KR101657890B1

KR101657890B1 - Economic analysis of production rate of reservoir using multi-objective genetic algorithm and real option

Info

Publication number: KR101657890B1
Application number: KR1020150048233A
Authority: KR
Inventors: 강주명; 문동호
Original assignee: 서울대학교산학협력단
Priority date: 2015-04-06
Filing date: 2015-04-06
Publication date: 2016-09-20

Abstract

According to an embodiment of the present invention, there is provided a method of evaluating the productivity of a reservoir, comprising the steps of: (a) applying a multipurpose genetic algorithm to initial condition data and production history data on a reservoir layer to obtain m (m is an integer of 2 or more) ; (b) calculating m prediction results of resource production over time using each of the reservoir models; (c) calculating a net present value (NPV) based on each of the m production yield prediction results for each of the k (where k is an integer equal to or greater than 2) scenarios regarding the presence or absence of additional drilling in the reservoir ; (d) calculating variability (?) based on the calculated net present value (NVP); And (e) for each of the k scenarios, calculating a present value C of the real option.

Description

[0001] The present invention relates to a multi-objective genetic algorithm and a real option,

The present invention relates to a method for evaluating the productivity of a reservoir, and more particularly, to a method for evaluating the productivity of a reservoir based on a multipurpose genetic algorithm and a real option.

In the production of energy resources such as oil and natural gas, it is necessary to accurately predict future resource production from data such as reservoir geological data and past actual production history. Static data and dynamic data are used to predict the yield. Static data are data obtained by analyzing characteristics such as porosity and fluidity from samples taken from a reservoir to analyze the geological structure of the reservoir. Dynamic data is the production history of resources actually produced in the reservoir.

There is a difference between the estimated and actual values of production for each well in the reservoir. Therefore, as shown in FIG. 1, the predicted production amount can be fed back to the optimization algorithm and dynamic data such as the actual production amount can be input to the optimization algorithm to more accurately predict the production amount. Thus, it is called history matching that static data and dynamic data are integrated to more precisely model the structure of the ground and reduce the prediction error of the production amount.

On the other hand, there is a need to estimate the asset value of the reservoir by estimating the future production of the reservoir. In the past, the net present value (NPV) of the reservoir was calculated to evaluate the asset value. However, the asset valuation of reserves through NPV has a disadvantage that it is difficult to effectively reflect the various risk factors associated with the business and the resulting volatility of the decision-making process due to the deterministic assumption of future cash flows.

Patent Document: Korean Patent Laid-Open Publication No. 2014-0137210 (published on December 02, 2014)

According to an embodiment of the present invention, an optimization method for additional well drilling is proposed by combining the multipurpose history matching and the real option evaluation.

According to an embodiment of the present invention, there is provided a method for evaluating the productivity of a reservoir using a computer, comprising the steps of: (a) applying a multipurpose genetic algorithm to initial condition data and production history data for a reservoir, Constant) reservoir model; (b) calculating m prediction results of resource production over time using each of the reservoir models; (c) calculating a net present value (NPV) based on each of the m production yield prediction results for each of the k (where k is an integer equal to or greater than 2) scenarios regarding the presence or absence of additional drilling in the reservoir ; (d) calculating variability (?) based on the calculated net present value (NVP); And (e) for each of the k scenarios, calculating a present value C of the real option.

According to another aspect of the present invention, there is provided a computer-readable recording medium having recorded thereon a program for causing a computer to perform the method of evaluating the productivity of the reservoir.

According to the embodiment of the present invention, the productivity of the reservoir is evaluated according to the multipurpose history matching and the real option evaluation method, thereby improving the expected profit of the reservoir as much as the option premium compared to the conventional net present value method. Therefore, it is possible to reduce the uncertainty of the economic analysis and increase the flexibility of decision making by combining the analysis of the production of the reservoir and the real option evaluation method.

