Prediction of Oil Recovery Factor in Stratified Reservoirs after Immiscible Water-Alternating Gas Injection Based on PSO-, GSA-, GWO-, and GA-LSSVM
<p>The geometrical configuration of the model (modified from [<a href="#B47-energies-15-00656" class="html-bibr">47</a>]). is the distance from the injector, while is the distance from the top of the reservoir.</p> "> Figure 2
<p>Workflow demonstrating the development, assessment and application of the models.</p> "> Figure 3
<p>Datapoints plotted against corresponding values of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </semantics></math> for MOD1, defined using a third-order polynomial (blue line) of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>0</mn> </msub> </mrow> </semantics></math>.</p> "> Figure 4
<p>Comparison of estimated <math display="inline"><semantics> <mrow> <mi>RF</mi> </mrow> </semantics></math> with MOD1 and actual datapoints (<b>a</b>) and a histogram of the residuals (<b>b</b>).</p> "> Figure 5
<p>Illustration of optimizer performance in terms of the best solution’s <span class="html-italic">R</span><sup>2</sup> (<b>a</b>), RMSE (<b>b</b>) and search parameter values <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>γ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<b>c</b>) and <math display="inline"><semantics> <mrow> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>σ</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> (<b>d</b>), at a given iteration. In total, 20 solutions were initiated and run for 30 iterations in each case. Two identical initializations (marked 1 and 2) were run for each algorithm.</p> "> Figure 6
<p>Comparison of estimated <math display="inline"><semantics> <mrow> <mi>RF</mi> </mrow> </semantics></math> and actual datapoints on (<b>a</b>) the training set, (<b>b</b>) validation set and (<b>c</b>) test set. Estimated points are based on MOD2 (optimized LSSVM). The orange line represents perfect match.</p> "> Figure 7
<p>Histogram of residual errors (estimated <math display="inline"><semantics> <mrow> <mi>RF</mi> </mrow> </semantics></math> minus actual <math display="inline"><semantics> <mrow> <mi>RF</mi> </mrow> </semantics></math> ) for the total dataset based on MOD2 (optimized LSSVM model).</p> "> Figure 8
<p>Histogram of partial derivatives for the total dataset based on MOD2 (the optimized LSSVM model). Each partial derivative is evaluated numerically with a small or large difference <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <mi>x</mi> </mrow> </semantics></math>.</p> "> Figure 9
<p>Contour plots of recovery factor RF plotted against <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>r</mi> <mi>w</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>5</mn> </msub> <mo>=</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>M</mi> <mrow> <mi>g</mi> <mi>o</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>. The latter represents variation in oil viscosity, which affects all of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>5</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>6</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>. The four cases are for low heterogeneity and hysteresis (<b>a</b>), high heterogeneity and low hysteresis (<b>b</b>), low heterogeneity and high hysteresis (<b>c</b>) and high heterogeneity and hysteresis (<b>d</b>). See all input values in <a href="#energies-15-00656-t005" class="html-table">Table 5</a>.</p> "> Figure 10
<p>Contour plots of recovery factor RF plotted against <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <msub> <mi>F</mi> <mi>H</mi> </msub> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>5</mn> </msub> <mo>=</mo> <mi>l</mi> <mi>o</mi> <mi>g</mi> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>M</mi> <mrow> <mi>g</mi> <mi>o</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>)</mo> </mrow> </mrow> </semantics></math>. The latter represents variation in oil viscosity, which affects all of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>5</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>6</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>7</mn> </msub> <mo>,</mo> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>. The cases are for WAG injection with <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>w</mi> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </semantics></math> and either low (<b>a</b>) or high (<b>b</b>) hysteresis. See all input values in <a href="#energies-15-00656-t005" class="html-table">Table 5</a>.</p> "> Figure 11
