# Integration of static and dynamic reservoir data to optimize the generation of subsurface fracture map

- 1.7k Downloads

## Abstract

This paper presents a new three-dimensional fully coupled poroelastic numerical model to simulate pressure transient response of naturally fractured reservoirs. One of the main applications of the new approach is to improve the reservoir characterization by decreasing the uncertainties associated with subsurface fracture map and to understand the interaction between fracture and matrix. The model is based on a hybrid methodology to simulate fluid flow by combining a single continuum and discrete fracture network approaches. To decrease the uncertainty associated with subsurface fracture map, a different realizations of the discrete fracture systems are generated based on image logs, seismic, geological features and the tectonic history of the studied reservoir. An iterative loops have been used between the reservoir static model and dynamic well-test data to optimize the generation of subsurface fracture maps. At each loop, a new discrete fracture system is used and the simulated pressure transient data are compared with the available field data. The process is repeated till the matching between the simulated and the measured pressure transient data is achieved using the most appropriate fracture realization. The numerical model is validated against an analytical pressure transient solution for dual-porosity system, and then applied to a real case taken from fractured basement reservoir in offshore Southern Vietnam. The developed hybrid methodology used to simulate fluid flow and rock deformation to improve the characterization of the fractured basement by simulating the pressure transient testing. The results predicted by the presented model are in a good agreement with field data; also the model was able to predict the fractures network distribution and fractures inherent properties around the tested well.

## Keywords

Dynamic well test Naturally fractured reservoirs Finite element modelling## Introduction

Flow transport in fractured medium differs from that in porous medium, an intergranular porous medium. In naturally fractured reservoirs, the matrix provides the main storage for fluids, while flow transport takes place through fracture network system. The first step in fluid flow simulation is to characterize the fracture network, therefore the length, geometry and orientation of fractures. Characterization of fracture system has been carried out by integrating information from two different sources; static data (seismic, well logs, core description, borehole images, tectonic history, geological structures, etc.) and dynamic data (well-test data and well production history). Readers can be referred to the publication by “Gholizadeh Doonechaly and Rahman (2012)” for interpretation of static data and generation of subsurface fracture map using various techniques. The dynamic data, on the other hand, have been used to further improve subsurface fracture properties. To date the fractured medium, however, is represented by bulk macroscopic values of averaged point-to-point variations of relevant properties over a representative elementary volume (REV) instead of discrete fractures.

Currently three major approaches have been used to simulate fluid flow in a fractured reservoir which includes single continuum, dual-porosity and discrete fracture network.

In the single continuum approach, the reservoir is divided into a number of blocks and the fracture properties in each block are averaged by using a representative effective permeability tensor. Estimation of the effective permeability tensor for regular fracture pattern of simple geometries was first proposed by Lough (Lough et al. 1997). The approach was further improved by Teimoori et al. (2005) to simulate fluid flow in arbitrary oriented and intersected fracture system (Teimoori et al. 2005). Despite the improved computational efficiency of the single continuum approach, it does not adequately address the flow behaviour of fractures (Tarahhom et al. 2009).

The limitations of dual-porosity/permeability approach are as follow: (1) the fluid distribution within the matrix blocks remains constant during the simulation period, (2) the model cannot be applied to disconnected and discrete fratured (oriented fractures) media and (3) a small number of large-scale fractures can be considered for flow simulation. Therefore, the developed numerical model presented in this paper overcomes all above mentiond limitations by considering fluid flows through matrix porous media and discrete fractures.

The discrete fracture approach, on the other hand, has been proposed as an explicit means of considering the fluid flow and transport inside individual fractures (Karimi-Fard et al. 2004).

The transmissivity of individual fractures and their effect on fluid flow have been studied by considering fracture properties, namely orientation, size and location into the flow calculation. This approach was first introduced for single phase flow. Among of the earliest authors that represent the fracture as 1D entity in 2D fractured porous system were Noorishad et al. (1984) and Baca et al. (1984). Further studies were done by Wei et al. (1998), Karimi-Fard et al. (2004), Rogers et al. (2007) and Watanabe et al. (2010). The main difficulty of discrete fracture approach is the need for extensive computation involved in reservoir scale flow simulation.

Wei et al. (1998) developed a 3D numerical model in order to simulate pressure transient through fracture/matrix system. The results indicated that the simulated pressure derivative showed a different behaviour for each fracture pattern configuration. Also authors showed that dual-porosity model failed to describe the behaviour of fluid flow through fractured system in many cases. Carlson (2003) was using specific transfer functions to simulate the flow transfer from fractures to matrix. It was assumed that the fractures provide the main flow conduit and matrix acts as a source/sink to the fractures.