FIG. 1 is a conceptual diagram for explaining history matching for predicting resource production of a reservoir,
FIG. 2 is a conceptual diagram illustrating a reservoir scenario for evaluating reservoir productivity in accordance with an embodiment;
3 is an exemplary flow chart of a method for evaluating the productivity of a reservoir according to one embodiment,
4 is a diagram for explaining a genetic algorithm-II (NSGA-II) according to an embodiment,
5 is a diagram for explaining a non-dominant alignment method,
6 is a view for explaining a cluster distance sorting method,
FIG. 7 is an exemplary flow chart of the reservoir model generation step (SlO) of FIG. 3,
8 is a diagram for explaining parameters used in the NSGA-II algorithm,
FIG. 9 is a diagram for explaining variables when a real option is applied to a reservoir scenario,
FIGS. 10A and 10B are diagrams for explaining a binomial lattice model,
FIG. 11 is an exemplary flow chart of step S50 of calculating the present value of the real option of FIG. 3;
12 is a diagram for explaining a method of calculating an underlying asset according to a lattice model,
13 is a view for explaining a retention layer model according to an experimental example,
14 is a diagram for explaining parameters used in an experimental example,
15 is a view for explaining a reservoir scenario used in an experimental example,
16 is a view for explaining parameters used in a reservoir scenario in an experimental example,
17 is a view for explaining NPV parameters used for reservoir productivity evaluation,
18 is a view for explaining an ROV parameter used for reservoir productivity evaluation,
19 is a view showing the result of evaluation of the reservoir productivity according to the conventional method,
FIG. 20 is a diagram showing an exemplary result of a reservoir productivity evaluation according to an embodiment;
FIG. 21 is a view for explaining a comparative result of a reservoir productivity evaluation result according to a conventional method and an embodiment of the present invention; FIG.
22 is a block diagram for explaining an exemplary system configuration for evaluating the productivity of a storage layer according to an embodiment.

BRIEF DESCRIPTION OF THE DRAWINGS The above and other objects, features, and advantages of the present invention will become more readily apparent from the following description of preferred embodiments with reference to the accompanying drawings. However, the present invention is not limited to the embodiments described herein but may be embodied in other forms. Rather, the embodiments disclosed herein are provided so that the disclosure can be thorough and complete, and will fully convey the scope of the invention to those skilled in the art.

In the present specification, when an element is referred to as being on another element, it may be directly formed on another element, or a third element may be interposed therebetween.

Where the terms first, second, etc. are used herein to describe components, these components should not be limited by such terms. These terms have only been used to distinguish one component from another. The embodiments described and exemplified herein also include their complementary embodiments.

In the present specification, the singular form includes plural forms unless otherwise specified in the specification. The terms "comprise" and / or "comprising" used in the specification do not exclude the presence or addition of one or more other elements.

Hereinafter, the present invention will be described in detail with reference to the drawings. Various specific details are set forth in the following description of specific embodiments in order to provide a more detailed description of the invention and to aid in understanding the invention. However, it will be appreciated by those skilled in the art that the present invention may be understood by those skilled in the art without departing from such specific details. In some cases, it is noted that parts of the invention that are not commonly known in the art and are not largely related to the invention are not described in order to avoid confusion in describing the invention.

2 is a conceptual diagram illustrating a reservoir scenario for evaluating reservoir productivity in accordance with an embodiment. Referring to the drawings, it is assumed that a well is already drilled in a reservoir shown by a dotted line in FIG. 2 to develop resources in the following embodiment. Where 'resources' may include, for example, oil, gas, and water. In the embodiment of the present invention, it is assumed that two wells W1 and W2 are installed in the reservoir to produce resources, and further one well W3 is further drilled in the reservoir. There are three candidate locations as installation positions of the oil well W3 to be added at this time, and the first candidate W3-1, the second candidate W3-2, and the third candidate W3-3 Respectively.

It is also assumed that the time point at which drilling of the additional well W3 is started may be any time between the third and 10th years after the start of the first production of the reservoir by the existing wells W1 and W2 do. For example, if a year is divided into 3 years to 10 years, there are a total of 8 cases. Therefore, according to the embodiment of the present invention, 24 drilling scenes (i.e., [3 candidates] X [8 drilling points] = 24). Accordingly, the present invention provides a method for assessing productivity for each scenario and determining when to drill further in a reservoir.

3 is an exemplary flow chart of a method for evaluating the productivity of a reservoir according to one embodiment.

Referring to FIG. 3, in step S10, m (m is an integer of 2 or more) reservoir model is generated by applying a multipurpose genetic algorithm to initial condition data and production history data about a reservoir layer. In one embodiment, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is used as a multipurpose genetic algorithm. As an example of using NSGA-II, a number of objective functions used for production history history matching are set up, and then NSGA-II is used to set the desired aspiration level Select solutions. NSGA-II calculates the cluster distance for each solution of the objective function by assigning rankings for each year by non-dominant sorting for convergence and cluster distance sorting for diversity. Then optimal settlement models can be generated by selecting the solution based on the rank and cluster distance of each solution.

