Study on Physical Property Prediction Method of Tight Sandstone Reservoir Based on Logging While Drilling Parameters

Abstract

The pore degree prediction method based on well logging interpretation for tight sandstone reservoirs cannot meet the requirements of timeliness and rapidity for well exploration decisions. This paper utilizes the logging parameters during drilling, combined with acoustic time difference experiments, dynamic and static parameter experiments, and full-scale drill bit rock-breaking simulation, to reveal the response characteristics of reservoir properties to the feedback information from logging and rock-breaking and establishes a pore degree prediction method. The results show that as the pore degree decreases, the dynamic and static elastic modulus increases, the rate of penetration decreases, the torque increases, the mechanical specific energy increases, and a mathematical relationship model between pore degree and mechanical specific energy is established, achieving real-time drilling prediction of pore degree. The new method has been applied in the NB block, and the coincidence rate with the well-logging interpretation results reaches over 83%. The research results have provided real-time predictions of reservoir pore degrees and improved the efficiency of exploration decisions.

1. Introduction

In recent years, oil and gas exploration in deep ultra-deep tight sandstone reservoirs has made great breakthroughs, showing good exploration prospects. Tight sandstone reservoirs are characterized by high diagenetic strength, tight lithology, complex pore structure, and strong heterogeneity, and the evaluation of reservoir physical properties is an important part of oil and gas exploration and development. Nowadays, with the acceleration of the pace of exploration and development and the increasing difficulty of exploration, new requirements are put forward for reservoir physical property evaluation, which should not only ensure the accuracy and reliability of evaluation results but also emphasize its timeliness and rapidity. The existing reservoir physical property evaluation methods mainly include core identification technology, seismic wave monitoring technology, logging technology, etc. [1,2,3]. Core identification technology is based on core porosity experiment, which requires on-site coring and has the disadvantages of high cost and discontinuity. Seismic wave monitoring technology is pre-drilling prediction, which indirectly reflects reservoir physical properties through geophysical information. Due to its large scale and multiple solutions, interpretation accuracy is low and prediction accuracy is not enough. Logging technology should be carried out after drilling. Commonly used logging methods include natural gamma, neutron, acoustic, density and imaging logging, etc. [4,5,6,7]. Different logging methods can reflect changes in reservoir physical properties to a certain extent, with high accuracy and reliability, but logging technology has a certain lag and cannot explain reservoir physical properties in real time. The above method has some problems in the evaluation of reservoir physical properties, such as low interpretation accuracy or lack of timeliness and speed, which leads to the lack of effective basis for decision-making such as drilling in advance, deepening drilling, and intermediate testing, and restricts deep and ultra-deep oil and gas exploration. Well-logging engineering parameters are the most direct and effective response to reservoir lithology and development when the reservoir is drilled, and they are the key basis for reservoir physical property evaluation. In recent years, some scholars have utilized logging while drilling technology to conduct qualitative identification of the physical properties of tight reservoirs, achieving satisfactory results. However, the quantitative prediction of the physical properties of tight reservoirs is still in the exploratory stage [8,9,10]. In terms of rock-breaking simulation of bits, many scholars have established geometric, kinematic, and drilling–formation interaction mechanical models of bits, which provide guidance for bit selection and design, but there are few studies on the inversion of reservoir physical property changes through rock-breaking feedback information [11,12,13,14]. Based on this, this paper takes the NB tight sandstone reservoir as the research object, carries out acoustic time difference experiment, dynamic and static parameter experiment, and PDC bit rock breaking simulation research, and establishes the porosity prediction method while drilling of tight sandstone reservoir. This method has the advantages of low cost, good continuity, and good real-time performance.

2. Characteristic Analysis of Variation of Porosity with Static Elastic Modulus

2.1. Relationship Model Between Porosity and Acoustic Time Difference

The porosity and acoustic time difference data sets of 256 sample points in the working area were statistically analyzed. As shown in Figure 1, core porosity increased with the increase in acoustic time difference, and the two showed a positive correlation.

As shown in

Table 1. Porosity and acoustic time difference.

