CHINESE JOURNAL OF GEOPHYSICS  2016, Vol. 59 Issue (6): 703-716   PDF    
EVALUATION OF RESERVOIR PERMEABILITY USING ARRAY INDUCTION LOGGING
ZHOU Feng1,2, MENG Qing-Xin3, HU Xiang-Yun2, SLOB Evert4, PAN He-Ping2, MA Huo-Lin2     
1 School of Mechanics and Electronic Information, China University of Geosciences (Wuhan), Wuhan 430074, China;
2 Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074, China;
3 Exploration Technology and Engineering College, Shijiazhuang University of Economics, Shijiazhuang 050031, China;
4 Department of Geoscience & Engineering, Delft University of Technology, Delft 2628 CN, the Netherlands
Abstract: During drilling, the mud column sustains a slightly higher pressure than the formation to maintain the stability of the well wall, which causes the mud filtrate to penetrate into formation pores and displace in-situ fluids. The invasion depth is affected by reservoir properties, especially the reservoir permeability. Therefore, it is possible to estimate the reservoir permeability if the invasion depth can be measured. A numerical study was conducted to investigate the feasibility of evaluating reservoir permeability with array induction logging. A mud invasion model was built up by coupling mud cake growth with multiple-phase fluid flow, and an array induction logging model was established based on the Born geometric factor theory. Joint forward simulations of mud invasion and array induction logging indicated that the responses of array induction logging can reflect the effect of mud invasion on the formation resistivity. Inversion based on the damped least square method revealed that the invasion depth can be acquired from array induction logging data. We investigated the association between reservoir permeability and invasion depth, and found that in a reservoir with a permeability of 1 to 100 mD (1 mD=0.987×10-3 μm2), the reservoir permeability governs the invasion depth, and thus the permeability can be evaluated according to invasion depth. A two-dimensional numerical simulation showed that the inversed invasion depth curve had a similar fluctuation to the permeability variation. For a layered formation, a series of interpretation charts can be produced to evaluate the permeability of every layer with tolerable errors. The numerical investigation proves the feasibility of estimating reservoir permeability with array induction logging.
Key words: Array induction logging     Permeability evaluation     Mud invasion    
1 INTRODUCTION

In the process of oil drilling, there exists a pressure difference between the downhole mud and the reservoir, whereby the mud filtrate invades into the formation pores. The invasion alters the properties of the rock and the components of the fluids in the zone adjacent to the wellbore, and contaminates the signals acquired with logging tools. Therefore, it is crucial to investigate the effects of the mud invasion on logging data and find out the correction methods for reservoir evaluation (Liu et al., 2012). Zhang et al. (1994) performed a one-dimensional numerical simulation of mud invasion. Chen and Sun (1996) set up a sand-box experiment to investigate the resistivity of the formation penetrated by mud filtrate. Dewan et al. (2001) established a mathematical model of mud cake growth based on a physical experiment. Li et al. (2006) analyzed the mechanics of the mud cake forming. Chang et al. (2010) implemented a two-dimensional simulation of mud invasion in a cylinder coordinate. Wu et al. (2004) and Deng et al. (2008) numerically simulated the mud invasion in a deviated well, and Salazar and Torres-Verdĺn (2009) compared the characteristics of reservoirs invaded by water-and oil-based mud filtrate. The response of array induction logging can be influenced by the mud invasion. Wu et al. (2009) simulated the induction logging in a piston-like mud invasion model. Deng et al. (2010) inversed the resistivity of virgin zone with array lateral logging in the mud invasion of a deviated well, and Li et al. (2013) carried out a joint inversion of array induction and self-potential loggings to acquire the formation water resistivity.

The previous work deemed the mud invasion an adverse effect on logging data, and sought methods to eliminate its effects. However, we think that the logging signals influenced by mud invasion also carried some useful information. For instance, the invasion depth has a close relationship with the percolation properties of the formation. Zhang et al. (2005) suggested that oil productivity can be predicted through the extent of mud displacing the in-situ fluids. Wang et al. (2009) thought that reservoir permeability was one of the crucial parameters influencing the depth of mud invasion. This study proposes to evaluate permeability with the aid of mud invasion effect, and a semi-quantitative or quantitative permeability evaluation can be implemented by linking reservoir permeability to invasion depth which is able to be inversed from array induction logging data.