<p>Contour plot of recovery factor RF plotted against <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>r</mi> <mi>w</mi> </msub> </mrow> </semantics></math> and log gravity number with equal values of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>. Low-heterogeneity (<b>a</b>) and high-heterogeneity (<b>b</b>) cases are shown (see all input values in <a href="#energies-15-00656-t006" class="html-table">Table 6</a>).</p> "> Figure 12
<p>Contour plot of recovery factor RF plotted against <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>r</mi> <mi>w</mi> </msub> </mrow> </semantics></math> and log gravity number with equal values of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>. Favorable (<b>a</b>) and unfavorable (<b>b</b>) mobility ratio cases are shown (see all input values in <a href="#energies-15-00656-t006" class="html-table">Table 6</a>).</p> "> Figure 13
<p>Contour plot of recovery factor RF plotted against <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>=</mo> <msub> <mi>r</mi> <mi>w</mi> </msub> </mrow> </semantics></math> and log gravity number with equal values of <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>7</mn> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>8</mn> </msub> </mrow> </semantics></math>. Low- (<b>a</b>) and high- (<b>b</b>) hysteresis cases are presented (see all input values in <a href="#energies-15-00656-t006" class="html-table">Table 6</a>).</p> "> Figure 14
<p>Contour plots of recovery factor RF as function of varying water fraction (horizontal axis) and the indicated parameter (<math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>3</mn> </msub> </mrow> </semantics></math> in (<b>a</b>), <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>4</mn> </msub> </mrow> </semantics></math> in (<b>b</b>), <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>5</mn> </msub> </mrow> </semantics></math> in (<b>c</b>) and <math display="inline"><semantics> <mrow> <msub> <mi>x</mi> <mn>6</mn> </msub> </mrow> </semantics></math> in (<b>d</b>)) on the vertical axis while holding other parameters fixed. <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>w</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> indicates gas injection and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>w</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> water injection.</p> "> Figure 15
<p>Illustration of the 3D model, where permeability and well placements are indicated.</p> "> Figure 16
<p>RF after 1.5 PV calculated for different injected WAG fractions (<span class="html-italic">r<sub>w</sub></span>), low or high oil viscosity and low or high degree of hysteresis, calculated based on a 3D Eclipse model (<b>a</b>), MOD1 (<b>b</b>) or MOD2 (<b>c</b>).</p> ">
Abstract
:1. Introduction
- -
- How well do the models predict WAG performance?
- -
- Which parameters affect RF the most?
- -
- Do the parameters have a positive or negative effect on RF?
- -
- Will the models properly account for WAG injection and single phase injection?
2. Theory
2.1. Mathematical Model
2.2. WAG Efficiency Characterization Using Dimensionless Number
2.3. Workflow
2.3.1. Model Input Parameters
2.3.2. Reservoir Simulation Dataset and Model Approaches
2.3.3. Machine Learning Dataset Preparation
2.3.4. Machine Learning Workflow
3. Results and Discussion
3.1. Preliminary Dataset Analysis
3.2. Development of MOD1
3.3. Development of LSSVM Model MOD2
3.4. Sensitivity Analyses with Optimized LSSVM Model MOD2
3.4.1. Variation of Oil Viscosity
- -
- Optimal RF values were mainly obtained at an intermediate water fraction (consider any line parallel with the x-axis), suggesting that WAG gives higher RF than single-phase injection. Cases with low hysteresis and favorable mobility ratios seem to give similar RF for water injection and WAG (although WAG with a low water fraction seems optimal) (see Figure 9a,b (low and high heterogeneity)).
- -
- The advantage of WAG over single-phase injection was most clear when hysteresis was significant (see Figure 9c,d). The best water fraction produced RF up to 0.3 units higher than the worst fraction. This strong impact was mainly at low oil viscosity (low ) with optimal water fraction around 0.5–0.6. For higher oil viscosity or lower heterogeneity cases, WAG was in many cases only marginally better (~0.05 units) than the best single-phase injection.
- -
- Increased oil viscosity reduced RF for a given water fraction (follow any line parallel with the y-axis). This was dominant over the WAG fraction at high viscosities, except for the highly heterogeneous cases with high hysteresis (Figure 9d). This demonstrates the benefit of WAG in heterogeneous formations and that hysteresis is an important contributor.
