102 the time step is incremented by one, and the iteration counter is set to the number of iterations

<p>20 The non-linearity performed during the current time step has to be zero. During step 104, a Jacobite matrix is ​​created from the store data. In step 106, the resulting system of linear equations (19) is then solved using sparse preconditioners (Youssef Saad, iterative methods for sparse linear systems,</p>

Bulletin of the Industrial Society and Applied Mathematics (SIAM), 2003).

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During step 108, a convergence step is performed to determine whether the nonlinear frequencies have converged or not. The residuals of the resulting equations from step 106 are checked each against user-specified tolerances. If these tolerances are acceptable, the nonlinear iteration loop is exited, the solution outputs are written to the current time step file, and the processing process returns to step

<p>5 102 for the time step to be submitted, and preparation is made for the time step that has been increased and then continues</p>

As shown. If the user-defined tolerances are determined to be unsatisfactory during step 108, the processing according to the nonlinear iteration loop returns to step 104 and continues. If the number of nonlinear iterations becomes too large, a decision may be required to reduce the time step size and return to step 102.

<p>10 However, based on the power of preconditioning, this method can also be very costly in computation time, as there is no accurate way to represent the full matrix in Equation 19. For difficult problems, with high heterogeneity and small layer thickness, it may not be The iterative method converges.</p>

In addition, for tanks with severe heterogeneity that have some layers that are not

<p>15th Continuous ARCA, the above models do not give the well the correct physical solution. Alternatively, they can give incorrect flow charts, and sometimes they can cause affinity problems for the emulator.</p>

The present invention: The fully explicit and implicit models can give completely different flowcharts in the case of some LBDs. This is shown in Figure 5. As shown in

<p>20 Figure 5, V-storage model consisting of an upper layer 50 of relatively low permeability, which has ground flow, and is located on top of a high permeability insulated layer 52 that does not have a ground contact of the flow with adjacent layers. The flow barrier layer 52 in storage V is located on top of layer 54 that is medium porosity and has a vertical connection to the flow. As can be seen in Figure 5, the production rates qT for the V-well model are the same in both the explicit and implicit well modeling methods.</p>

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However, the production rates q2, q1, and q3 for layers 50, 52 and 54 differ significantly from each other. The production rate q2 for layer 52 is the largest contributor to the total production rate qT as indicated by curve 56 of the explicit model. Conversely, for the implicit model as shown by curve 58, the production rate q2 for layer 52 is much lower.

<p>5 In the fully implied well model, the production rate for Layer 2 is much lower due to the fact that this method takes into account the internal heterogeneity of the reservoir (all properties of the reservoir throughout the reservoir) and heterogeneity around the well blocks as well as the hole modulus (or properties of the stratum). 2 alone as used by the correct method as the correct data to assign the rate ratio to this hole). For example, the whole well implied method shows that no fluid reaches the</p>

<p>10 Layer 2 of Layer 1 and Layer 3 is due to the impermeable barrier layer between Layer 2 and Layer 1 and 3. Therefore, once some fluid is produced from the well model 2 layer, the pressure of the layer 2 must fall and this layer should not be supplying at a high rate to the well, even though the layer has a very high permeability.</p>

On the other hand, the correct method determines the rate for layer 2 based on the permeability of this layer alone without taking into account the connection of the layer with the upper and lower layers. Based on this, the correct way

<p>15th You will assign a very high rate to this layer and keep it for the next simulation time step. In the final time steps of the simulator, this will cause the production rates to become unstable, i.e. the simulator will reduce the time step size and it will take a very long time to complete the simulation. It is not acceptable for a reservoir simulation to have models that give divergent results for the same input data based on the model making technique that is chosen to use.</p>

<p>20 According to the present invention, a higher quality borehole model is presented. The well model according to the current invention is called</p>

The model of the well-lakh-zen is paired. The accompanying numerical solution is referred to as the completely implicit solution, the complete conjunction and the conjunction. The fully coupled and fully implied reservoir etc. model gives a proper flow rate along the borehole stage, as will be explained. As shown in Figure 4, the O storage model consists of a z number of i of discrete layers from 1 to Nz, each with a permeability kx,i, thickness Δzi, and voltage Φi

<p>25 Defined as shown in Figure 4, upper and lower layer 40 have low permeability</p>

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Relatively speaking, and having a land flow, there is above and below, respectively, a highly permeable insulated layer 42 that does not have a vertical connection to the flow with the other layers. As can be seen in Fig. 4, the qi production rates for layer i of the O model are determined by the expression shown in Fig. 4.

The well model of perfectly coupled and implied reservoir V is presented in Fig. 5 in Equation No. 20

<p>5 It is presented here also in the form of a matrix for further explanation:</p>

^ARR

AWR

ARW   pR AWW   pw

^b_R

^b_w

)21(

The present invention is based on the fact that the downhole pressure of a layered reservoir with a ground well is the same as the system according to the present invention. The system according to the current invention consists of identifying flow barriers and grouping them together or merging them for the purpose of treating the layers of the reservoir around the well that are connected to each other in the direction

<p>10 the rc. Care must be taken according to the present invention when configuring the reducer system. The system must be configured</p>

properly reducer, or otherwise errors in the configuration of the reduced system can increase the total number of nonlinear Newton iterations.

The system is resolved according to the present invention to obtain the downhole pressure. The solution is implemented by treating the well as the specified downhole pressure. The action is entirely implied; However, it is not a temporary solution. instead of

<p>15th So, the solution is sequential. The method of the present invention is an asymptotic method because it is part of the simulator's overall iteration of Newton. Therefore, if the model according to the present invention is constructed correctly, any possible error in the calculation rate will be small and will vanish with the Newtonian iterations of the simulator.</p>

Flow diagram F (Fig. 11) shows the basic computerized processing sequence according to the present invention and the treatment approach that occurs in typical models of a fully implicit sequential well model to simulate 20 reservoirs in the present invention.