In this study, a mud invasion model was established by coupling the mud cake growth with the multi-phase and multi-component flow. Then, an array induction logging model was built up based on the theory of Born geometric factor, and the invasion depth was inversed by the damped least square method. After analyzing the correlation between the invasion depth and the permeability, a set of field data were used for the forward and inversion of the mud invasion and array induction logging, in order to verify the feasibility of evaluating permeability by array induction logging.

2 MUD INVASION MODEL

Besides the formation properties, the mud cake also plays a significant role in the invasion rate (Wang et al., 2009). Therefore, it is required to consider the effect of the mud cake in the process of mud invasion. We developed an integrated mud invasion model by coupling the mud cake growth to the multi-phase and multi-component flow.

2.1 Multi-phase and Multi-component Flow

Assuming that water-based mud filtrate invades an oil-bearing formation by neglecting gas phase, the pore pressure and water saturation in the near-well zone can be expressed by the two-phase isothermal Darcy flow equations (Aziz et al., 1979),

(1)
(2)

where ρw and ρo are the density of water and oil, respectively, kg·m-3; k is the reservoir permeability, m2; krw and kro are the relative permeability of water and oil, respectively, dimensionless; g is the gravity acceleration vector, m·s-2; D is the depth, m; µw and µo are the viscosity of water and oil, respectively, Pa·s; Pw and Po are the pressure of water and oil, respectively, Pa; ϕ is the porosity, dimensionless; Sw and So are the saturation of water and oil, dimensionless; and t is the invasion time, s.

There occurs a salt mixture between the formation water and the invaded mud filtrate. The salinity of the mixing fluids is expressed by the convective-diffusive equation (Navarro, 2007):

(3)

where Cw is the salinity, mg/L; and KD is the dispersion coefficient, m2·s-1, expressed by KD=(αLkkrwPw)/ (ϕSwµw), where αL is the longitudinal dispersivity, m. The first term in the left part of Eq.(3) stands for the salinity change caused by the convective transport, while the second term represents the salinity variation caused by the salt concentration difference.

The above equations were discretized in a cylindrical coordinate system with the finite difference method. The pressure and salinity were solved with an implicit approach, while the saturation was solved with an explicit way. The radial distributions of water saturation and salinity were thereby acquired, and then the formation resistivity was calculated through Archie's law, as described by (Archie, 1942):

(4)

and

(5)

where Rf and Rw are respectively the resistivity of the formation and the in-situ water, Ωm; m and n denote the cementation and saturation exponents, dimensionless; α is the tortuosity factor, dimensionless; and T is the formation temperature in ℃.

2.2 Mud Cake Growth Model

The mud contains solid particles to sustain a slightly high downhole pressure with respect to the reservoir, which causes that the solid component deposits in the well wall to form a mud cake. The growth of mud cake influences the invasion rate, and its permeability and porosity evolve with time, as described by (Wu et al., 2005):

(6)

and

(7)

where k mc and ϕmc are the permeability and porosity of the mud cake, respectively; Pmc is the pressure difference across the mud cake; kmc0 and ϕmc0 are the referenced permeability and porosity of the mud cake, respectively, defined by the measurement in 1 psi pressure difference; and v and δ are dimensionless compressibility exponent and multiplier reflecting the relationship between the permeability and porosity of the compressed mud cake, and they are also measurable in the laboratory. In Eqs.(6) and (7), the permeability is in mD, and the pressure is in psi.

The instantaneous invasion rate is expressed by (Wu et al., 2005)

(8)

where qmc is the instantaneous invasion rate, m3·s-1; h is the objective layer thickness, m; Pm is the mud column pressure, Pa; µmc is the mud filtrate viscosity, Pa·s; rw is the radius of the wellbore, m; rmc is the inner radius of the mud cake annulus, m; Pc is the capillary pressure, Pa; and the subscript i implies the serial number of the grids, where i=1 denotes the grid of the mud cake, and i=N stands for the grid of radial outer boundary in the modeled domain. In the case of water-based mud invasion, the outer mud cake that is attached to the well wall is taken into account only (Salazar and Torres-Verdĺn, 2009; Wang et al., 2009), and thus there is rw > rmc. The first and second terms in the denominator of Eq.(8) denote the flow resistivities of the formation and the mud cake, respectively. The mud cake thickness growth over time can be expressed by (Wu et al., 2005)

(9)

where fs is the dimensionless volumetric fraction of the solid in the mud.

At every simulated time step, the permeability, porosity, and thickness of the mud cake were solved, and their values were then substituted into the variables of the first grid in the flow model, realizing the coupling of the mud cake and the multi-phase and multi-component flow models. The simulated domain was non-uniformly discretized in the radial direction, and uniformly in the vertical direction. The inner and outer boundaries were both defined as constant pressure. The mud invasion program was developed by MATLAB.