Basquet et al. (2005) used a homogenization method to simulate pressure transient through fractured system. The idea is to simplify discrete fracture network approach by reducing number of generated fracture nodes. This approach keeps the actual fracture network geometry and also the hydraulic properties of the whole system. Casabianca et al. (2007) presented a discrete fracture network model by using an integrated interpretation methodology to improve the characterization of a fractured chalk reservoir.

Recently, there are many studies on using pressure transient data for naturally fractured reservoir modelling. Morton (2012) presented two new techniques used to calibrate numerical-based fracture model with well-test data by integrating a reservoir model inversion technique and boundary element method for determining the pressure transient behaviour of the reservoir with arbitrary distributed vertical fractures. Kuchuk and Biryukov (2012) presented semi-analytical solution in order to understand pressure behaviour of continuously and discretely fractured reservoirs. This solution used to interpret well-test data of formation containing network of discrete conductive fractures. The author showed that Warren and Root's (1963) dual-porosity model is not adequate for pressure transient well-test interpretation as it does not capture the behaviour of these reservoirs.

In this study, a hybrid methodology—combining the single continuum and the discrete fracture approaches—is utilized to increase the efficiency of the fluid flow simulation. The reservoir domain is discretized using tetrahedral elements, and fluid flow is then simulated in these elements by using the single continuum approach. In the proposed methodology, a threshold value for fracture radius is defined. Fractures, with the radius smaller than the threshold value, are used to generate the grid-based permeability tensor. Fractures, with radius longer than the threshold value, are explicitly discretized in the domain by using the triangular elements, and the fluid flow is modelled using the discrete fracture approach.

## Model validation

Input data for a sugar cube model used in a numerical simulation validation process

Parameter | Value |
---|---|

Reservoir dimensions | 7500 m × 7500 m × 1620 m |

Fracture spacing | 250 m |

Matrix permeability | 0.01 mD |

Matrix porosity | 0.01 |

Fracture permeability | 1000 mD |

Wellbore storage | 0 bbl/psi |

Initial reservoir pressure | 10,000 psia |

Fluid viscosity | 0.2 cp |

Fluid compressibility | 22.4E−06 psi |

Horizontal stresses | 9000 psi |

Vertical stress | 12,000 psi |

*ω*). As the (ω) gets smaller, the dip gets deeper and starts earlier.

The horizontal portion of the pressure derivative curve from 1000 to 40,000 h indicates the ending of transition period and starting of the composite system flow. This flow period is controlled by the value of interporosity flow coefficient (*λ*).

The unit slope of pressure derivative curve between 10,000 and 100,000 h indicates pseudo-steady-state condition for the entire reservoir volume. By using this flow period, a reservoir volume and shape can be calculated.

At early-time response for idealized dual-porosity transient behaviour with a very low wellbore storage effects, a first radial flow regime is expected to appear before starting of transition flow period. This radial flow regime is governed by the flow only inside the fractures network. The simulation result does not show that, as the response of discrete fracture network model before 10 h is not clear and the presented simulation model ignored the wellbore storage effect.

## Case study

The test case is taken from granitic oil-bearing formation in southern offshore Vietnam (Farag et al. 2010). The formation is highly fractured with fractures having short lengths identified from image logs and forming the storage capacity of the reservoir. Geological interpretation showed that the reservoir has very low matrix porosity and permeability. Pore space in the rock is formed through the fractures network and digenetic processes. A Drill Stem Test (DST) was conducted in this formation with controlled flow periods before shutting to understand the extent of the reservoir from the wellbore, prove the possibility of the hydrocarbon existence, and evaluate well deliverability and reservoir performance.

Farag et al. (2010) used a simple model of parallel vertical fractures with a vertical well to simulate main build-up period of DST test by ignoring the actual distribution of fracture network around the tested well.

The aim of this study is to generate a subsurface fracture map using available field data, and to use the presented model to simulate the main build-up period of the DST test to calibrate logs permeability values in the area under study.

## Generation of discrete fracture map of a typical basement reservoir

The author used an innovative methodology to generate the 3D subsurface fracture map of the studied reservoir by integrating field data, such as wellbore images and conventional well logs. In this approach, an object-based conditional global optimization technique is used to generate the subsurface fracture map of the reservoir which combines the following: (1) statistical analysis of different sources of data (as mentioned above); (2) finite element-based modelling of tectonic history of the reservoir structure to generate probabilistic fracture attributes; (3) development of complex relationship between different sources of data (data sources mentioned in (1) and the data generated in (2)) using back propagation neural network; (4) sequential Gaussian stochastic simulation to generate object-based 3D subsurface fracture map and (5) simulated annealing optimization technique to generate an optimum subsurface fracture map. In object-based model, each single fracture is treated as a single object with its specific properties such as location (centre point), dip, azimuth and size (radius). Each object possesses a variety of rules for behaviour in space such as shift, rotate, grow, shrink, multiply or disappear. The optimization process involves a series of trial and errors utilizing the nominated rules to minimize the objective function which is the difference between each fracture system realization and the target. The procedure is detailed in Gholizadeh Doonechaly and Rahman (2012).