In one embodiment, the early conditions relating to the reservoir layer may include, for example, data regarding reservoir and fluid as shown in FIG. Production history data may include production data such as oil, gas, and water produced in the reservoir.

Also, at least some of the genetic algorithm parameters of FIG. 8 and / or the history matching and prediction data of FIG. 14 may be input to the multipurpose genetic algorithm for history matching using a multipurpose genetic algorithm. And, the objective function in this multi-objective genetic algorithm can be a function of resource production in the reservoir and can include, for example, functions relating to the reservoir oil production, gas production, and water production as in FIG. Such data or parameters will be described later with reference to Figs. 8 and 14, respectively.

Referring again to FIG. 3, a plurality of reservoir models are generated at step S10, and at step S20, each reservoir model is used to predict resource production over time. That is, the reservoir model generated in step S10 is input to the reservoir simulator to calculate a predicted value of future resource production.

For example, if 47 reservoir models are generated by the multipurpose genetic algorithm in step S10 (i.e., m = 47), these models are input to the reservoir simulator, respectively, to obtain 47 production yield predictions.

Thereafter, for each of the k (where k is an integer equal to or greater than 2) scenarios regarding whether or not to drill additional oil wells in the reservoir, a net present value (NPV ). For example, if there are 24 scenarios (ie, k = 24) depending on the number of additional drilling candidates and drilling times, it is assumed that there are 47 models in each scenario, so a total of 1,175 47X24 + 47), the NPV is calculated. The NPV for each scenario can be obtained by discounting the future production amount calculated in step S20 by the present value at each point in time, and the method of calculating the NPV is known, so the explanation is omitted.

Next, in step S40, the variability? Is calculated based on the net present value (NPV) calculated in the above step S30. In one embodiment of the present invention, various methods for estimating volatility are known, and in one embodiment of the present invention, the method proposed by Copland and Antikarov (2001, Real Options, NY: Texere) We then use the method to determine the variability from the standard deviation of NPV. In the case of the above example, if there are 25 scenarios in total (24 scenarios for additional drilling + 1 scenario for non-drilling), variability can be calculated based on NPV for each reservoir model for each scenario.

Then, at step S50, the present value C of the real option is calculated for each of the reservoir models of the entire scenario. In one embodiment, a binomial-lattice option valuation (BLOV) model may be used to determine the present value of an option. When using the BLOV model, future cash flows (or underlying assets), investment costs, volatility, and interest rates can be applied to this model to calculate the present value of options. This will be described later with reference to Figs. 9 to 12.

When the current value C of the real option is calculated for each of the reservoir models of the respective scenarios in this manner, at step S60, based on the present value C of the real option, the scenario having the largest real option price is selected . In an embodiment, since there are m reservoir models for each scenario, the expected profit of the present value C of the real option is calculated using the present value C of the real option of m reservoir models for each scenario, A scenario in which the expected return is the largest can be presented to the user.

(S10 in Fig. 3) of generating a plurality of reservoir model using non-dominant sorted genetic algorithm-II (NSGA-II) with reference to Figs. 4 to 8 below.

Non-dominant Sort Genetic Algorithm ( NSGA -II)

4 is a diagram for illustrating a non-dominant sorted genetic algorithm-II (NSGA-II) according to one embodiment. Generally, a genetic algorithm is one of the representative methods for solving the optimization problem, and is a type of evolutionary computation that imitates the evolution of living things. Genetic algorithms are algorithms that approximate the optimal solutions for the problem (objective function) to be solved by a data structure of a given type, and then access the most optimized solution by repeating the search of these solutions.

4, a population N of solutions of the current generation (i.e., the i-th generation) for a given objective function becomes the parent solution Gp, and a crossover from the parent solution Gp is obtained. And the same number of descendant solutions Go are generated by the mutation.

(E.g., non-dominated sorting) for a mating pool (Gp∪Go) having a size of 2N summing the parent solution (Gp) and the descendant solution (Go) Each solution is assigned to non-dominated fronts F1, F2, ..., Fn. Here, the number of front means the priority to be selected as the parent of the next generation. Solutions from the first face (F1) to the i-th face (Fi) are sorted, respectively, until the number of accumulated solutions is equal to or greater than N.

A second classifier (e.g., crowding distance sorting) then truncates the solutions to Fi based on the adjacency of each solution to select the population (N) for the next generation. The solutions of the selected number of individuals (N) become the parents of the next generation, that is, the (i + 1) th generation. By repeating the above procedure, it becomes possible to gradually find an optimal solution to the objective function.