2.3 Model Validation

Salazar and Torres-Verdĺn (2009) developed a mud invasion model by including a mud cake model into the commercial reservoir simulator-CMG-STAR. We compared the simulation results of our autonomous simulator with Salazar and Torres-Verdĺn (2009)'s in the same parameter prescription for validation. The basic properties of rock and fluids are listed as Table 1, and the simulations were performed for 100 hours of mud invasion in the rock types of 10, 30, and 100 mD, respectively. Figs. 1a and 1b show the curves of invasion rate and mud cake thickness versus invasion time by our simulator, and Figs. 2a and 2b are the corresponding results in the literature (Salazar and Torres-Verdĺn, 2009). The comparison reveals that the two sets of curves agree well, validating the effectiveness of the simulator developed in our study.

Table 1 Properties of rock and fluids (Salazar and Torres-Verdĺn, 2009)

Fig. 1 Invasion rate (a) and mud cake growth (b) versus time from the autonomous program

Fig. 2 Invasion rate (a) and mud cake growth (b) versus time in the publication (Salazar and Torres-Verdĺn, 2009)
3 FORWARD AND INVERSION OF ARRAY INDUCTION LOGGING

The forward and inversion of array induction logging was performed based on the commercial logging tool-High-Resolution Array Induction (HRAI). This tool provides five curves of apparent resistivity presenting different detection depth of 10 inch (0.25 m), 20 inch (0.5 m), 30 inch (0.75 m), 60 inch (1.5 m), and 90 inch (2.25 m). Considering that the coil array with the smallest polar distance reflects the shallow signal for the purpose of calibration, this study discarded the apparent resistivity curve with the detection depth of 10 inch in the inversion.

3.1 Forward Method

The forward model was established based on the geometric factor theory. It can model the array induction logging in a direct and fast way, and a variety of methods have been developed based on this principle to suit different geoelectric models, among which the so-called Born geometric factor method is able to depict the perturbation of the conductivity in the heterogeneous formation and is suitable to model the formation invaded by mud filtrate. The forward formulas of the apparent resistivity in the array induction logging are described by (Wang et al., 2011)

(10)

and

(11)

where σa is the apparent conductivity of the dual-coil system, S·m-1, corresponding to the sub-arrays with different electrode distances; gBorn(r, z) is the Born geometric factor of the unit loop located in the vertical direction (z) and the radial direction (r); gDoll is the Doll geometric factor; k is the complex wave number; rT and rR are respectively the distances from the transmitter and receiver to the unit loop, m; i is the symbol of imaginary part; σ(r, z) is the conductivity of the unit loop located in the vertical direction (z) and the radial direction (r), S·m-1. The radial hierarchic model can be written as (Wang et al., 2011)

(12)

where σt is the conductivity of the virgin formation, S·m-1; σi is the conductivity of the invaded zone, S·m-1; and σm is the mud conductivity, S·m-1. According to the geometric factor theory, Gm, Gi, and Gt are respectively the integral geometric factors reflecting the contributions of the borehole mud, virgin formation and the invaded zone to the logging responses. Calculating the above equations, we can acquire the apparent resistivity of every sub-array.

3.2 Inversion Method

Based on the forward model, N sets of logging data were used corresponding to w unknown parameters in the forward model for inversion purpose, as described by (Li et al., 2013)

(13)

where dn denotes the observed logging data, Fn denotes the forward model, and p1, p2, p3, …, pw denote the unknown parameters to be inversed in the model. The inversion problem was solved with the damped least square method, and the objective function was described by

(14)

where P=(p1, p2, p3, …, pw)T is the transpose matrix of the inversed parameters, and the necessary condition of the minimal solution of P should satisfy that the gradient of O(P) is zero at P. Taylor expanded the nonlinear function F (P) at the initial approximation P(0), neglected the quadratic and higher order terms, and obtained the matrix expression of the objective function as

(15)

where J0 is the initial stiffness matrix, and ε0 is the initial residual.

If the stiffness matrix J is nonsingular, based on the relational expression JTJP=JTε, the minimum value of F (P) can be approximated according to

(16)

If J0 is nonsingular, then J0T J0 is a symmetrical positive definite matrix. By multiplying both sides of Eq.(16) by (J0T J0)-1 and introducing a damping factor, the kth recursion formula can be written as

(17)

where P(k) is the solution for the kth iteration, Jk is the inversed Jacobi matrix, λk is the damping factor, εk is the residual for kth iteration step.