During step 200, the simulation begins by reading stock and production data. Data etc. Stock and production

The ones read in step 200 are of the type previously discussed. The simulator is also initialized

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etc. Balance during step 200, giving simulation day and time step the number zero. During step 202 the time step is incremented by one, and the iteration counter is set for the number of nonlinear iterations completed during the current time step to equal zero.

During step 204, a Jacobian matrix for the store data is created. In step 206, a system is created

<p>5 A reducer such as that defined by the aforementioned R model according to the present invention and the matrix for downhole voltage Φw is solved in the manner previously explained. During step 208, the modified linear system matrix A according to the present invention is solved by the method previously described.</p>

Figure 15 shows the method for constructing the reduced-well model system matrix R and the solution to obtain the downhole voltage Φw according to steps 204 and 206 in Fig. 11. As shown in step 10 210, bed flow baffles are defined in an original well model system. This can be done based on

The data of the well log or with the specifications set by the storage analyzer from the data in the original stockpile form.

After steps 210, a reduced well model system is then configured by Data Processing System D during step 212. These layers are incorporated into the well model and are placed between the 15 flow barrier layers and have ground flow together for the purpose of the analytical model.

Then, during step 214, the resulting reduced well model system is solved by computer processing for downhole voltage Φw and reservoir unknowns using the techniques previously discussed in equations (17), (17a), and (17b). Step 216 then solves using a process system D Data The structural matrix of the entire well model system of Equation (27) using a direct solution method or other technique.

<p>20 appropriate from the previously described techniques. The completion rates qi and the total well flow rate qT are then determined using the data processing system D based on the results of step 216.</p>

Referring back to Figure 11, during step 220, a convergence step is performed to determine whether the nonlinear frequencies converge or not. The residuals of the equations resulting from step 216 are checked individually against the tolerances specified by the user. If you these disparities

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Accepted, the nonlinear iteration loop is exited, the solution output is written to the current time step file and the processing process returns to step 202 for the time step to be submitted, and is processed for the time incremented time step as shown. If the user-defined tolerances are determined to be unsatisfactory during step 208, the processing process returns to the unsatisfactory iteration loop.

<p>5 Linear to step 204 and continue working. If the number of nonlinear iterations becomes too large, a decision may be required to modify the model.</p>

Horizontal wells:

Figure 19 shows a 300 horizontal well oriented in the y direction in a three-dimensional storage model H.

The H model according to Fig. 19 is like Fig. 6, a definite difference grid, but for a horizontal well 300. Well 10 300 is located in the middle of the central cell in each of the subterranean Formation 304 segments sequence in the y direction extending

In vertical planes or in the z direction. Figures 24a and 24b show symbols for grid cells in a horizontal parietal pattern H according to Figure 19. As shown in Figure 19, well 300 is completed in the horizontal or y direction through the Ny cells, and the voltages in the adjacent cells are:

ΦΒ^,ΦΒ,ΦB^^,ΦΒ

<p>15th They are constants and are known from the extent of the simulation (previous time step or repetition value). Bottom B indicates the boundary, Up indicates the top neighborhood, E indicates the eastern neighborhood, down indicates the bottom neighborhood, and W indicates the western neighborhood, with Φ describing again Fluid voltage or corrected reference pressure.In Fig. 19, well 300 extends horizontally along the longitudinal axis through each of the sequence of mesh blocks 302 in the y direction.</p>

<p>20 Known, qT is an input into a reservoir simulation, and the reservoir simulator's calculations of voltage values ​​Φ for each time step for each 302 grid block are shown in Figure (19).</p>

As will be shown, the present invention improves the performance of the computer as a buffer simulator in forming measurements of the perforation rate of the layers which are added to the known overall rate qT.

Similar to equation (16), the hole rate qi for each network block can be expressed as:

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<p>(29) («-)g</p>

In equation (29), the yield factor is adjusted by

<p>(30) (///)</p>

7=9

2 )=0

<img file="SA8656B1_D0002.tif" />

The term reservoir variables and their physical relationships above are according to Chen and Zhang, "well flow models of various numerical methods". International Journal of Numerical Analysis and Modeling, Volume 6, Issue 3, pp. 378-388.

<p>10 Collectively, Figures 21 and 22 represent a G flow map showing the basic computer processing sequence according to the present invention and the computational methodology that takes place during a typical embodiment of a fully implicit sequential well model for horizontal well models, such as shown in Figure (19) for reservoir simulation using the present invention. During step 400, the simulation begins with initialization of tank model H in data processing system D and reading of tank and production data. Reservoir and production data read during step</p>

<p>15th 400 is of the above discussed types of vertical well models in relation to the flowchart F and step 200 (Fig. 11).</p>

During step 400 the estimation of the k cell voltages is made for the horizontal well model H. As shown schematically in Fig. 19,002 = k. During step 402, the estimate for the well effort is made according to equation (32) as shown below:

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∑PIiΦi q_t

-

^∑PIi∑PIi )32(

Φw

where Φ in equation (32) is calculated from the initial voltage distribution specified in step 400.

During step 404, perforation rates for each cell I are determined according to the relationship expressed in equation (29) above. In step 406, the buffer simulator is initialized and the simulator repeat counter is set

<p>5 υ to zero. The simulation time step t is also initialized to zero for an initial iteration. The iteration counter and time step counter, as will be explained below, are then incremented before step 406 is performed during subsequent iterations. The grid mass voltage of the initial time step is determined during step 406 by solving a three-dimensional voltage equation using a reservoir simulator according to equation (1) for a single-phase oil flow. During step 408 the boundary voltages are determined around each hole, B, ΦB,Up, ΦBW,</p>

<p>10 ΦB,Down, for each hole (i), for i = 1,2,Ny and stored in the memory of the data processing system D.</p>

Then step 410 is performed to form a reduced-well model 1-H (Figure 20b) by assembling grid blocks 302 with no flow baffles between them as shown at 306 in Figure 20a. To perform step 410, horizontal flow baffles are identified as shown at 303 in Original horizontal well model system H. This can be done based on well log data or by specification by a stock analyst from 15 data in the original stock model etc. The reduced well model system formed during step 410 leads to those layers 302 in the H well model which lie between the blocks of the buffer network or layers 303 and have a horizontal flow between them merging them together for the analytical purpose of the model.