Non-dominant Non-dominated sorting

5 is a diagram for explaining a non-dominant alignment method of NSGA-II. In general, the multi-objective optimization problem deals with optimization in the case where there are a plurality of objective functions. However, FIG. 5 shows a case where only two objective functions f1 and f2 exist for convenience of explanation, Alignment.

In the figure, the x-axis represents the fitness for the objective function (f1) of each solution and the y-axis represents the fitness for the objective function (f2) of each solution. Here, "fitness" is a numerical value indicating how appropriate solutions each solution is to each objective function (f1, f2) according to a preset fitness function, and is an "objective function value" or an " objective value & It is also called. That is, FIG. 5A shows the solutions distributed on the two-dimensional plane according to the objective function values for the objective functions f1 and f2 of the respective solutions. In the example of FIG. 5A, the smaller the objective function value, the more suitable the objective function.

5, when comparing P (x1) and Q (x2) represented by black circles, P (x1) is not a good solution to the objective function f1 but is good for the objective function f2 (X2) is an appropriate solution of the objective function (f1), but it is not suitable for the objective function (f2). In other words, P (x1) and Q (x2) are equivalent relations which are difficult to evaluate the superiority when considering the two objective functions (f1, f2) at the same time. In this way, the two-year relationship, which is difficult to evaluate, is defined as a non-dominated relationship.

The non-dominant sorting algorithm sorts and ranks the solutions in non-dominant relations. For example, in FIG. 5, solutions of black circles including P (x1) and Q (x2) are solutions that are in a non-dominant relationship with each other, and assign a first rank to these solutions. Solutions of the gray squares p1 and q1 are in a non-dominant relation to each other, but inferior to the solutions of the first order (P (x1) and Q (x2)) and governed by the solution of the first order. Therefore, solutions of gray squares are assigned i-th (i> 1) ranks. Likewise, the solutions of the rhombus, p2 and q2, are non-dominant among each other, but are assigned to the nth (n> i) order because they are dominated by solutions in the ith order. Therefore, in general, the solution having the i-th rank is inferior to the solutions from the first rank (black circle) to the (i-1) th rank, but compared with the solutions from the (i + 1) great.

Crowding distance sorting

FIG. 6 is a view for explaining a cluster distance sorting method of NSGA-II. FIG. 6 shows only the first order solution (black circles) in FIG. Generally, the cluster distance is a numerical value of the distribution density of the population as defined by the following equation.

[Equation 1]

This equation represents the distance to the surrounding solutions for any solution lying on the same non-backplane as shown in FIG. Where σ ⁱ is the population distance of i objective function values, m is the total number of objective functions, d _k ⁱ is the objective distance between the objective function and (i + 1) objective function, f _k ^max is the maximum linear distance in the k objective function direction.

In the same Pareto optimal plane, f _k ^max is constant in each objective function direction, meaning that the objective function value with large cluster distance is far from the values located around the objective function value. Therefore, the diversity between the optimal solutions can be secured by comparing the cluster distance of each objective function value and selecting the cluster distance in order of the objective function value.

NSGA -II flow chart

FIG. 7 is a flowchart illustrating an exemplary step of creating a reservoir model (S10) using the NSGA-II algorithm described above.

First, an objective function of an initial population to be used for production history history matching is set in step S110. For example, in a reservoir model, the objective function may include an objective function of the production error for the oil production in the reservoir, an objective function for the production error for the gas production, and an objective function for the production error for the water production. In this case, as shown in FIG. 14, in one embodiment, the number of populations is 100, and the genetic algorithm can be applied over 10 generations, which may vary according to the embodiment.

Then, in steps S130 through S160, the solutions are selected based on the predetermined target level among the solutions of the objective functions using the NSGA-II. As a first step, in step S130, a descendent solution Go of a predetermined number of individuals is generated by crossing and / or mutating from a parent solution Gp of a predetermined number of individuals. In other words, genetic algorithm is used to reconstruct the variables from the initial population (parent solution) to generate the descendant solution. In this case, crossover and mutation are used according to the genetic algorithm. For this, crossover and mutation parameters can be set as shown in FIG. 14, respectively.

Next, in step S140, an objective function value is calculated for each of the whole solutions (i.e., all parent solutions and child solutions). In this step, the fitness of the solution is evaluated by calculating the objective function value for each objective function for all solutions.