For the case of low-resistivity mud invasion, because there is not an obvious difference of resistivity between the flush zone and low-resistivity annulus, we can consider the two zones as a whole. Therefore, in this study, a three-parameter inversion was carried out to acquire the invasion radius, invaded zone resistivity, and virgin zone resistivity.

3.3 Method Validation

The forward and inversion models were validated in a typical low resistivity invasion scenario. Figs. 3(a-c) show the radial profiles of water saturation, water salinity, and formation resistivity over invasion time. As shown in Fig. 3a, the invasion depth (i.e., the distance from the invasion front to the well wall) is 0.50 m, 0.75 m, 0.95 m, and 1.1 m, respectively after 24, 48, 72, and 96 hours of mud invasion. Due to the cylindrical invasion, the deeper the mud invades, the slower the increment of the invasion depth is. The water salinity has the similar changing trend as the water saturation, but slightly lags behind it caused by the miscibility of salt molecules (Fig. 3b). In Fig. 3c, a low-resistivity zone ranging from 10 to 15 Ωm can be observed closely adjacent to the well wall, corresponding to the flush zone; the far part in the profile is the virgin zone with a resistivity of 47 Ωm; and there is a low-resistivity annulus, ranging from 5 to 10 Ωm, between the virgin and flush zones. The low-resistivity annulus forms because of the lagging salinity. The interface between the low-resistivity annulus and the virgin zone corresponds to the water saturation front, while the interface between the low-resistivity annulus and the flush zone corresponds to the salinity front. Therefore, if two perturbations are observed in the electrical resistivity profile, the second one corresponds to the position of the invasion front. This phenomenon should be noticed in the high-resistivity invasion. In the low-resistivity invasion, the difference of resistivity is not obvious between the flush zone and the low-resistivity annulus, and thus it is feasible to consider the flush zone and the low-resistivity annulus as a whole in the array induction inversion to get the invasion depth.

Fig. 3 Radial distribution of water saturation (a), water salinity (b), and comprehensive resistivity (c)

We simulated array induction logging with the geoelectric model of Fig. 3c, and got the logging responses as shown in Fig. 4. It can be seen that the apparent resistivity is relatively small in the zone adjacent to the well wall, and it is caused by the great contribution of the low-resistivity invasion zone to the coils with small polar distance. With the increase of the invasion depth, the resistivity responses of sub-arrays gradually decrease, especially for the apparent resistivities of R60 and R90; in the mean time, the spatial differentiation of the sub-array responses is decreasing and the apparent resistivities get low. The variation of array induction logging responses agrees well with an increasing invasion depth over time.

Fig. 4 Apparent resistivity responses of array induction logging

Using the above array induction logging responses, we implemented a three-parameter inversion, and got the invasion zone resistivity, virgin zone resistivity, and invasion depth, as shown in Fig. 5. Compared with the results of mud invasion simulation, the inversion of array induction logging correctly acquires the electrical structure of the invaded formation. For the invasion depth concerned in this study, the inversion results agree well with the simulated ones, verifying the validation of the inversion method.

Fig. 5 Invasion zone resistivity, virgin zone resistivity, and invasion depth inversed from apparent resistivity curves
4 PERMEABILITY EVALUATION APPLICATIONS

The previous studies of array induction logging inversion generally paid attention to how to correct the virgin formation resistivity, whereas deemed the invasion depth useless. Our study thinks that the inversed invasion depth has a potential application to estimate reservoir permeability.