As can be seen in the example from Figures 20a and 20b, the horizontal well model H transforms from Figure 20a with two sets of four mesh blocks 302 at opposite ends of the flow barrier mesh block 20 303 to the reduced-well model 1-H as a result of step 410, and the reduced-well model 1-H his

Two grid blocks 308, one on each side of block 303.

The reduced-well model equations for the 1-H reduced-well model system in Fig. 20b as illustrated in Fig. 20c become:

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<tr><td><p>^Tc1</p></td><td><p>^TE1</p></td><td><p>0</p></td><td><p>PI </p></td><td></td><td><p>_{ Φ}~ _{1 }</p></td><td colspan="2"><p>0</p></td><td></td></tr><tr><td><p> Tw2</p></td><td><p>T_C2</p></td><td><p>T_E2</p></td><td><p>PI2 </p></td><td><p>^</p></td><td><p>_Φ~ _</p></td><td><p>^</p></td><td><p>0</p></td><td></td></tr><tr><td><p>0</p></td><td><p>^Tw3</p></td><td><p>^TC3</p></td><td><p>PI</p></td><td><p>^</p></td><td><p>_Φ~_3</p></td><td><p></p></td><td><p>0</p></td><td></td></tr><tr><td><p>PI1</p></td><td><p>PI</p></td><td><p>PI</p></td><td><p>- PIT </p></td><td><p></p></td><td><p>^ΦW </p></td><td><p></p></td><td><p>qt</p></td><td><p>)18(</p></td></tr>

where ^{i=1 PIi} = ^{PI T}∑ .

Then, during step 410 (Fig. 22) the reduced well model for Φ2, Φ3 is solved^̃ , Φ1, and wΦ^̃, where Φ represents the grid mass potential of the 1-H reduced horizontal well model.

5 During step 412, the well model is converted to a horizontal downstream constant flow voltage using Φw. Step 414 includes a solution to the three-diameter matrix system of Figure 20c of the reduced horizontal well model 1-H shown in Figure 20b to quantify the voltages for each 302 mesh shown in Figure (19).

Referring back to Figure 22, during step 416, a convergence step is performed to determine if 10 nonlinear frequencies are converged. The remaining equations from step 414 . are checked

All on vs. user defined tolerances. If these tolerances are acceptable, the nonlinear iteration loop is exited and the solution outputs are written to a file and stored in the memory of the data processing system D for the current time step and the processing process returns to step 418 for the time step t to be presented, the incremented time step is processed and then Continue to step 406 as is

<p>15th explained. If the user-defined tolerances are determined to be unsatisfactory during step 416, the processing according to the nonlinear iteration loop returns to step 406 and continues. If the number of nonlinear iterations becomes too large, a decision may be required to adjust the model.</p>

Multiple ballistic wells

A three-dimensional reservoir model M is illustrated in Figure 23 with several 500 ballistic wells, each 20 with an assumed single-phase, slightly compressible oil flow. The M model is organized according to the convention in the notations shown schematically in Figures 25a, 25b, 25c and 25d.

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The M model according to Figure 23 is like Figure 6, a defined difference network, but for a number of vertical wells. Each of the 500 wells is located in the middle of a central cell in each of the sequences of 504 subterranean formation segments extending in the horizontally Z direction or in the y and y directions.

As in Figure 6, a well of 500 is completed in the vertical or Z direction through the 5 Nz cells, and the voltages in the adjacent cells:

,Oh,,

They are constants and are known from the simulation range (previous time step or repetition value). As in Figure 6, the low B indicates the boundary, No indicates the upper neighborhood, E indicates the eastern neighborhood, down indicates the below neighborhood, W indicates the western neighborhood, and with Φ again 10 describes the fluid voltage or corrected reference pressure.

Each 500 well runs vertically along the longitudinal axis through both a sequence of 502 grid blocks in direction 2, and in some formation layers at different depths each 500 well intersects by 506 completions. Figures 25 to 25 schematically illustrate the numbering features in Model M for 50 wells named as well 1 and well 2 in Fig. 23.

15th If the total well rate is known, 96, per 500 well is provided as an input variable to a reservoir simulator, and the reservoir simulator's calculations for each time step of the voltage values ​​for each 502 grid block are shown in Figure 23.

For a generalized case of a 3D vertical reservoir model M, the number of wells is represented by nw, the total well per well rates for 500 are given and indicated by 1 = a,() 81, and nw are 20 known from the production data and provided as input variables to the reservoir simulator .

Figure 26 represents a process flow map according to the present invention where there are several vertical wells, as in the M model of Figure 23. Thus, the initialization of the 3D vertical reservoir model M, in step 602, and the reservoir and production is read from memory for processing. This is done in a similar way to step

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200 In Figure 11. The simulation continues in 602 shown in Figure 26, where the estimate for the wellbore effort consists of Φ, 1 = 1, ^2, ...^ for each well according to Equation (32), with the PI determined according to for the measurements expressed in equation (17). During step 604, perforation rates are calculated,()_^ = 1,000^ per well, based on my estimate

<p>5 The wellbore efforts generated by step 602.</p>

Step 606 comprises shaping of reduced well models for each well 1,2,000 = i^ of a three-dimensional M multi-well model. The reservoir simulation is performed by summing or merging the 502 adjacent well cells of the formation layers that have fluid contact between each other and are also located Between layers of the flow barrier that have no flow through them. This is done in a way to layer 3D in a way like this

<p>10 Shown schematically in Figures 1A and 1B for the layers adjacent to a single vertical depression well, and in Figures 20A and 20B for the layers adjacent to horizontal flow wells.</p>

In step 608, the reduced well arrays are generated for each well based on the reduced well models that make up step 606, in a similar way to the reduced well matrix from Figure 20C for the horizontal well model H from Figure 19.