Regression Method	Mathematical Model	Sample Size	Correlation Coefficient	Selection Model
Exponential function	$\varphi =1.2495e^{0.0287AC}$	256	0.5617
Linear function	$\varphi =0.3939AC-17.697$	256	0.7605
Logarithmic function	$\varphi =34.976\ln AC-138.94$	256	0.793	√
Power function	$\varphi =0.0001A{C}^{2.616}$	256	0.6597

, Exponential function, linear function, logarithmic function, and power function are used to fit the relationship between the two. According to the fitting results, the logarithmic function form has the highest fitting precision, and the correlation coefficient is 0.793. Therefore, the logarithmic function equation is selected as the relationship model between porosity and acoustic time difference, as shown in Equation (1).

$$\varphi =34.976\ln AC-138.94$$

(1)

In the equation, $\varphi$ represents porosity (%), and $AC$ represents acoustic time difference (µs/ft).

2.2. Relationship Model Between Dynamic Elastic Modulus and Acoustic Time Difference

The data sets of dynamic elastic modulus and acoustic time difference of 1970 sample points in the work area were statistically analyzed. As can be seen from Figure 2, with the increase in acoustic time difference, the dynamic elastic modulus gradually decreases, showing a negative correlation between the two.

As shown in

Table 2. Dynamic elastic modulus and acoustic time difference.

Regression Method	Mathematical Model	Sample Size	Correlation Coefficient	Selection Model
Exponential function	$E_d = 493.89e^{-0.035AC}$	1970	0.9092	√
Linear function	$E_d=-1.5803AC+153.69$	1970	0.8867
Logarithmic function	$E_d=-108.7ln\left(AC\right)+504.43$	1970	0.9003
Power function	$E_d=1E^{6}A{C}^{-2.395}$	1970	0.9090

, Exponential function, linear function, logarithmic function, and power function are used to fit the relationship between the two. According to the fitting results, the exponential function form has the highest fitting accuracy, and the correlation coefficient is 0.9092. Therefore, the exponential function equation is selected as the relationship model between dynamic elastic modulus and acoustic time difference, as shown in Equation (2).

$$E_d = 493.89e^{-0.035AC}$$

(2)

In the equation, $E_d$ represents dynamic elastic modulus (GPa), and $AC$ represents acoustic time difference (µs/ft).

2.3. Relationship Model Between Static Elastic Modulus and Dynamic Elastic Modulus

The static elastic modulus and dynamic elastic modulus data sets of 12 sample points in the work area were statistically analyzed. It can be seen from Figure 3 that as the dynamic elastic modulus increases, the static elastic modulus increases, and the two present a positive correlation.

As shown in

Table 3. Static elastic modulus and dynamic elastic modulus.

Regression Method	Mathematical Model	Sample Size	Correlation Coefficient	Selection Model
Exponential function	$E_s = 7.5053e^{0.0274E_d}$	12	0.9822	√
Linear function	$E_s = 0.6394E_d - 2.7082$	12	0.9786
Logarithmic function	$E_s = 25.675ln\left(E_d\right) - 71.445$	12	0.9664
Power function	$E_s = 0.3851E_d^{1.1066}$	12	0.9794
Power function	$E_s = 0.3851E_d^{1.1066}$	12	0.9794

, Exponential function, linear function, logarithmic function, and power function are used to fit the relationship between the two. According to the fitting results, the exponential function form has the highest fitting accuracy, and the correlation coefficient is 0.9822. Therefore, the exponential function equation is selected as the relationship model between static elastic modulus and dynamic elastic modulus, as shown in Equation (3).

$$E_s = 7.5053e^{0.0274E_d}$$

(3)

In the equation, $E_s$ represents static elastic modulus (GPa), and $E_d$ represents dynamic elastic modulus (GPa).

2.4. Relationship Model Between Porosity and Static Elastic Modulus

Static elastic modulus and dynamic elastic modulus data are tested and analyzed. With the increase in dynamic elastic modulus, static modulus also increases correspondingly, and the two are linearly correlated. Based on the mathematical model of porosity and acoustic time difference, dynamic elastic modulus and acoustic time difference, and static elastic modulus and dynamic elastic modulus, the relationship model of porosity and static elastic modulus is derived, as shown in Equation (4).

$$\varphi =-4.0576E_s+93.058$$

(4)

In the equation, $\varphi$ represents porosity (%), and $E_s$ represents static elastic modulus (GPa).