- -
- For a given heterogeneity (low or high), increased hysteresis improved RF (compare Figure 9c,d (high hyst) with Figure 9a,b (low hyst)). This was related to the improved gas–oil mobility ratio and reduced gravity segregation, which improves volumetric sweep. The optimal water fraction shifted to more central values, since both phases are needed for hysteresis.
- -
- -
- For low hysteresis (Figure 10a), RF was very sensitive to heterogeneity for low oil viscosities and increased heterogeneity reduced RF. For high viscosity, RF changed little with heterogeneity.
- -
- With significant hysteresis (Figure 10b), low-viscosity cases produced reduced RF at higher heterogeneity, while high-viscosity cases produced increased RF.
3.4.2. Variation of Well Distance, Injection Rate or Density Difference
3.4.3. Handling Single Phase Data
3.5. Application to a 3D Model
4. Conclusions
- -
- We demonstrated that it is possible to predict the recovery factor during single-phase and WAG injection.
- -
- The LSSVM model optimized by GWO or PSO performed better than when optimized by GA or GSA.
- -
- MOD2 with eight input variables clearly performed better than MOD1 with one input. Based on the total dataset, the RMSE and R2 were 0.0080 and 0.998 for MOD2 and 0.050 and 0.889 for MOD1, respectively.
- -
- The physics-based training of MOD2 was applied successfully. Single-phase injection data points were duplicated using different values in the input variables that should not affect RF, while keeping the same values for the relevant input variables and the output. The model correctly displayed little response to the irrelevant variables, but not for all conditions. Improvements could be made by adding more of these points or by training the model to include such constraints via an added penalty term in the objective function. MOD1 was analytically independent of these variables during single-phase injection.
- -
- Plotting histograms of partial derivatives of RF showed that for most input variables, increasing them would increase RF for some conditions, but reduce RF under others, demonstrating coupling in the data.
- -
- The best model (MOD2) predicted that under identical conditions, an optimal injected WAG fraction existed that outperformed single-phase injection (water or gas). The benefit of WAG was much clearer when gas relative permeability hysteresis was significant.
- -
- The mobility ratios were important input variables. Increased values tended to reduce RF.
- -
- The roles of gravity numbers, heterogeneity and hysteresis were coupled. Strong gravity effects reduced RF in low-heterogeneity cases, but improved RF in heterogeneous cases.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
Roman | |
LSSVM constant | |
Land’s trapping parameter | |
Heterogeneity multiplier | |
Gravity multiplier | |
Layer height, m | |
Relative permeability | |
Relative permeability endpoints | |
Horizontal and vertical absolute permeability, m | |
Distance from injector to producer, m | |
Width of reservoir, m | |
Total height of reservoir, m | |
Mobility ratio | |
Effective mobility ratios between gas-oil and between water-oil | |
Effective three phase mobility ratio accounting for all mechanisms | |
Corey exponents, | |
Number of particles | |
Number of PSO iterations | |
Gravity number, - | |
Coefficient of determination, - | |
Pearson correlation coefficient between vectors x and y, - | |
rw | Water volume fraction in a WAG cycle, - |
Recovery factor, - | |
Phase saturation, - | |
Residual phase saturation, - | |
Time, seconds | |
Horizontal direction towards producer, m | |
Input vector, - | |
Standard deviance multiplier, - | |
LSSVM output / RF, - | |
Vertical direction downwards, m | |
Greek | |
Carlson hysteresis parameter | |
LSSVM coefficients | |
Regularization coefficient | |
Density difference, kg/m3 | |
Phase mobility | |
μi | Viscosity, Pa⋅s |
ρi | Phase density, kg/m3 |
RBK width parameter | |
Porosity | |
Acceleration constants | |
Damping factor | |
Indices | |
* | characteristic value, |
arithmetic | |
gas | |
gravity | |
harmonic | |
phase | |
layer | |
oil | |
residence | |
initial reservoir conditions | |