<p>15th Then, in step 610, the downhole voltage is determined,()^ = 1, 2,000^ per</p>

well by solving the reduced well matrices generated from step 608. In step 612, the diameter is adjusted _^,^̃ and the term _^ On the right side of the main matrix for each well according to the relationships according to equations 18, 18a and 18b mentioned above. Figure 27 is an example of a reduced well matrix diagram of a linear system of equations to simplify two wells, a 3D reservoir model, or

<p>20 Storage model 2 x 3 x 3 using the numbering system shown in Figures 24A and 24B and Figures 25A to 25D.</p>

During step 614, a complete matrix is ​​formed, like the example in Figure 27, of all 502 network blocks for unknowns of the M model. Then the processing continues after step 614 of Figure 26 to test for convergence

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By the method of step 416 of Figure 27 and the iteration step and time that are added back to step 602 for more iterations of treatment for the whole system including each of the nw wells.

Data processing system: As shown in Figure 16, a data processing system D according to the current invention contains a computer 240 with a processor 242 and memory 244 associated with a processor 242 to store

<p>5 Operating instructions, control information and database records. The computer 240 can, if desired, be a portable digital processor, such as a personal computer in the form of a laptop, or a microcomputer or other suitable digital data processing device programmed or not, such as a desktop computer. Also be aware that the 240 could be a multi-core processor with nodes like those manufactured by Intel Corporation or Advanced</p>

<p>10 Micro Devices (AMD), or any conventional mainframe computer with adequate processing capacity</p>

International Business Machines (IBM) of Armonk, NY such as those available at

or any other source.

The computer 240 has a user interface 246 and an output screen 248 to display the output data or the processing records of the well record data measurements executed according to the current invention to obtain measurements

<p>15th And the formation of models for the production of the specified well from the formation layers in the well or wells of underground formations. The output monitor 48 contains components such as a printer and an output display capable of providing printed output information or visual presentations in the form of graphs, spreadsheets, graphs, data charts and the like as records or output images.</p>

The user interface 246 to the computer 240 also contains another suitable user input device 20 or an I/O controller 250 to provide access for the user to control information

Login, database records and computer operation 240. Data processing system D also contains database 252 stored in computer memory, which can have 244 internal memory, external memory, network memory, or non-network memory as shown at 254 In a server suitable for database 256.

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The data processing system D includes program code 260 stored in non-transitional memory modules 244 for computer 240. Program code 260, according to the present invention in the form of computer-readable instructions, causes the data processor 242 to create a fully implicit sequential well model to simulate the reservoir according to For the current sister, the method previously explained.

<p>5 It should be realized that program code 260 can be microcode, programs, subprograms, or languages ​​interoperable by a token computer that provides a specific set of organized processes that control and direct the operation of the data processing system D. Program code instructions 260 can be stored in memory 244 for computer 240, or in a computer disk, magnetic tape, conventional hard disk drive, electronic read-only memory, optical storage device, or storage device</p>

<p>10 Other suitable data with a non-computer-usable transitional medium stored in it. Program code 260 may also be located in a data processing device such as Server 64 as a computer-readable non-transitional medium, as shown.</p>

Two illustrative issues for an example model are presented below: a seven-layer heterogeneous reservoir with one fault flow barrier (Fig. 7);

Seven-layer homogeneous well model

Figure 7A shows a storage with seven layers and properties of the original model 70 and a reduced model 71. As it is clear, it was assumed that the stock has seven layers. The thickness of the 72 tier of RC flow is 10 ft. Layer 73, which represents a fault without a land flow, is present and has a thickness of 1 foot. It was also assumed 20 that layer 73 does not connect with layers 72 above and below. It has been assumed that there is an anchored well in

center, as indicated by the arrow. The basic reservoir voltage (corrected reference pressure) is 3000 psi in the model in Fig. 7a. It is assumed that each layer 72 has 10 mDi kx and ky air permeability and 1 mDSA ground permeability kz.

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Table No. 1 summarizes the storage and network properties of Model 70. It was assumed that the network size in the direction of the area (square mesh) is 840 feet. The viscosity of the oil was set to be 1 cP and it was assumed that the oil formation volume factor was 1. The rate was set Oil production to be 1,000 bbl/d The PI layer yield factor was calculated to complete each layer using the Peaceman method, as described, which is

<p>5 Also shown in Table 1.</p>

Table No. 1: Problem No. 1 - Properties of Etc. Weight

<tr><td><p>Layer, PIb/day/psi</p></td><td><p>Kz,</p><p>Milli Darcy</p></td><td><p>Kx=ky,</p><p>Milli Darcy</p></td><td><p>fish feet</p></td><td><p>class</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>1</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>2</p></td></tr><tr><td><p>12,14</p></td><td><p>9-10×1</p></td><td><p>10000</p></td><td><p>1</p></td><td><p>3</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>4</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>5</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>6</p></td></tr><tr><td><p>0,12</p></td><td><p>1</p></td><td><p>10</p></td><td><p>10</p></td><td><p>7</p></td></tr>

Fully implicit and fully coupled real-time solution

The matrix of equations is formed to solve the reservoir pressures and the downhole pressure in a similar way previously explained for equations (18-19) and as shown in Figure 13. It can be noted that there are only

10 8 unknowns (7 corrected reference stresses or stresses and downhole effort), and that the coefficients matrix is ​​not

Analytical. The system of linear equations can be solved in a direct way, such as removal by Gaussian method, for the unknown storage voltages (layer)^{, = , i} And the other unknown ^W .

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Results

Table 2 summarizes the calculated layer effort, well bed effort and layer flow rates (completion) for Model 70 in Figure 7a.

Table No. 2 - The exact solution to the original problem

<tr><td><p>average/day</p></td><td><p>Downhole (wellbore) effort, pounds per square inch</p></td><td><p>Voltage, pounds per square inch</p></td><td><p>class</p></td></tr><tr><td><p>166,67</p></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>1</p></td></tr><tr><td><p>166,67</p></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>2</p></td></tr><tr><td><p>0,0</p></td><td><p>1257,36</p></td><td><p>1257,37</p></td><td><p>3</p></td></tr><tr><td><p>166,67</p></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>4</p></td></tr><tr><td><p>166,67</p></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>5</p></td></tr><tr><td><p>166,67</p></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>6</p></td></tr><tr><td></td><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>7</p></td></tr>

5 From the calculated results we note that the calculated downhole effort

1257,36 =^ΦW Pounds per square inch.