3. Finite Element Modeling of Full-Size PDC Bit

3.1. Theoretical Model of Rock Breakage

Drucker–Prager (D–P) damage constitutive model in rock mechanics can well reflect the dynamic response of rock subjected to external compressive impact and shear. Its specific parameters are obtained by rock mechanics experiments and converted by the molar Coulomb model. In the D–P model, the basic principle of strain equivalence and generalized Hooke’s law is used to derive the damage constitutive evolution equation by introducing the strength of the element as the basic parameter of the damage variable.

The damage evolution equation is as follows:

$$D=1-e^{\left[-{(\frac{F}{F_0})}^m\right]}$$

(5)

In the equation, $D$ represents the damage variable; $F$ represents particle strength; $F_0$ represents the macroscopic strength of the rock; and $m$ represents the parameter that reflects the brittleness of the rock.

The damage constitutive equation is as follows:

$${\sigma }_1=E{\epsilon }_1{e}^{\left[-{(\frac{F}{F_0})}^m\right]}+2\mu {\sigma }_2$$

(6)

In the equation, ${\sigma }_1$ represents the nominal axial stress; $E$ represents the elastic modulus; ${\epsilon }_1$ represents the axial strain; $\mu$ represents the Poisson’s ratio; and ${\sigma }_2$ represents the lateral nominal stress.

3.2. Geometric Model and Material Parameters

Based on the 8.5-inch PDC six-blade bit commonly used in the field of NB work area, the PDC bit rock-breaking simulation model is created by using the 2021 version of the finite element simulation software. The model consists of two parts: the drill bit and the rock. The specific parameters are as follows.

(1) Bit parameters: the diameter of the PDC bit is 215.9 mm, the number of main cutters is 52, of which 30 are large teeth, 22 are small teeth, the diameter of the large cutter is 16.2 mm, the diameter of the small cutter is 13.6 mm, the bit density is 7.8 g/cm³, and the elastic modulus is 210 Gpa (as shown in Figure 4). (2) Rock parameters: the rock diameter is 700 mm, the tensile thickness is 200 mm, the rock material is tight sandstone, the density is 2.636 g/cm³, and the elastic modulus is 25 GPa.

3.3. Contact Setup and Meshing

The surface–node contact type is used to set the surface of the cutter as the main plane, encrypt the mesh of the contact part between the rock and the bit, and set the encrypted unit node as the slave plane. The friction type of the contact surface is set to penalty contact; considering the friction action of the contact surface, the friction factor is set to 0.9, and the normal direction is set to hard contact. Since the PDC bit is set as a rigid body, the mesh quality has little influence on the solution results, so the tetrahedral mesh is used, the mesh type is C3D4, and the mesh size is 4 mm. The rock has a hexahedral grid of type C3D8R, and the area below the blade is an encrypted grid, with the mesh density reduced away from the blade to help minimize the number of cells and the associated run time. The number of meshes in the encrypted part of the rock is 150, and the number of meshes away from the encrypted part is 60. Set the automatic deletion of mesh cells; that is, when the rock unit reaches the failure condition, the cells will disappear (as shown in Figure 5).

3.4. Boundary Conditions and Load Settings

The drill is considered an integral rigid body component, and its deformation and wear are not considered during the whole rock-breaking process. The rock mass is regarded as a continuous, uniform, and isotropic medium, and it is assumed that the broken rock debris can leave the drilling hole quickly; that is, the broken rock mass unit is deleted immediately. The rock underside is set to be fully restrained, allowing only axial movement and rotation of the PDC bit, limiting the lateral movement of weight on the bit. The weight on the bit was fixed at 55,000 N, the revolutions per minute were fixed at 60 r/min, and the simulation time was 10 s (as shown in Figure 6).

3.5. Rock Grid Sensitivity Analysis

According to the established geometric model, the meshing was carried out using the finite element numerical simulation software, and the C3D8R type hexahedral element was selected for the meshing of the rock. Since the part where the drill bit cuts, the rock is the core area, grid encryption processing has been carried out for the cutting area of the drill bit to improve the calculation accuracy. Meanwhile, to understand the influence of the number of grids on the numerical simulation results, in this section, seven grid number schemes are designed, namely 27,568, 33,116, 40,212, 48,355, 58,640, 67,872, and 79,024, to conduct numerical simulation analysis on the grid sensitivity. The grids of different densities are shown in Figure 7.