Thereafter, in step S150, a rank is assigned to each year by non-dominant sorting, and the size of the cluster distance of each year is calculated by the cluster distance sorting. As described with reference to FIG. 5, first, a ranking is assigned to each solution by non-dominant sorting, and then the cluster distance of each solution is calculated for solutions as described with reference to FIG. Based on the rank and cluster distance size calculated in this step S150, a solution of the predetermined population to be a population of the next generation is selected in step S160.

The step S160 of calculating the cluster distance for each year by assigning the order of the solutions by the non-dominant sorting and the cluster distance sorting (S150) and selecting the solutions to be the population of the next generation is performed in step S160. (See steps S120, S170, and S180), and the solutions selected in step S160 in the last generation are selected as the final reservoir model.

Binomial lattice Option evaluation ( BLOV ) Present value of real option using model

Hereinafter, a method of calculating a present value of an option by applying a real option to a reservoir scenario will be described with reference to FIGS. 9 to 12. FIG.

FIG. 9 is a diagram for explaining variables when a real option is applied to a reservoir scenario. FIG. The variables used for the real option evaluation can be matched one-to-one with the variables used to evaluate the financial options. For example, as shown in FIG. 9, a real option for developing a reservoir corresponds to a call option of finance.

In the reservoir scenario, the net present value (NPV) may correspond to the underlying asset S of the financial option (eg, stock price). In general, the NPV can be expressed as a sum of values obtained by discounting the cash flow predicted at predetermined time intervals to the present value.

The drilling cost in the real option of the reservoir scenario corresponds to the running cost (X) in the gold option and the time to drilling in the real option corresponds to the maturity (T) of the financial option. The risk-free interest rate and volatility of real options can also respond to risk-free interest rates and volatility, respectively, in the gold option. The risk-free interest rate can be, for example, a three-year government bond interest rate.

There are several ways to determine volatility. In the embodiment of the present invention, a method proposed by Copeland & Antikarov 2001 is used. According to this, the variability (?) Is calculated one for each of the k scenarios, and each variability (?) Is calculated for each scenario. Assuming that there are 47 reservoir models in each scenario, as in the example above, volatility is calculated for each of the 47 reservoir models. As an example, the standard deviation of the annual cash flow of the future NPV in each reservoir model can be set to the variability of the corresponding reservoir model, and thus the variability can be calculated for each reservoir model.

FIGS. 10A and 10B illustrate a method for calculating the present value of a real option using a binomial grating option evaluation (BLOV) model. The BLOV model uses two lattices, a lattice of underlying asset and a valuation lattice.

Referring to FIG. 10A, the underlying asset grid progresses from the left to the right of the grid model according to time intervals, and shows how future asset values change. The leftmost node can generally contain the net present value (NPV) of the underlying asset. The underlying asset is incremented or decremented by the increment rate (u) (u ≥ 1) or the drop rate (d) (where 0 <d ≤ 1). Thus, for example, if the current underlying asset is S ₀ , then the assets at a time step after one step are u * S ₀ and d * S ₀ . At this time, the rate of rise (u) and the rate of decrease (d) are functions of the volatility and the time step, respectively, and can be expressed by Equation (2) below.

&Quot; (2) "

The evaluation grid is a grid with nodes and branches that are the same as the underlying asset grid. At the time of expiration (T) (ie, in the rightmost grid), the underlying asset of each node is generally expressed as MAX [(Sn-K), 0]. Where K is the capital investment cost (CAPEX) for asset development and Sn is the asset value at maturity. In the evaluation grid, the base value of each node at maturity is shifted to the left by one grid, and the option value at each node is calculated to finally calculate the option value at the leftmost node, that is, at the current time point.

Therefore, for example, as shown in FIG. 10B, if the asset at the current node is increased by one unit of time step according to the rate of rise (u) is denoted by A, and is decreased by one unit time step according to the downward rate (B), the value of the real option at the present time, that is, the present value (C) of the real option, is expressed by Equation (3) below.

&Quot; (3) "

Where rf is the risk free rate, ΔT is a time step in one unit, and P is expressed as Equation 4 below.

&Quot; (4) "

According to Equation (3), the present option value means that the future option values A and B are weighted by p and (1-P), respectively, and are discounted at the risk-free interest rate. Since the sum of the weights is 1, Equation (3) can also be regarded as an expected value of the option at the time of? T. In other words, the present option value is the discounted value of the future option value as the risk-free interest rate. And P can be interpreted as a probability of assuming a kind of risk neutrality.