segregation | |
total | |
water | |
Abbreviations | |
EOR | Enhanced oil recovery |
LSSVM | Least squares support vector machine |
PSO | Particle swarm optimization |
RMSE | Root mean square error |
WAG | Water alternating gas |
Appendix A. Reservoir Model Parameters
100 | 1000 m | 0.30 | 1014.6 m3/d | Half cycle duration | 45 d | ||||
1 | 100 m | 3 m | 1014.6 m3/d | Total injection volume, PVs | 1.5 PVs | ||||
81 | 81 m |
0.25 | 2 | 0.842 | |||
0.25 | 2 | 0.158 | |||
0.05 | 2 | 0.00 | |||
0.005 | 2 | 0.20 | |||
0.10 |
Layer 1 (top) | 300 | 300 | 500 | 1000 |
2 | 300 | 100 | 50 | 20 |
3 | 300 | 900 | 500 | 1000 |
4 | 300 | 300 | 50 | 20 |
5 | 300 | 100 | 500 | 1000 |
6 | 300 | 900 | 50 | 20 |
7 | 300 | 300 | 500 | 1000 |
8 | 300 | 100 | 50 | 20 |
9 (bottom) | 300 | 900 | 500 | 1000 |
FH | 1.0 | 2.1 | 3.0 | 12.9 |
Appendix B. Least Squares Support Vector Machines (LSSVM)
Appendix C. Optimization Algorithms
Common | PSO | GA | ||||||
# particles /chromosomes/wolves | Acceleration constants | Mutation rate | ||||||
# variables/genes | Damping factor | Mutation factor | ||||||
# iterations | GSA | # elite chromosomes | ||||||
Search range variable 1 | Initial gravity | GWO | ||||||
Search range variable 2 | Gravity reduction factor | - | ||||||
Initial velocity range | Small constant |
Appendix C.1. Particle Swarm Optimization (PSO)
- Generate an initial set of ‘particles’, which are random solution vectors , all in . The entire set of particles is called the swarm.
- The indices and refer, respectively, to the particle and the parameter in the and vector while refers to the uniform probability distribution over the specified range.
- c.
- At a given iteration, the solution estimate of particle corresponds to its current ‘position’ in the search space, termed . The quality of each of the solution estimates is evaluated by the coefficient of determination . The best solution position (with highest ) a particle obtains while it moves in the search space is saved and updated if it improves. These solution vectors are called . Similarly, the best solution of all the particles (the swarm) is termed . This position updates if the particles find a better solution.
- d.
- New velocities are calculated for each particle based on the old velocity and how far the particle is from its historic best position and from the swarm’s historic best position :
- e.
- The position of each particle at the next iteration is updated by adding the velocity:
- f.
- Finally, the ‘new’ parameters are set as ‘old’ and a new iteration starts from point c. The procedure stops when a set number of iterations is completed.
Appendix C.2. Gravitational Search Algorithm (GSA)
- Assign initial positions and velocities according to (A16) and (A17).
- The gravitational constant is reduced from an initial value at iteration according to a reduction factor down to at the last iteration:
- c.
- For a given particle , the force working on it from another particle is given by:
- d.
- The acceleration of particle is then its net force divided by the mass, where random weight components are introduced:
- e.
- The velocities and new positions are calculated as:
Appendix C.3. Genetic Algorithm (GA)
- a.
- A first generation of chromosomes is initialized using (A16).
- b.
- In ‘Selection’, pairs of two chromosomes from the previous generation, called parents, are combined to produce a new generation of chromosomes, ‘children’. The selection of the parents is random with probability proportional to their relative fitness:
- c.
- ‘Crossover’ is then used to define the new generation chromosomes. In child 1 of a parent pair, the first gene is from parent 1 and the second gene from parent 2. For child 2 of that pair, the first gene is from parent 2 and the second from parent 1.
- d.
- ‘Mutation’ is the operation of randomly modifying one or both genes in a child. The probability that a given gene is mutated is the mutation rate . Thus, for the fraction of new genes we perform the following modification (while the rest are not modified):
- e.
- ‘Elitism’ involves keeping some of the best chromosomes from the previous generation unmodified into the new generation.