It can be known from Figure 8 that when the number of grids increases from 27,568 to 67,872, the mean mechanical specific energy increases rapidly. When the number of grids increased from 67,872 to 79,024, the mean mechanical specific energy remained basically unchanged and no longer changed with the increase in the number of grids. It is indicated that when the number of grids is 150, the condition of no change in grid sensitivity is achieved. Therefore, 150 meshes were selected as the meshing for the rock-breaking model of the full-size PDC drill bit.

4. Analysis of Rock Breaking Characteristics of Full-Size PDC Bit

There is a good mathematical relationship between static elastic modulus and porosity of tight sandstone reservoirs, and it is also a key parameter affecting the rock-breaking effect. Therefore, taking the static elastic modulus as the link and the six-blade PDC bit commonly used in tight sandstone reservoirs in the working area as the object, rock-breaking simulation under different static elastic modulus was carried out to monitor the changes in the rate of penetration, torque, mechanical specific energy, and other parameters, and explore the response characteristics of static elastic modulus on rock breaking feedback parameters. It lays a foundation for constructing reservoir physical property evaluation based on logging engineering parameters.

4.1. Relationship Model Between Mises Stress and Static Elastic Modulus

The static elastic modulus was set as 5 GPa, 10 GPa, 15 GPa, 20 GPa, 25 GPa, 30 GPa, 35 GPa, 40 GPa, 45 GPa, and 50 GPa, respectively, and the variation characteristics of Mises stress maximum with different static elastic modulus were compared, as shown in Figure 9.

Mises stress is associated with static elastic modulus, as shown in

Table 4. Static elastic modulus and dynamic elastic modulus.

Static elastic modulus (GPa)	5	10	15	20	25	30	35	40	45	50
Mises stress maximum (MPa)	322	324	325	347	349	360	382	422	442	492

.

It can be seen from Table 4 that the Mises stress maximum increases with the increase in static elastic modulus, and the two are positively correlated. The Mises stress maximum fluctuated from 322 MPa to 492 MPa. Mises stress maximum and static elastic modulus were fitted, and the results are shown in Figure 10. The Mises stress maximum and static elastic modulus presented an exponential function-increasing relationship with a correlation coefficient of 0.916.

4.2. Relationship Model Between PEEQ Strain and Static Elastic Modulus

The static elastic modulus was set as 5 GPa, 10 GPa, 15 GPa, 20 GPa, 25 GPa, 30 GPa, 35 GPa, 40 GPa, 45 GPa, and 50 GPa, respectively, and variation characteristics of the PEEQ strain maximum with different static elastic modulus were compared, as shown in Figure 11.

The relationship between PEEQ strain and static elastic modulus is shown in

Table 5. PEEQ strain and static elastic modulus.

Static elastic modulus (GPa)	5	10	15	20	25	30	35	40	45	50
PEEQ strain maximum	0.496	0.472	0.47	0.469	0.457	0.456	0.454	0.449	0.438	0.42

.

As can be seen from Table 5, the PEEQ strain maximum decreases with the increase in static elastic modulus, and the two are negatively correlated. The PEEQ strain maximum fluctuated from 0.42 to 0.496. The fitting curve of PEEQ maximum strain and static elastic modulus is drawn. The results are shown in Figure 12. PEEQ strain maximum and static elastic modulus show an exponential function decreasing relationship, and the correlation coefficient is 0.9046.

4.3. Relationship Model Between Rate of Penetration and Static Elastic Modulus

The static elastic modulus was set as 5 GPa, 10 GPa, 15 GPa, 20 GPa, 25 GPa, 30 GPa, 35 GPa, 40 GPa, 45 GPa, and 50 GPa, respectively, and variation characteristics of the rate of penetration with different static elastic modulus were compared, as shown in Figure 13.

The relationship between the rate of penetration and static elastic modulus is shown in

Table 6. Rate of penetration and static elastic modulus.

Static elastic modulus (GPa)	5	10	15	20	25	30	35	40	45	50
Average rate of penetration (m/h)	4.449	4.297	4.248	4.051	3.98	3.499	3.465	3.19	3.173	3.172

.

As can be seen from Table 6, the average rate of penetration decreases with the increase in static elastic modulus, and the two are negatively correlated. The average rate of penetration fluctuated from 3.172 m/h to 4.449 m/h. The fitting curve of the mean rate of penetration and static elastic modulus is drawn. The results are shown in Figure 14. The average rate of penetration and static elastic modulus show an exponential function decreasing relationship, and the correlation coefficient is 0.9522.