FIG. 11 is an exemplary flow chart of the step S50 of calculating the present value of the real option of FIG. 3, and FIG. 12 shows the BLOV model at this time.

In an embodiment of the present invention, each of the case where the drilling is not performed (the first case) and the case where the drilling is performed (the second case) is applied to the underlying asset grid model, Since switching is performed, the switching option is applied. Assume that the underlying asset grid model for each case has the same node and grid. Also, as shown in FIG. 11, the process of calculating the present value C of the real option is performed for each of the m reservoir models for each of the k reservoir models, that is, k scenarios.

11, first, at step S510, a first underlying asset An at maturity is calculated when additional drilling is not performed in the reservoir according to the underlying asset grid model. For example, assuming that 47 reservoir models have been created by NSGA-II in step S10 of FIG. 3, step S510 is performed for each of the 47 reservoir models.

This step S510 corresponds to the grid model of the first case of the underlying asset grid model of FIG. 12, that is, "1) without drilling ". Assuming that the underlying asset at the present time is S1, each time a unit time step passes, the future asset is calculated by separating branches according to the increase rate (u) and the drop rate (d) in each grid. Therefore, when the n time steps have passed, the first basis asset An is the number of (n + 1) cases, and each of them is u ⁿ S ₁ , u ^n-1 d ¹ S ₁ , ..., d ⁿ S ₁ , and so on.

Next, in step S520, the second underlying asset Bn at the time of additional drilling in the reservoir according to the underlying asset grid model is calculated. This step S520 is performed for all reservoir scenario. For example, if there are 24 scenarios depending on the candidate to be drilled and the time of drilling, and there are 47 reservoir models in each scenario, this step (S520) is performed for a total of 24 * 47 models.

This step S520 corresponds to the lattice model of the second case of the underlying asset grid model of Fig. 12, i.e., "2) drilling decision ". Assuming that the underlying asset at the present time is S2, each time a unit time step passes, the future asset is calculated by branching according to the increase rate (u) and the drop rate (d) in each grid. As shown in FIG. 12, the second underlying asset Bn when the n time steps have passed is (n + 1) cases, and each of the second underlying assets Bn has u ⁿ S ₂ , u ^n-1 d ¹ S ₂ , ..., d ⁿ S ₂ , and so on.

Thereafter, in step S530, the asset at maturity is determined according to the evaluation grid model. For this, a larger value of the limiting value (Bn-X) of the drilling cost (X) is selected as the asset of the corresponding node in the first basic asset (An) and the second basic asset. That is, as shown in FIG. 12, the value of Max (An, Bn-X) is calculated for each node. Thus, selecting the larger of the two values (An, Bn-X) is intended to reflect the choice of the better choice at each expiration time in each situation.

Thereafter, in step S540, the present value C of the real option is calculated based on the respective values at maturity calculated in step S530. That is, as described with reference to FIG. 10B, the option value is sequentially calculated while proceeding leftward by one time step according to Equation 3 and Equation 4, and finally the discounted real option value C ).

Experimental Example

Hereinafter, the results of applying the evaluation method of the reservoir layer according to an embodiment of the present invention to an arbitrary experimental model are shown.

13 shows the reservoir model used in an experimental example. This reservoir model includes 19 × 28 × 5 uniform grid grid blocks in the area of 180 m × width × height. As shown, it is assumed that two wells (W1, W2) have been developed and have a production history for two years. The production history at this time includes, for example, the production history (oil production amount, gas production amount, and production history of water production amount) of the past 760 days as the initial input data for the history matching as shown in Fig.

The reservoir and fluid data of FIG. 14 includes parameters relating to the reservoir properties used in the reservoir model of FIG. 13, which may include parameters, for example, regarding reservoir size, porosity and permeability.

This reservoir model is also set to predict the production over 20 years based on the production history in the past two years (exactly 760 days) as shown in Fig. For the application of the genetic algorithm, assume that the initial population includes 100 models and selects the final model through 10 generations.

FIG. 15 is a view for explaining a reservoir scenario used in an experimental example, and FIG. 16 is a diagram for explaining parameters used in a reservoir scenario in an experimental example.

It is assumed that two wells (W1, W2) have already been developed and the third well (W3) is further drilled while producing resources. The third well W3 may be located in one of the three candidate areas W3-1, W3-2, W3-3 shown in Fig.