4.1 Correlation of Reservoir Permeability and Invasion Depth

In the process of drilling, the bit penetrates the formation at a high shear velocity. In this process, there are a portion of solid particles in the mud depositing at the well wall to form mud cake, but the mud cake thickness is small and the mud cake permeability is large due to the high rotation speed of the bit. Therefore, the instantaneous filtration rate of the mud filtrate is large. After stopping drilling, the liquid in the hole presents a status of static filtration, and thus more portions of solid particles are attached to the well wall to thicken the mud cake. Under the great pressure difference across the mud cake, the permeability of the mud cake decreases and the flow resistivity increases, reducing the loss rate of the mud filtrate (Peng and Peden, 1992). We assumed that the drilling time was 12 hours. In the drilling stage, the thickness of the mud cake is 0.1 mm, the permeability is 0.1 mD, and the porosity is 0.45 (Navarro, 2007). The remaining parameters are the same as Table 1. After stopping drilling, the dynamics of the mud cake properties follow Eqs.(6)-(7). The sensitivity analysis of mud invasion indicated that the invasion rate grows with the increase of reservoir permeability, while the invasion depth reduces with the increase of the porosity for the case of the constant invasion volume (Fan et al., 2013). In the realistic reservoirs, there exists a close correlation between the permeability and porosity of the rock. Therefore, it is necessary to consider the influence of both reservoir permeability and porosity on the invasion depth. We used different types of reservoir rock given by Salazar and Torres-Verdĺn (2009) for mud invasion simulations. The formation porosity is respectively 15%, 20%, 25%, 28% and 30%, and the corresponding permeability is 3, 10, 30, 100 and 300 mD, respectively. The remaining parameters were kept same as Table 1, and we simulated a mud invasion of 100 hours.

Figures 6a and 6b show the instantaneous invasion rates and cumulative invasion volumes versus invasion time. Within the 12 hours of drilling, the mud filtrate invades into the formation at a high rate due to the low flow resistivity of the mud cake, and a high-permeability formation corresponds to a high invasion rate (Fig. 6a) and thus a large invasion volume (Fig. 6b). In this stage, the formation permeability is the primary parameter influencing the invasion rate as well as invasion volume. After the drilling stops, the mud cake grows and its permeability decreases, causing that the invasion rates go down to the minimum in a short time (Fig. 6a). In this period, the formation types with different permeability have small differences in the invasion rates (Fig. 6a), and the cumulative invasion volumes rise slowly with time (Fig. 6b). The main reason is because the mud cake has a great thickness and low permeability in this phase, and thus it is the mud cake that plays a dominant role in the invasion rather than the formation permeability. This tendency is more obvious in a high-permeability formation than a low-permeability one.

Fig. 6 Invasion rate (a) and invasion volume (b) versus invasion time for reservoirs with different porosity and permeability

Considering that there is not an obvious improvement in the invasion volume after the drilling stops, we extracted the water saturation profiles for different reservoir types after 24 hours of mud invasion (Fig. 7a), and got the relationship between formation permeability and invasion depth, as described by Fig. 7b. It can be seen that the invasion depth increases with the reservoir permeability, but at a gradually decreasing increment. On the one hand, with the increase of the reservoir permeability, the pressure drop across the mud cake gets large thereby decreasing the pressure gradient within the reservoir (Fig. 8), and thus the variation of reservoir permeability influences little on the invasion rate; on the other hand, a reservoir with a high permeability generally has a high porosity, which counteracts the effect of the increasing reservoir permeability on the invasion depth. We can infer that the invasion depth hardly increases with the reservoir permeability when the permeability is up to a few Darcy.

Fig. 7 Radial distribution of water saturation (a), and invasion depth vs reservoir permeability (b) after 24 hours of mud invasion

Fig. 8 Radial distribution of formation pressure after 24 hours of mud invasion

The above analysis comes to the conclusion that the reservoir permeability can be reflected by the invasion depth in a certain range (in the order of 1 mD to 100 mD). Note that the reservoirs with the permeability below 1 mD are not discussed in this study due to the fact that Darcy flow law is not applied in this kind of reservoirs.

4.2 Semi-quantitative Estimation

We simulated a mud invasion process with the logging and coring data in the North China oil field. The used well data are in the depth from 1036 to 1096 m, the well diameter is 0.2 m, the mud salinity is 12000 mg/L, the mud density is 1130 kg·m-3, the viscosity of water and oil is 0.968 Pa·s and 2.99 Pa·s, the initial pressure difference between the downhole and reservoir is 2 MPa, and the gravity acceleration is 9.8 m·s-2. Figs. 9a and 9b show the horizontal permeability and porosity curves from the logging, and the ratio of horizontal and vertical permeability is 10.

Fig. 9 Permeability (a) and porosity (b) curves of an oil well in the North China oil field

Figures 10a and 10b show the water saturation and resistivity profiles for a mud invasion simulation of 24 hours.

Fig. 10 Water saturation (a) and resistivity (b) profiles after 24 hours of mud invasion

We inversed the array induction data layer by layer, and got the invasion depth as shown in Fig. 11. The comparison between the inversed invasion depth (red curve) and the prescribed permeability (blue curve) presents a similar variation tendency. Especially, the fluctuation of the inversed invasion depth curve describes the characteristics of two low-permeability zones and a high-permeability zone.