With the increase in static elastic modulus, the average rate of penetration decreases, and the two are negatively correlated. The rate penetration and static elastic modulus are exponential function relationship models, and the correlation coefficient is 0.9522.

4.4. Relationship Model Between Torque and Static Elastic Modulus

The static elastic modulus was set as 5 GPa, 10 GPa, 15 GPa, 20 GPa, 25 GPa, 30 GPa, 35 GPa, 40 GPa, 45 GPa, and 50 GPa, respectively, and the change characteristics of torque with different static elastic modulus were compared, as shown in Figure 15.

The relationship between torque and static elastic modulus is shown in

Table 7. Torque and static elastic modulus.

Static elastic modulus (GPa)	5	10	15	20	25	30	35	40	45	50
Average torque (kN·m)	12.84	13.36	13.43	13.5	13.61	13.7	13.78	13.91	13.97	14.47

.

As can be seen from Table 7, the average torque increases with the increase in static elastic modulus, and the two are positively correlated. The average torque fluctuation range is 12.84 kN·m~14.47 kN·m. The fitting curve of average torque and static elastic modulus was drawn, and the results are shown in Figure 16. The average torque and static elastic modulus presented an exponential function-increasing relationship, and the correlation coefficient was 0.8978.

4.5. Relationship Model Between Mechanical Specific Energy and Static Elastic Modulus

The mechanical specific energy is defined as the energy consumed by the bit to break the rock per unit volume, which is mainly composed of the work done by bit weight (vertical work) and the work done by torque (tangential work). In this paper, the classical mechanical specific energy model proposed by R. Teale is taken as the basic calculation model, and its formula is as follows [15].

$$E={\displaystyle \frac{4W}{\pi D_{\mathrm{b}}^2}}+{\displaystyle \frac{480N{T}_{\mathrm{b}}}{D_b^2{v}_{\mathrm{ROP}}}}$$

(7)

In the equation, $E$ represents the mechanical specific energy (MPa); $W$ represents bit pressure (N); $N$ represents revolutions per minute, r/min; $T_{\mathrm{b}}$ represents torque (N·m); ${\nu }_{\mathrm{ROP}}$ represents the rate of penetration (m/h); and $D_{\mathrm{b}}$ represents the drill diameter (mm).

Static elastic modulus was set as 5 GPa, 10 GPa, 15 GPa, 20 GPa, 25 GPa, 30 GPa, 35 GPa, 40 GPa, 45 GPa, and 50 GPa, respectively, and the characteristics of mechanical specific energy changes with different static elastic modulus were compared, as shown in Figure 17.

The relationship between mechanical-specific energy and static elastic modulus is shown in

Table 8. Mechanical specific energy and static elastic modulus.

Static elastic modulus (GPa)	5	10	15	20	25	30	35	40	45	50
Average mechanical specific energy (MPa)	2454	2507	2560	2695	2697	2735	2743	2781	2826	2861

.

As can be seen from Table 8, the average mechanical specific energy increases with the increase in static elastic modulus, and the two are positively correlated. The average mechanical specific energy fluctuated from 2454 MPa to 2861 MPa. The fitting curve between the average mechanical specific energy and static elastic modulus is drawn. The results are shown in Figure 18. The average mechanical specific energy and static elastic modulus show an exponential function-increasing relationship, and the correlation coefficient is 0.9297.

4.6. Relationship Model Between Porosity and Mechanical Specific Energy

Based on the mathematical relation between porosity and static elastic modulus, as well as the mathematical relation between mechanical specific energy and static elastic modulus, the relation model between porosity and mechanical specific energy is derived simultaneously, as shown in

Table 9. Mechanical specific energy and porosity.

Mechanical specific energy (MPa)	2454	2507	2560	2695	2697	2735	2743	2781	2826	2861
Porosity (%)	5.03	4.89	4.35	4.15	4.03	3.93	3.91	3.87	3.7	3.61

.

As can be seen from Table 9, porosity decreases with the increase in mechanical specific energy, and the two are negatively correlated. The fluctuation from mechanical specific energy is 2454 MPa to 2861 MPa, and the fluctuation from porosity is 3.61% to 5.03%. The fitting curve of porosity and mechanical specific energy was drawn, and the results are shown in Figure 19. Porosity and mechanical specific energy presented a linear function-decreasing relationship with a correlation coefficient of 0.9534.