Formation of the problem according to the present invention

According to the storage data in Table No. 1 and as shown in Figure 7A, there is only one layer

73 Arsia is not related to another class. Therefore, as shown in Figure 7b, . is combined

10 Layers 72 over fault layer 73 in a single layer according to the formula of the reduced well model according to the present invention. Similarly, layers 72 below layer 73 are merged into one layer. It is possible now

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Watch the reduced model with only three layers. The total number of unknowns is 4 as opposed to 8 in the full form.

Table No. 3 shows the characteristics of the reduced well model 71 formed according to the treatment with the current invention.

Table 3 - Reduced Well Model

<tr><td><p>PI, barrels/day/psi</p></td><td><p>Kz,</p><p>Milli Darcy</p></td><td><p>Kx=Ky,</p><p>Milli Darcy</p></td><td><p>fish feet</p></td><td><p>class</p></td></tr><tr><td><p>0,24</p></td><td><p>1</p></td><td><p>10</p></td><td><p>20</p></td><td><p>1</p></td></tr><tr><td><p>12,14</p></td><td><p>0</p></td><td><p>10000</p></td><td><p>1</p></td><td><p>2</p></td></tr><tr><td><p>0,40</p></td><td><p>1</p></td><td><p>10</p></td><td><p>40</p></td><td><p>3</p></td></tr>

5 The system of linear equations (Equation No. 20) for the reduced system still has an unstructured coefficient matrix, but has 50% fewer unknowns. In actual reservoirs, which have hundreds of layers and few baffles, reducing the size of the well model according to the present invention will Critical, for example, a reduced well model system model according to the present invention can account for 1 percent of the volume of the complete system.

10 Table 4 represents the results.

Table No. 4 - Results of the reduced system

<tr><td><p>Downhole (wellbore) effort, pounds per square inch</p></td><td><p>Voltage, pounds per square inch</p></td><td><p>class</p></td></tr><tr><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>1</p></td></tr><tr><td><p>1257,36</p></td><td><p>1257,37</p></td><td><p>2</p></td></tr>

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<tr><td><p>1257,36</p></td><td><p>2630,61</p></td><td><p>3</p></td></tr>

It can be seen that the calculated downhole effort is:

1257,36=^ΦW pounds per square inch

It is exactly equal to the calculated value of the full model.

The specific voltage of the well is the only information required for the next step. Then the well is treated as

5 Specific downhole pressure (voltage) model. CNC processing according to the procedure described in the matrix in Figure 14 and equations (16 and 18) followed by the calculation of the flow chart (layer rates) and the overall rate of the well. In Figure 14, the solid line represents the top diameter of the matrix TUp,i as defined by equation (11), and the solid line describes the bottom diameter of the matrix elements called Tup,i as also defined by equation (2). The central term TC,i is given

10 By equation (17a), the right-hand side of bi is defined by equation (17b).

The results are summarized in Table 5. It is noted that the calculated total well rate is exactly equal to the input value of 1000 bbl/day.

Table No. 5- Results for the whole system using the current invention

<tr><td><p>average/day</p></td><td><p>Voltage, pounds per square inch</p></td><td><p>class</p></td></tr><tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>1</p></td></tr><tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>2</p></td></tr><tr><td><p>0,0</p></td><td><p>1257,37</p></td><td><p>3</p></td></tr><tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>4</p></td></tr><tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>5</p></td></tr>

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<tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>6</p></td></tr><tr><td><p>166,67</p></td><td><p>2630,61</p></td><td><p>7</p></td></tr><tr><td><p>1000</p></td><td></td><td><p>Total</p></td></tr>

The results presented in Table 5 are the same as in Table (1) for the entire implied well model. The difference or error between the well rates for the calculated and entered well data was zero in this case and no further replicates were needed. This is due to the fact that the reservoir It was homogeneous and no magnification errors were made during the configuration of the short system.Matrix diameter elements and right side

5 It is the same as in Figure (14), meaning that the solid line representing the bottom diagonal of the matrix represents Tup,i as defined by equation (11), and the solid line representing the upper diagonal

The matrix represents the elements called TDown, i previously explained. The central term TC,i is defined by equation (17a) and the right-hand side bi is defined by equation (17b).

The PI limits that appear in Equation No. (17) are indicators of the hole productivity of a defined square network

10 as follows:

^{PIi = 2}π^kx,i ln(0.2Δⁱx / r )

where rw is the diameter of the wellbore.

Comparison with the implicit well model

In many reservoir simulators, semi-implied well models or implied well models are used.

<p>15th If the well formula is semi-implied but converts to explicit in the pressure variable, then this formula is converted to implicit well models. The implied well model for this problem is obtained by following the matrix processing procedure shown in Fig. 12 and equations (12-14). In Fig. 12, the boundaries TDown,i, TUp,i that appear on the diameter elements are defined by equation (11) , and TC, bi, and is determined by equation (14a) and equation (14b). Figure 8a shows the layers</p>

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The seven stocks and properties of an implicit well model 80 and Figure 8b and an implicit well model 81, with a structure similar to the model in Figures 7a and 7b. It is noted that it has been assumed that the storage has seven layers. The 82 layers each have a voltage Φ of 2,630 psi.

Layer 83, which represents a fault, which has also been assumed to not connect with layers 72 above and below

5 It has a voltage Φ of 1257 psi. It is assumed that there is a mooring well in the middle, as indicated by the arrow.

Figure 8a and 8b compare the results of the implicit and explicit models. The calculated perforation rates (layer) are summarized in Table 6.