Reservoir inputs parameters for numerical simulation model

Parameter | Value |
---|---|

Reservoir dimensions | 600 m × 600 m × 90 m, Vertical well is partially penetrated the formation thickness |

Matrix permeability | 0.01 mD |

Matrix porosity | 0.002 |

Fracture aperture | 0.04 mm |

Fracture permeability | 100 D |

Fracture porosity | 0.1 |

Fracture compressibility | 3 × 10 |

Initial reservoir pressure | 5063 psia |

Fluid viscosity | 1.38 cp |

Fluid compressibility | 1.0E−06 psi |

Production time before shut in ( | 72 h |

Production flow rate before shut in | 5571 bbl/d |

Horizontal stresses | 4800 psia |

Vertical stress | 6000 psia |

## The hybrid approach

*l*≥ 40 m) along with their original properties (orientations and locations) are discretized explicitly within the reservoir domain.

As shown in Fig. 8, a poor matching occurred between build-up history and simulated data at first trial using fracture aperture = 0.04 mm using the best generated fracture realization. In addition, the figure (see Fig. 8) shows the simulated pressure curve is higher than measured one. This behaviour is obtained due to the use of a large fracture aperture that enables pressure to build up quickly around the wellbore.

Since the simulated results were moving in the direction as expected as it has almost the same trend of the history data, the decision is taken by keeping the fracture realization that has been predicted using the iteration process as described before, and further trials were continued by changing fracture aperture.

After several trials, the simulated data are matched with the history data by using fracture aperture of 0.004 mm. The early-time response is truncated from gauge data after 20 min from the beginning of the test by using Horner plot (Aguilera 1980); wellbore storage effect has been neglected. The numerical model was able to match the build-up test reasonably well for about 52 h.

*P*

_{ws}−

*P*

_{wf}) versus ∆

*t*

_{e}(equivalent time), where

Figure 9 shows a good match between measured and simulated pressure change using fracture aperture = 0.004 mm. The simulated and measured data before 0.1 h does not show the effect of wellbore storage (slope of plotted data before 0.1 h is not a unit slope).

_{.}By using this plot most of flow regimes can be defined. The first flow regime as expected is a spherical flow which occurs due to partially penetrated well used in the numerical model and is seen in the derivative plot as a negative slope trend. The second flow regime is a radial flow which appears in the derivative curve as a flat line with zero slope (

*m*= 0). The third flow regime is a linear flow recognized as a positive half-slope trend caused by the fractures network.

The build-up period was simulated successfully using the generated subsurface fracture map around the area under study. The new model was able to characterize the area around the tested well and also the fracture aperture value has been predicted.

## Conclusion

A new numerical simulation model is developed using a hybrid technique of single continuum and Discrete Fracture Network approaches to simulate well pressure transient response for improving reservoir static model by decreasing uncertainties in reservoir characterization process. The new model used a permeability tensor concept to replace fractures with a short length by an equivalent tensor in a three-dimensional space using a finite element technique. A discrete fracture network approach used to simulate fluid flow inside long fractures to observe the effect of these fractures on the pressure response at the tested well.

A model was validated against analytical solution of Warren and Root using dual-porosity reservoir to test its robustness and accuracy, and then the applicability of the model on how to simulate actual build-up test is performed. The model is able to characterize the simulated area around the studied well by predicting the proper fractures network distribution and also the fractures network inherent parameters.