4.7. Application of LWD Engineering Parameters for Porosity Prediction in Field Environments

The reservoir physical property prediction method based on the engineering parameters of logging while drilling has been applied in the tight sandstone reservoirs of the NB block. Through the real-time acquisition of engineering parameters such as drilling pressure, revolutions per minute, torque, and rate of penetration by comprehensive logging instruments, the mechanical energy value was calculated to predict the reservoir porosity. At the same time, the logging interpretation results were compared. Taking the NB-1 well as an example (with a drill bit diameter of 215.9 mm and using PDC drill bits), the porosity comparison results are shown in

Table 10. Physical property prediction results of tight sandstone reservoir in well NB-1.

Depth/m	Bit Weight/t	Revolutions per Minute/r·min−1	Torque/kN·m	Rate of Penetration/m·h−1	Mechanical Specific Energy/Mpa	Predicted Porosity/%	Logging Porosity/%	Absolute Porosity Error	Relative Porosity Error/%
4370	5	21.65	25.93	2.77	2088.46	6.25	7.1	0.85	11.97
4371	5	21.72	24.59	2.76	1994	6.57	7.1	0.53	7.46
4372	5	21.73	24.94	2.76	2023.27	6.47	7.1	0.63	8.87
4373	6	20.68	25.49	2.9	1873.43	6.98	7.3	0.32	4.38
4374	6	20.18	25.79	2.97	1806.21	7.21	7.3	0.09	1.23
4375	5	20.97	23.4	2.86	1768.27	7.34	7.3	0.04	0.55
4376	7	16.74	25.8	3.58	1244.34	9.12	8.5	0.62	7.29
4377	6	17.05	25.95	3.52	1295.91	8.94	8.5	0.44	5.18
4378	7	18.07	26.21	3.32	1470.85	8.35	8.5	0.15	1.76
4379	4	19.12	24.48	3.14	1536.2	8.13	8.5	0.37	4.35
4380	6	19.71	27.86	3.04	1861.76	7.02	7.2	0.18	2.50
4381	6	19.65	27.52	3.05	1827.33	7.14	7.2	0.06	0.83
4382	3	18.53	24.06	3.24	1417.69	8.53	7.2	1.33	18.47
4383	4	17.21	26.36	3.49	1339.65	8.80	9	0.21	2.33
4384	4	17.05	25.87	3.52	1291.51	8.96	9	0.04	0.44
4385	4	17.91	26.12	3.35	1439.13	8.46	9	0.54	6.00
4386	6	6.03	24.68	9.95	155.7	12.82	12	0.82	6.83
4387	4	7.73	23.52	7.76	242.27	12.53	12	0.53	4.42
4388	7	9.46	27.71	6.35	427	11.90	12	0.1	0.83
4389	6	12.13	27.63	4.94	700.17	10.97	9.5	1.47	15.47
4390	5	17.71	27.4	3.39	1475.33	8.33	9.5	1.17	12.32
4391	6	17.96	28.11	3.34	1558.26	8.05	9.5	1.45	15.26

, and the on-site application analysis is shown in Figure 20. In Figure 20, the blue line represents the predicted porosity, and the red square represents the logging porosity. The calculation method for the absolute error of porosity is as shown in Formula (8), and the calculation method for the relative error rate of porosity is as shown in Formula (9).

$$\mathrm{Absolute} \mathrm{porosity} \mathrm{error}=\left|\mathrm{Predicted} \mathrm{porosity}-\mathrm{Logging} \mathrm{porosity}\right|$$

(8)

$$\mathrm{Relative} \mathrm{porosity} \mathrm{error}={\displaystyle \frac{\mathrm{Absolute} \mathrm{porosity} \mathrm{error}}{\mathrm{Logging} \mathrm{porosity}}}\times 100\%$$

(9)

The distribution range of well depth is from 4370 m to 4391 m; the distribution range of mechanical specific energy is from 155.7 MPa to 2088.46 MPa, with an average value of 1401.67 MPa; the predicted porosity distribution range is from 6.25% to 12.82%, with an average value of 8.58%; the measured porosity distribution range is from 7.1% to 12%, with an average value of 8.65%; the absolute error of porosity distribution range is from 0.04 to 1.47, with an average value of 0.54; the relative error rate of porosity distribution range is from 0.44% to 18.47%, with an average value of 6.31%; the distribution range of porosity compliance rate is from 81.53% to 99.56%, with an average value of 93.69%. The porosity predicted based on engineering logging parameters is in agreement with the logging interpretation result, with a compliance rate of 93.69%.