Table 6 - Comparison of hole rates (layer) for different well models

10

<tr><td><p>Implicit method</p><p>Rate: Barrels/day</p></td><td><p>the new way</p><p>Rate: Barrels/day</p></td><td><p>Correct solution (completely implied instantaneous solution fully coupled) Average: barrels/day</p></td><td><p>class/</p><p>the hole</p></td></tr><tr><td><p>9,43</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>1</p></td></tr><tr><td><p>9,73</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>2</p></td></tr><tr><td><p>943,40</p></td><td><p>0,0</p></td><td><p>0,0</p></td><td><p>3</p></td></tr><tr><td><p>9,43</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>4</p></td></tr><tr><td><p>9,43</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>5</p></td></tr><tr><td><p>9,43</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>6</p></td></tr><tr><td><p>9,43</p></td><td><p>166,67</p></td><td><p>166,67</p></td><td><p>7</p></td></tr>

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As can be seen, we see that model 81 according to the explicit method is an inaccurate model; It calculates the tracking rate completely wrong. The explicit modeling method allocates practically all the well production from the 83rd thin fracture layer as shown in Figure 8b considering that this layer has the largest productivity index.

<p>5 Implicit methods (whether it is the fully computationally intensive implicit computational model or the reduced model according to the present invention) do not implement such a referral, instead they specify that layer 83 does not get fluid support from the above and below 82 layers. The only fluid support is in a crack from this The type is shown as No. 83 when it is present in an actual reservoir it can be obtained from its adjacent planar cells.However, considering that the fault layer is a very thin layer, we find that the transition in these</p>

<p>10 Directions is by nature petite. Therefore, the fault layer cannot provide fluid at the rates simulated by the explicit model.</p>

In fact, implicit conventional models show that during the transition period fault layers support most of the well's production as do proper methods. However, the pressure at layer 83 drops rapidly and takes the value of the well-uniform effort (constant borehole bottom pressure). After the pressure drops, it reaches

<p>15th At steady state, the rate of production of the well is actually a contribution from the layers 82 above and below the 83 rc flow barrier.</p>

Heterogeneous storage model with 22 layers

Model of a 90 grid system containing 22 layers as shown in Figure 9. The position of high permeability fault layers 6 and 12 as calculated by moving down through the layer is shown

<p>20 Schematically numbers 91 and 92. There are five layers 93, numbered from 1 to 5, above layer 91, each with a ground flow. There are also five layers 94 in model 90 with a ground flow between the flow barrier layers 91 and 92, and ten layers 95 with ground flow located below the flow barrier layer 92. Data etc. for the model 90 are shown in Table 7.</p>

Table No. 7- Storage data for the 22-layer problem

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<tr><td><p>ground permeability,</p><p>Kz, Milli Darcy</p></td><td><p>Permeability, mD</p><p>(Kx=Ky)</p></td><td><p>fish feet</p></td><td><p>class</p></td></tr><tr><td><p>2</p></td><td><p>2</p></td><td><p>10</p></td><td><p>1</p></td></tr><tr><td><p>1</p></td><td><p>5</p></td><td><p>10</p></td><td><p>2</p></td></tr><tr><td><p>3</p></td><td><p>3</p></td><td><p>10</p></td><td><p>3</p></td></tr><tr><td><p>5</p></td><td><p>10</p></td><td><p>10</p></td><td><p>4</p></td></tr><tr><td><p>4</p></td><td><p>5</p></td><td><p>10</p></td><td><p>5</p></td></tr><tr><td><p>9-10×1</p></td><td><p>1000</p></td><td><p>1</p></td><td><p>6</p></td></tr><tr><td><p>6</p></td><td><p>6</p></td><td><p>10</p></td><td><p>7</p></td></tr><tr><td><p>3</p></td><td><p>3</p></td><td><p>10</p></td><td><p>8</p></td></tr><tr><td><p>6</p></td><td><p>9</p></td><td><p>10</p></td><td><p>9</p></td></tr><tr><td><p>2</p></td><td><p>12</p></td><td><p>10</p></td><td><p>10</p></td></tr><tr><td><p>5</p></td><td><p>5</p></td><td><p>10</p></td><td><p>11</p></td></tr><tr><td><p>9-10×1</p></td><td><p>1000</p></td><td><p>1</p></td><td><p>12</p></td></tr><tr><td><p>3,5</p></td><td><p>7,5</p></td><td><p>10</p></td><td><p>13</p></td></tr><tr><td><p>3,5</p></td><td><p>7,5</p></td><td><p>10</p></td><td><p>14</p></td></tr><tr><td><p>3,5</p></td><td><p>7,5</p></td><td><p>10</p></td><td><p>15</p></td></tr><tr><td><p>3,5</p></td><td><p>7,5</p></td><td><p>10</p></td><td><p>16</p></td></tr>

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<tr><td><p>3,5</p></td><td><p>7,5</p></td><td><p>10</p></td><td><p>17</p></td></tr><tr><td><p>1,2</p></td><td><p>9,2</p></td><td><p>10</p></td><td><p>18</p></td></tr><tr><td><p>1,2</p></td><td><p>9,2</p></td><td><p>10</p></td><td><p>19</p></td></tr><tr><td><p>1,2</p></td><td><p>9,2</p></td><td><p>10</p></td><td><p>20</p></td></tr><tr><td><p>1,2</p></td><td><p>9,2</p></td><td><p>10</p></td><td><p>21</p></td></tr><tr><td><p>1,2</p></td><td><p>9,2</p></td><td><p>10</p></td><td><p>22</p></td></tr>

Air permeability of the adjacent cell = 20 mm Darcy. Overall rate of production of the well = 2,500 barrels / day The well has been completed in all layers.