As shown in FIG. 16, the time point at which the drilling of the additional oil well W3 is started can be started at any point between the third and the tenth years after the start of the first production of the reservoir by the existing wells W1 and W2 Lt; / RTI > Accordingly, there are 24 scenarios for further drilling of oil wells.

In the case of no additional drilling (first case) and the case of additional drilling (second case), they are independent of each other. In the case of the first case, the production behavior for 20 years after the history matching is predicted. The NPV is calculated based on the past 760 day production history. The input conditions used for NPV calculation may include, for example, the parameters shown in Fig.

For the second case of additional drilling, there are a total of 24 scenarios depending on the three candidates and the eight drilling points, and for example, the parameters shown in Fig. 18 may be used to evaluate the real option value (ROV) .

FIG. 19 shows the results of the reservoir productivity evaluation according to the conventional method when the reservoir model was simulated according to the above-described experimental conditions. In the conventional method used here, a reservoir model was generated according to a conventional single-objective genetic algorithm (SOGA), and economic evaluation was performed using only the net present value (NPV) for the generated reservoir model. For the NPV calculation, the parameters of FIG. 17 were used and the NPV values were calculated according to the accumulated production of the resources (oil, gas, and water) for 20 years.

Of the total 24 scenarios in the case of drilling, FIG. 19 shows only eight scenarios as examples of drilling in the third candidate (W3-3). That is, in all cases of Figs. 19 (a) to 19 (h), the drilling candidates are the same as W3-3 and the drilling times are different from the third year to the tenth year.

In each table, P10, P50, and P90 represent intermediate values (P50), upper 10% values (P10), and lower 10% values (P90), respectively, .

According to this conventional method, when the NPV of P50 in all 24 scenarios is compared, when NPV is drilled at the third candidate (W3-3) in the third year (that is, in the case of FIG. 19 (a)) as $ 8,704M , This scenario is the most economically optimal scenario.

20 is a view showing an exemplary evaluation result of the reservoir productivity according to an embodiment of the present invention. That is, the results of the reservoir productivity evaluation using the non-dominant sorted genetic algorithm (NSGA-II) and the real option valuation (ROV) method described above. For this, data on the reservoir layer of Fig. 14 and the ROV parameter of Fig. 18 are used.

Of the 24 scenarios in the case of drilling, Figure 20 shows the expected profit of the real option for eight cases when drilling on the third candidate (W3-3). That is, in all the cases of Figs. 20 (a) to 20 (h), the drilling candidates are the same as W3-3 and the drilling times are different from the third year to the tenth year.

Each graph in FIG. 20 is a histogram (distribution chart) of option values. The X axis is the option value calculated in step S540 of the flowchart of FIG. 11 for the value C of the real option, that is, the model of each scenario (for example, 47 models), and the Y axis is the frequency. Therefore, each graph in FIG. 20 is a distribution chart in which real option values according to 47 models for each scenario are distributed in units of $ 1000M, and expected profit values are obtained by multiplying each real option value with a probability frequency.

According to the method of the present invention, when the expected revenues of the 24 scenarios are compared, the expected profit is most advantageous as the expected profit is $ 9,083M when the fifth candidate (W3-1) is drilled in the fifth year.

FIG. 21 is a diagram for explaining a comparative comparison of the results of the reservoir productivity evaluation according to the conventional method and the embodiment of the present invention. According to the economical evaluation method of the present invention, when the first candidate (W3-1) of the 24 scenarios was drilled for the fifth year, the expected profit was the highest as $ 9,083M (see FIG. 21 (b)). Compared with the NPV value according to the conventional method at this time, the NPV value at P50 is $ 8,408M (see Fig. 21 (a)). Therefore, the option premium can be interpreted as the expected profit of the real option minus the NPV of P50, ie $ 9083M - $ 8408M = $ 675M.

It is worth having this option as you have the option to postpone the drilling and choose the drilling timing and drilling location.

Also, since the NPV is $ 8,704M in the scenario in which the NPV value is highest in the economical evaluation according to the conventional method, that is, in the scenario in which the third candidate (W3-3) is drilled at the third year, the NPV and the maximum expected profit Compared with the expected revenue of $ 9083M, the option premium is $ 9083M - $ 8,704M = $ 379M.

As described above, according to the embodiment of the present invention, the productivity of the reservoir layer is evaluated using the multipurpose history matching method and the real option evaluation method, which is advantageous in that the expected profit of the reservoir layer is improved by the option premium as compared with the conventional net present value method.