The research results were applied to 20 wells in the NB area. Based on the engineering logging parameters, the porosity of the reservoir was quantitatively predicted, and the correlation rate with the logging interpretation results reached over 83%. This proves that this method can be used for real-time prediction of the physical properties of tight sandstone reservoirs.

A correlation analysis was conducted between the logging porosity and the predicted porosity in Table 10. The analysis results are shown in Figure 21. The Pearson correlation coefficient between the logging porosity and the predicted porosity is 0.93, indicating a highly consistent linear growth trend between the logging values and the predicted values. This demonstrates a strong positive linear correlation between the two. It proves that the porosity prediction model in this study has a very high application value within the target area.

5. Analysis of the Causes of Relative Porosity Error and Suggestions for Improvement

5.1. Analysis of Sources of Higher Relative Porosity Error

In exploration operations, the accurate measurement of porosity is crucial for stratigraphic evaluation, fluid reserves, and production potential prediction. As shown in Figure 20, for the layer section with a well depth of 4382 m, the relative error rate of porosity is 18.47%; for the layer section with a well depth of 4389 m, the relative error rate of porosity is 15.47%; and for the layer section with a well depth of 4391 m, the relative error rate of porosity is 15.26%. The relative error rates of porosity in these layer sections are relatively high, and they may be caused by the following reasons:

(1)

Measurement Technology and Methods:

①

Instrument accuracy: the used logging instruments may have accuracy limitations, resulting in deviations between the measured values and the actual values.

②

Measurement environment: the complex environment in the formation (such as high temperature, high pressure, high salinity, etc.) may affect the performance and accuracy of the logging instruments.

(2)

Formation Characteristics:

①

Heterogeneity: the heterogeneity of the formation (such as bedding, fractures, lithology changes, etc.) may lead to significant differences in porosity at different locations, increasing the measurement difficulty.

②

Fluid effects: the fluids in the formation (such as oil, gas, and water) and their distribution state may affect the logging response, thereby influencing the measurement results of porosity.

(3)

Data Processing and Interpretation:

①

Interpretation model: the adopted interpretation model may not be fully applicable to the current formation conditions, resulting in deviations in porosity calculation.

②

Data correction: there may be errors in the data correction process, such as inaccurate scales, improper environmental correction, etc.

5.2. Improvement Suggestions

Based on the above analysis, the following improvement suggestions are proposed:

(1)

Enhance measurement technology:

①

Adopt more precise logging instruments to improve measurement accuracy.

②

Develop logging technologies suitable for complex environments to reduce the influence of environmental factors on measurement results.

(2)

Strengthen stratum research:

①

Deeply understand stratum characteristics, including lithology, physical properties, and fluid distribution, to provide an accurate geological basis for logging interpretation.

②

Conduct research on stratum heterogeneity to establish more precise geological models.

(3)

Optimize data processing and interpretation:

①

Improve the logging data processing procedure to enhance the accuracy of data correction.

②

Select appropriate interpretation models based on stratum conditions to avoid errors caused by model inapplicability.

In conclusion, the reasons for the relatively high porosity error rate may involve multiple aspects, including measurement techniques, geological formation characteristics, data processing and interpretation, etc. By taking targeted improvement measures, the relative error rate of porosity measurement can be effectively reduced, and the accuracy of formation evaluation can be improved.

6. Conclusions

• The porosity, dynamic elastic modulus, and static elastic modulus of tight sandstone reservoirs have a good correlation with the acoustic time difference. Using the acoustic time difference as the transition parameter, the dynamic and static elastic modulus conversion model and the relationship model between porosity and static elastic modulus are constructed.
• The rock-breaking simulation method of the PDC bit is established, and the response characteristics of rock-breaking feedback parameters of strata with different static elastic modulus are revealed. With the increase in static elastic modulus, the rate of penetration decreases exponentially while the torque and mechanical specific energy increase exponentially.
• The physical property prediction method of tight sandstone reservoirs based on well logging parameters has been applied in more than 20 exploration wells of tight sandstone reservoirs in the NB block. The coincidence rate of prediction results and logging interpretation results has reached more than 83%, which provides an effective basis for exploration decisions.