## References

- Aguilera R (1980) Naturally fractured reservoirs. Petroleum Publishing Company. Tulsa, OK, pp 200–220Google Scholar
- Baca RG, Arnett RC, Langford DW (1984) Modelling fluid flow in fractured porous rock masses by finite-element techniques. Int J Numer Meth Fluids 4(4):337–348CrossRefGoogle Scholar
- Basquet R, Cohen CE, Bourbiaux B (2005). Fracture flow property identification: an optimized implementation of discrete fracture network models, paper SPE 93748 presented at the 14th SPE middle east oil and gas show and conference, 12–15 March, BahrainGoogle Scholar
- Carlson R (2003) Practical reservoir simulation: using, assessing, and developing results. PennWell, TulsaGoogle Scholar
- Casabianca D, Jolly RJH, Pollard R (2007) The machar oil field: water flooding a fractured chalk reservoir. Geol Soc Lond Spec Publ 270(1):171–191CrossRefGoogle Scholar
- Durlofsky LJ (1991) Numerical calculation of equivalent grid block permeability tensors for heterogeneous porous media. Water Resour Res 27(5):699–708CrossRefGoogle Scholar
- Farag SM, Mas C, Maizeret P-D, Li B, Le HV (2010) An integrated workflow for granitic basement reservoir evaluation. Soc Petroleum Eng. doi: 10.2118/123455-PA Google Scholar
- Gholizadeh Doonechaly N, Rahman SS (2012) 3D hybrid tectono-stochastic modeling of naturally fractured reservoir: application of finite element method and stochastic simulation technique. Tectonophysics 541–543:43–56CrossRefGoogle Scholar
- Gong B, Karimi-Fard M, Durlofsky LJ (2008) Upscaling discrete fracture characterizations to dual-porosity, dual-permeability models for efficient simulation of flow with strong gravitational effects. SPE J Richardson 13(1):58CrossRefGoogle Scholar
- Karimi-Fard M, Durlofsky LJ, Aziz K (2004) An efficient discrete fracture models applicable for general purpose reservoir simulators. SPE J 9(2):227–236CrossRefGoogle Scholar
- Kazemi H (1969) Pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution. SPE J 9:451–462CrossRefGoogle Scholar
- Kuchuk FJ, Biryukov D (2012). Transient pressure test interpretation from continuously and discretely fractured reservoirs. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers, San Antonio, TXGoogle Scholar
- Lee DA (1977) Flow in fractured porous media. Water Resour Res 26:351–356Google Scholar
- Lough MF, Lee SH, Kamath J (1997) A new method to calculate effective permeability of gridblocks used in the simulation of naturally fractured reservoirs. SPERE 12(3):219–224CrossRefGoogle Scholar
- Morton KL (2012) Integrated interpretation for pressure transient tests in discretely fractured reservoirs, paper SPE 154531 presented at the EAGE annual conference & exhibition incorporating SPE Europe, 4–7 June, Copenhagen, DenmarkGoogle Scholar
- Noorishad J, Tsang C, Witherspoon P (1984) Coupled thermal-hydraulic mechanical phenomena in saturated fractured porous rocks: numerical approach. J Geophys Res 89:10365–10373CrossRefGoogle Scholar
- Pride SR, Berryman JG (2003) Linear dynamics of double-porosity dual-permeability materials I Governing equations and acoustic attenuation. Phys Rev E 68(3):036603CrossRefGoogle Scholar
- Pruess K (1985) A practical method for modeling fluid and heat flow in fractured porous media. Soc Petrol Eng J 25(01):14–26CrossRefGoogle Scholar
- Rogers S, Enachescu C, Trice R, Buer K (2007) Integrating discrete fracture network models and pressure transient data for testing conceptual fracture models of the Valhall chalk reservoir, Norwegian North Sea. Geol Soc Lond, Spec Publ 270(1):193–204CrossRefGoogle Scholar
- Snow DT (1969) Anisotropie permeability of fractured media. Water Resour Res 5(6):1273–1289CrossRefGoogle Scholar
- Tankersley T, Pan Y, Narr W, Laidlaw CP, Flodin E, Hui M-H, Bateman P (2013) Integration of pressure transient data in modeling tengiz field, kazakhstan—a new way to characterize fractured reservoirs. Soc Petroleum Eng. doi: 10.2118/165322-MS
- Tarahhom F, Sepehrnoori K, Marcondes F (2009) A novel approach to integrate dual porosity model and full permeability tensor representation in fractures. Paper presented at the SPE reservoir simulation symposiumGoogle Scholar
- Teimoori A, Chen Z, Rahman SS, Tran T (2005) Effective permeability calculation using boundary element method in naturally fractured reservoirs. Pet Sci Technol 23(5–6):693–709CrossRefGoogle Scholar
- Warren JE, Root PJ (1963) The behaviour of naturally fractured reservoirs. SPE J 3:245–255CrossRefGoogle Scholar
- Watanabe N, Wang W, McDermott CI, Taniguchi T, Kolditz O (2010) Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media. Comput Mech 45(4):263–280CrossRefGoogle Scholar
- Watanabe N, Wang W, Taron J, Görke UJ, Kolditz O (2011) Lower-dimensional interface elements with local enrichment: application to coupled hydro-mechanical problems in discretely fractured porous media. Int J Numer Methods Eng 90(8):1010–1034. doi: 10.1002/nme.3353 Google Scholar
- Wei L, Hadwin J, Chaput E, Rawnsley K, Swaby P (1998) Discriminating fracture patterns in fractured reservoirs by pressure transient test, paper SPE 49233 presented at the SPE annual technical conference and exhibition, 27–30 September, New Orleans, LAGoogle Scholar
- Zienkiewicz OC, Taylor RL (2000) The finite element method: solid mechanics, vol 2. Butterworth-heinemannGoogle Scholar
- Zimmerman RW, Bodvarsson GS (1996) Hydraulic conductivity of rock fractures. Transp Porous Media 23(1):1–30CrossRefGoogle Scholar
- Zoback MD (2007) Reservoir geomechanics. Cambridge University Press, ChicagoGoogle Scholar

## Copyright information

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.