22 is a block diagram for explaining an exemplary system configuration for evaluating the productivity of a storage layer according to an embodiment.

Referring to Figure 22, the retention productivity assessment system 100 according to one embodiment may be any terminal device or server capable of performing the steps of the flowcharts described with reference to Figures 3, 7, and 11, May include processor 110, memory 120, and storage 130 as shown.

The storage device 130 is a storage medium capable of semi-permanently storing data such as a hard disk drive or a flash memory. The storage device 130 stores various algorithms such as the multi-purpose genetic algorithm 131 such as NSGA-II, ROV Or an algorithm or program, such as a computation algorithm 132, for example.

In this configuration, these various programs and algorithms may be stored in the storage device 130 and loaded into the memory 120 under the control of the processor 110 and executed. Alternatively, some programs or algorithms may reside in an external device or server that is separate from the productivity assessment system 100, and when data or variables are transmitted to the external device or server from the system 100, The server may execute the program or algorithm and then pass the resulting data to the system 100.

As described above, although the present invention has been described with reference to the limited embodiments and drawings, the present invention is not limited to the above embodiments. It will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the present invention as defined by the appended claims. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined by the equivalents of the claims, as well as the claims.

100: Reservoir productivity evaluation system
110: Processor
120: Memory
130: Storage device

Claims

A method for evaluating the productivity of a reservoir using a computer,
(a) generating m (where m is an integer equal to or greater than 2) storage layer model by applying a multipurpose genetic algorithm to initial condition data and production history data about the storage layer;
(b) calculating m prediction results of resource production over time using each of the reservoir models;
(c) calculating a net present value (NPV) based on each of the m production yield prediction results for each of the k (where k is an integer equal to or greater than 2) scenarios regarding the presence or absence of additional drilling in the reservoir ;
(d) calculating variability (?) based on the calculated net present value (NVP);
(e) for each of the k scenarios, calculating a present value C of the real option; And
(f) selecting a scenario having the largest real option price among the k scenarios based on the calculated present value C of the real option,
(E) calculating a present value C of the real option, for each of the m reservoir models for each of the k scenarios,
(e-1) calculating a first underlying asset (An) at maturity when no additional drilling is performed in the reservoir, according to an underlying asset grid model;
(e-2) calculating a second underlying asset (Bn) at the time of additional drilling in the reservoir according to an underlying asset grid model;
(e-3) calculating a larger value of (the first underlying asset) and (the limiting value of the drilling cost in the second underlying asset), according to the evaluation grid model; And
(e-4) calculating a current value (C) of the real option based on the value calculated in the step (e-3).

The method according to claim 1, wherein (a)
(a-1) setting a plurality of objective functions related to prediction of a production amount;
(a-2) using the non-dominant sorted genetic algorithm-II (NSGA-II) to select solutions based on a predetermined target level among the solutions of the objective functions; And
(a-3) repeating the steps (a-1) and (a-2) until a predetermined number of generations is reached to derive the Pareto optimal surface.

3. The method of claim 2,
(A-2) selecting the solution,
(a-2-1) generating (S 130) a descendent solution Go of the predetermined number by crossing and / or mutating from a parent solution Gp of a predetermined number of individuals;
(a-2-2) calculating an objective function value for each of the parent solution and the child solutions (S140);
(a-2-3) calculating a cluster distance of each year by assigning a rank to each year by non-dominant sorting and cluster distance sorting; And
(a-2-4) selecting (S160) a predetermined number of solutions based on the rank and the cluster distance size (S160).

The method according to claim 1,
Wherein the net present value (NPV) is a sum of values obtained by discounting a cash flow predicted at predetermined time intervals to a present value.

The method according to claim 1,
Wherein the number of scenarios (k) is a product of a number in the case of a well location to be further drilled in the reservoir layer and a number in the case of a drilling time.

The method according to claim 1,
Wherein in the step (d), the variability (σ) calculates, for each of the k scenarios, the variability for each of the reservoir models based on NPVs of the m reservoir models for each scenario, .

delete

The method of claim 1, wherein the step (f)
(f-1) calculating, for each of the k scenarios, an expected profit of a current value (C) of a real option of each of k scenarios using the current value (C) of the real option of the m reservoir model step; And
(f-2) comparing the expected profit of each of the calculated scenarios to select a scenario having the largest expected profit.

A computer-readable recording medium having recorded thereon a program for causing a computer to execute the method according to any one of claims 1 to 6 and 9.