5 Results:

Fully implicit and fully coupled real-time solution

Calculated downhole effort 1421,247 = ^W pounds per square inch

Table 8 - Voltage distribution, psi

<tr><td><p>Φi</p></td><td><p>Φ_W</p></td><td><p>class</p></td></tr><tr><td><p>2901,32</p></td><td><p>1421,25</p></td><td><p>1</p></td></tr><tr><td><p>2900,82</p></td><td><p>1421,25</p></td><td><p>2</p></td></tr><tr><td><p>2900,38</p></td><td><p>1421,25</p></td><td><p>3</p></td></tr>

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<tr><td><p>2900,38</p></td><td><p>1421,25</p></td><td><p>4</p></td></tr><tr><td><p>2900,38</p></td><td><p>1421,25</p></td><td><p>5</p></td></tr><tr><td><p>1421,25</p></td><td><p>1421,25</p></td><td><p>6</p></td></tr><tr><td><p>2864,43</p></td><td><p>1421,25</p></td><td><p>7</p></td></tr><tr><td><p>2864,37</p></td><td><p>1421,25</p></td><td><p>8</p></td></tr><tr><td><p>2864,10</p></td><td><p>1421,25</p></td><td><p>9</p></td></tr><tr><td><p>2863,88</p></td><td><p>1421,25</p></td><td><p>10</p></td></tr><tr><td><p>2864,03</p></td><td><p>1421,25</p></td><td><p>11</p></td></tr><tr><td><p>1421,25</p></td><td><p>1421,25</p></td><td><p>12</p></td></tr><tr><td><p>2841,62</p></td><td><p>1421,25</p></td><td><p>13</p></td></tr><tr><td><p>2841,58</p></td><td><p>1421,25</p></td><td><p>14</p></td></tr><tr><td><p>2841,48</p></td><td><p>1421,25</p></td><td><p>15</p></td></tr><tr><td><p>2841,33</p></td><td><p>1421,25</p></td><td><p>16</p></td></tr><tr><td><p>2841,13</p></td><td><p>1421,25</p></td><td><p>17</p></td></tr><tr><td><p>2840,65</p></td><td><p>1421,25</p></td><td><p>18</p></td></tr><tr><td><p>2840,08</p></td><td><p>1421,25</p></td><td><p>19</p></td></tr><tr><td><p>2839,65</p></td><td><p>1421,25</p></td><td><p>20</p></td></tr><tr><td><p>2839,37</p></td><td><p>1421,25</p></td><td><p>21</p></td></tr>

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<tr><td><p>2839,24</p></td><td><p>1421,25</p></td><td><p>22</p></td></tr>

Model 90 was then subjected to explicit modeling techniques of the previously described type and data determination

Exchange. Comparison of the flow rate distribution with the fully implicit and explicit treatment of the stock 90 model using the previously explained techniques shown in Table 9.

Table 9 - Comparison of flow rates for fully implied and fully coupled well methods and methods

5 candid

<tr><td><p>sincere</p></td><td><p>implicit</p></td><td><p>class</p></td></tr><tr><td><p>14,56</p></td><td><p>35,93</p></td><td><p>1</p></td></tr><tr><td><p>36,39</p></td><td><p>89,78</p></td><td><p>2</p></td></tr><tr><td><p>21,83</p></td><td><p>53,85</p></td><td><p>3</p></td></tr><tr><td><p>72,78</p></td><td><p>179,48</p></td><td><p>4</p></td></tr><tr><td><p>36,39</p></td><td><p>89,74</p></td><td><p>5</p></td></tr><tr><td><p>727,80</p></td><td><p>0,00</p></td><td><p>6</p></td></tr><tr><td><p>43,67</p></td><td><p>105,09</p></td><td><p>7</p></td></tr><tr><td><p>21,83</p></td><td><p>52,54</p></td><td><p>8</p></td></tr><tr><td><p>65,50</p></td><td><p>157,60</p></td><td><p>9</p></td></tr><tr><td><p>87,34</p></td><td><p>210,10</p></td><td><p>10</p></td></tr><tr><td><p>36,39</p></td><td><p>87,55</p></td><td><p>11</p></td></tr><tr><td><p>727,80</p></td><td><p>0,00</p></td><td><p>12</p></td></tr>

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<tr><td><p>54,59</p></td><td><p>129,29</p></td><td><p>13</p></td></tr><tr><td><p>54,59</p></td><td><p>129,28</p></td><td><p>14</p></td></tr><tr><td><p>54,59</p></td><td><p>129,28</p></td><td><p>15</p></td></tr><tr><td><p>54,59</p></td><td><p>129,26</p></td><td><p>16</p></td></tr><tr><td><p>54,59</p></td><td><p>129,24</p></td><td><p>17</p></td></tr><tr><td><p>66,96</p></td><td><p>158,49</p></td><td><p>18</p></td></tr><tr><td><p>66,96</p></td><td><p>158,42</p></td><td><p>19</p></td></tr><tr><td><p>66,96</p></td><td><p>158,37</p></td><td><p>20</p></td></tr><tr><td><p>66,96</p></td><td><p>158,34</p></td><td><p>21</p></td></tr><tr><td><p>66,96</p></td><td><p>158,33</p></td><td><p>22</p></td></tr>

Create the reduced form

Since there are two LFT layers 91 and 92, layers 93 above layer 91 in Figure 9 can be combined into a single layer; and layers 94 below layer 91 in one layer,

5 And layers 95 are below layer 92 in one more layer. Therefore, the total number of layers according to the current invention is 5. The properties of the reduced model are as follows:

Table 10 - Characteristics of the reduced well model

<tr><td><p>PI . ratio</p></td><td><p>PI, barrels/day/psi</p></td><td><p>Kz, Milli Darcy</p></td><td><p>Kx, Milli Darcy</p></td><td><p>fish,</p><p>Foot</p></td><td><p>class</p></td></tr>

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<tr><td><p>0,07</p></td><td><p>0,3</p></td><td><p>2,19</p></td><td><p>5</p></td><td><p>50</p></td><td><p>1</p></td></tr><tr><td><p>0,29</p></td><td><p>1,21</p></td><td><p>0</p></td><td><p>1000</p></td><td><p>1</p></td><td><p>2</p></td></tr><tr><td><p>0,10</p></td><td><p>0,42</p></td><td><p>3,66</p></td><td><p>7</p></td><td><p>50</p></td><td><p>3</p></td></tr><tr><td><p>0,29</p></td><td><p>1,21</p></td><td><p>0</p></td><td><p>1000</p></td><td><p>1</p></td><td><p>4</p></td></tr><tr><td><p>0,24</p></td><td><p>1,01</p></td><td><p>1,79</p></td><td><p>8,35</p></td><td><p>100</p></td><td><p>5</p></td></tr>

Calculated downhole effort

1421,34 = ^ΦW pounds per square inch

The reduced model according to the present invention shows the downhole voltage Φw. The results of the five-layer reduced model are shown below in Table 11.