Fig. 11 Contrast between the invasion depth and the permeability curves
4.3 Estimation with Interpretation Charts

Our previous sensitivity analysis concluded that the reservoir permeability, porosity and water saturation are the primary formation parameters influencing the invasion depth, and they are also the parameters fluctuating with the formation depth, even in the same well (Zhou et al., 2015). In the field work, it is feasible to make a rough estimation of reservoir permeability with a series of interpretation charts linking the reservoir permeability, porosity, and water saturation with the invasion depth. For a specific well, when the other formation parameters are available with conventional well logging methods, we can position the unknown permeability from the corresponding chart after inverting the invasion depth with array induction logging data.

Before reservoir estimation, a sequence of mud invasion simulations should be implemented by changing the values of reservoir permeability, porosity and saturation to establish a set of interpretation chart atlas relating invasion depth to reservoir properties. The remaining parameters in the simulations can be obtained from logging, drilling and coring data. When estimating an objective layer, one firstly obtains the water saturation and porosity from logging data, and then selects their corresponding curves from the interpretation chart atlas. With the invasion depth value inversed from array induction logging data, one can position the corresponding permeability value from the curve.

We used a conceptual layered model to describe a reservoir with heterogeneous permeability, porosity and water saturation, as shown in Fig. 12. The porosity and water saturation were treated as the known parameters, the permeability was the variable to be solved, and the gravity effect was neglected. Fig. 13 shows the water saturation profile after 24 hours of mud invasion. The invasion depth values in every layer, which were inversed from array induction logging, are 0.37 m, 0.78 m, and 1.07 m, respectively, as shown in Fig. 14.

Fig. 12 Two-dimensional axisymmetric reservoir model

Fig. 13 Water saturation distribution after 24 hours of invasion

Fig. 14 Inversed invasion depth

Contrast between the invasion depth and the permeability curves the model, we selected three interpretation charts that contain the prescribed water saturation values, as shown in Figs. 15(a-c). For the first layer, we found the curve with the porosity of 0.1 in the chart with the water saturation of 0.2 (i.e., blue curve in Fig. 15a), and then positioned the permeability value as 3.5 mD in the vertical coordinate from the invasion depth value of 0.37 m in the horizontal coordinate (as indicated with the dashed line in Fig. 15a). In the same way, we estimated the permeability values of the second and third layers as 30 mD and 90 mD from Figs. 15b and 15c. Table 2 compares the estimated and prescribed permeability values. In the scale of reservoir estimation, the error is within the tolerable range. One of the error sources is the low resolution of the array induction logging, and the other is the gradual instead of piston-like invasion transition zone. The comparison implies that the interpretation chart method can quantitatively estimate the magnitude of the reservoir permeability. However, the disadvantage is that an enormous amount of simulations are required to make a sequence of charts for a wide variation of formation properties.

Fig. 15 Interpretation charts for the water saturation of 20% (a), 30% (b) and 40% (c)

Table 2 Estimated and prescribed permeability values (mD)
5 CONCLUSIONS

This study built up a numerical model of mud invasion by coupling mud cake growth with the multi-phase and multi-component flow. An array induction logging model was established based on the Born geometry factor theory. The damped least square method was used to inverse the invasion depth with the array induction logging data. A sensitivity analysis was conducted to analyze the association between the reservoir permeability and the invasion depth, and then the permeability was estimated using the array induction logging. We came to the conclusions that (1) in the reservoirs with the permeability ranging from 1 mD to 100 mD, there is a close correlation between the reservoir permeability and the invasion depth; (2) the invasion depth curves inversed from the array induction logging can reflect the variation of the permeability; (3) interpretation charts based on the mud invasion simulations can roughly estimate the reservoir permeability.

Even though there is a perfect mathematical model that can directly and precisely quantify the relationship between the reservoir permeability and the invasion depth, our study verified the feasibility of quantitatively estimating permeability using array induction logging, and provided theoretical basis for the direct inversion of reservoir permeability by means of array induction logging in the future.

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of China (41674138, 41304082, 41304078), the PetroChina Innovation Foundation (2015D-5006-0304), and the Foundation of State Key Laboratory of Petroleum Resources and Prospecting, China University of Petroleum (PRP/open-1302).

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EVALUATION OF RESERVOIR PERMEABILITY USING ARRAY INDUCTION LOGGING
ZHOU Feng, MENG Qing-Xin, HU Xiang-Yun, SLOB Evert, PAN He-Ping, MA Huo-Lin