5 Table No. 11 - Voltage Distribution:

<tr><td><p>Effort</p></td><td><p>Φ_W</p></td><td><p>class</p></td></tr><tr><td><p>2900,53</p></td><td><p>1421,34</p></td><td><p>1</p></td></tr><tr><td><p>1421,35</p></td><td><p>1421,34</p></td><td><p>2</p></td></tr><tr><td><p>2864,16</p></td><td><p>1421,34</p></td><td><p>3</p></td></tr><tr><td><p>1421,35</p></td><td><p>1421,34</p></td><td><p>4</p></td></tr><tr><td><p>2840,61</p></td><td><p>1421,34</p></td><td><p>5</p></td></tr>

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Using the downhole effort Φw computed from the reduced model and calculating the efforts using the specific downhole pressure for the whole model, the completion layer rates are calculated according to equation (17). The results are shown in Table 12.

Table No. 12 - Calculated Well Layer Rates

<tr><td><p>The complete method of conjugation</p></td><td><p>the new way</p></td><td><p>class</p></td></tr><tr><td><p>35,93</p></td><td><p>35,92</p></td><td><p>1</p></td></tr><tr><td><p>89,78</p></td><td><p>89,78</p></td><td><p>2</p></td></tr><tr><td><p>53,48</p></td><td><p>53,85</p></td><td><p>3</p></td></tr><tr><td><p>179,47</p></td><td><p>179,47</p></td><td><p>4</p></td></tr><tr><td><p>89,73</p></td><td><p>89,73</p></td><td><p>5</p></td></tr><tr><td><p>0,00</p></td><td><p>0,00</p></td><td><p>6</p></td></tr><tr><td><p>105,09</p></td><td><p>105,09</p></td><td><p>7</p></td></tr><tr><td><p>52,54</p></td><td><p>52,54</p></td><td><p>8</p></td></tr><tr><td><p>157,60</p></td><td><p>157,59</p></td><td><p>9</p></td></tr><tr><td><p>210,10</p></td><td><p>210,09</p></td><td><p>10</p></td></tr><tr><td><p>87,55</p></td><td><p>87,55</p></td><td><p>11</p></td></tr><tr><td><p>0,00</p></td><td><p>0,00</p></td><td><p>12</p></td></tr><tr><td><p>129,29</p></td><td><p>129,28</p></td><td><p>13</p></td></tr><tr><td><p>129,2</p></td><td><p>129,28</p></td><td><p>14</p></td></tr>

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<tr><td><p>129,28</p></td><td><p>129,27</p></td><td><p>15</p></td></tr><tr><td><p>129,26</p></td><td><p>129,25</p></td><td><p>16</p></td></tr><tr><td><p>129,24</p></td><td><p>129,24</p></td><td><p>17</p></td></tr><tr><td><p>158,49</p></td><td><p>158,48</p></td><td><p>18</p></td></tr><tr><td><p>158,42</p></td><td><p>158,41</p></td><td><p>19</p></td></tr><tr><td><p>158,37</p></td><td><p>158,37</p></td><td><p>20</p></td></tr><tr><td><p>158,34</p></td><td><p>158,33</p></td><td><p>21</p></td></tr><tr><td><p>158,33</p></td><td><p>158,32</p></td><td><p>22</p></td></tr>

Newly calculated qt = 2499.84 barrels/day

Error = 2500 – 2499,8488

= 0.15 barrels/day

The error disappears in the overall rate and bottom pressure calculated using the Carart Newton's simulator

<p>5 linear. The present invention presents a reduced model with a reasonably accurate production rate in comparison with the results obtained with fully implicit techniques, and fully coupled processing according to the previous technique, but with a significant reduction in model complexity and computer processing time.</p>

The present invention, as described above, does not require a special linear solving method for solving the associated reservoir and well equations. In contrast, the coefficient matrix of the previously used paired storage to

<p>10 The well equations have no ordinary scattered structure. Therefore, traditional types of reservoir and well coupling equations require special solving methods that can be costly and can also encounter convergence problems.</p>

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As explained above, it can be noted that the present invention does not require any special solution method in order to solve the associated equations for reservoir and well. It uses the same method as the solution used in the equations etc. The only adjustment made to the coefficient matrix is ​​within the diameter.

The present invention solves reservoir simulation problems where completion works can be found in land-based wells

<p>5 Many, which is common in safes etc. In recent well simulation studies, wells with more than 100 bed layers (completions) are very common. A fully coupled and fully implied well model with simultaneous solution is very expensive for these cases. The present invention can save long periods of computer time.</p>

The current invention is very useful for ^bars that have hundreds of holes completed in tanks with 10 large heterogeneities. The present invention reduces the significant problem of well simulation models

time consuming storages with large numbers of layers (completions) and turning it into a small problem by validation and utilization using relevant physical principles. With the present invention, it is shown that asymmetrically connected layers can be combined into a single layer. The formed reduced model maintains this The method is at the same downhole pressure as the original full model.Once the downhole Model 15 is resolved, the wells in the larger system are treated as specific downhole pressure and resolved

easily by means of a conventional linear solution. Thus, the present invention eliminates the need to write or have unstructured linear solving methods for many wells with hundreds of completions that would be costly.

The invention is described sufficiently that a person of average knowledge in these matters can

<p>20 Frequently obtains the results mentioned in the present invention. Notwithstanding this, any person with experience in the field, subject of the present invention, may make modifications not described herein, to apply such modifications to a specific composition, or to the manufacturing process itself, which requires the subjects in the following claims; These formulations are within the scope of the invention.</p>

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It should be noted and understood that there are improvements and modifications that can be made to the current invention described in detail above without deviating from the spirit or scope of the invention as provided in the accompanying claims.

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