Appendix C.4. Grey Wolf Optimization (GWO)
- a.
- Initialize the positions of the wolves according to (A16). In this algorithm, we call the positions instead of .
- b.
- At a given iteration the best, second-best and third-best solutions are called the alpha , beta and delta wolves, respectively. The others are grouped as omega wolves. The positions are denoted and , or for all the wolves.
- c.
- Assume the ‘prey’ is located at a position . A distance measure to the prey along coordinate is given by:
Appendix D. Statistical Measures
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MOD1 | Single Phase Cases | WAG Cases | Total |
---|---|---|---|
96 | 2472 | 2568 | |
MOD2 | Single phase cases | WAG cases | Total |
Training (70%) | 68 × 16 = 1088 | 1730 | 2818 |
Validation (15%) | 14 × 16 = 224 | 371 | 595 |
Testing (15%) | 14 × 16 = 224 | 371 | 595 |
Total | 96 × 16 = 1536 | 2472 | 4008 |
MOD1 | Train | Val | Test | Tot | ||||||||
Min | Mean | Max | Min | Mean | Max | Min | Mean | Max | Min | Mean | Max | |
−0.2 | 1.4 | 3.4 | −0.1 | 1.5 | 3.2 | −0.1 | 1.4 | 3.2 | −0.2 | 1.4 | 3.4 | |
0.14 | 0.49 | 0.88 | 0.20 | 0.49 | 0.84 | 0.19 | 0.50 | 0.85 | 0.14 | 0.49 | 0.88 | |
MOD2 | Train | Val | Test | Tot | ||||||||
Min | Mean | Max | Min | Mean | Max | Min | Mean | Max | Min | Mean | Max | |
0 | 0.5 | 1 | 0 | 0.5 | 1 | 0 | 0.4 | 1 | 0 | 0.5 | 1 | |
0 | 0.5 | 1.1 | 0 | 0.5 | 1.1 | 0 | 0.4 | 1.1 | 0 | 0.5 | 1.1 | |
0 | 1.2 | 2.5 | 0 | 1.2 | 2.5 | 0 | 1.1 | 2.5 | 0 | 1.2 | 2.5 | |
0 | 1.3 | 3 | 0 | 1.3 | 3 | 0 | 1.4 | 3 | 0 | 1.3 | 3 | |
0.1 | 1.4 | 2.4 | 0.1 | 1.4 | 2.4 | 0.1 | 1.4 | 2.4 | 0.1 | 1.4 | 2.4 | |
0.0 | 1.4 | 2.3 | 0.0 | 1.4 | 2.3 | 0.0 | 1.3 | 2.3 | 0.0 | 1.4 | 2.3 | |
−4.6 | −2.6 | −0.9 | −4.6 | −2.7 | −0.9 | −4.6 | −2.7 | −0.9 | −4.6 | −2.6 | −0.9 | |
−7.9 | −3.0 | −0.8 | −7.9 | −3.1 | −0.8 | −7.9 | −3.0 | −0.8 | −7.9 | −3.0 | −0.8 | |
0.14 | 0.45 | 0.88 | 0.20 | 0.44 | 0.84 | 0.19 | 0.48 | 0.85 | 0.14 | 0.45 | 0.88 |
MOD1 | |||||||||
---|---|---|---|---|---|---|---|---|---|
MOD2 | |||||||||
WAG cases | |||||||||
RMSE | R2 | ||||||||
---|---|---|---|---|---|---|---|---|---|
Seed | Train | Val | Test | Train | Val | Test | |||
LSSVM (preset) | |||||||||
PSO-LSSVM | |||||||||
GSA-LSSVM | |||||||||
GWO-LSSVM | |||||||||
GA-LSSVM | |||||||||
Range (opt.) | |||||||||
Final (MOD2) |
Low Het, Low Hyst | High Het, Low Hyst | Low Het, High Hyst | High Het, High Hyst | |
---|---|---|---|---|
x1 | 0:1 | |||
x2 | 0.25 | 1 | 0.25 | 1 |
x3 | 0 | 0 | 2.5 | 2.5 |
x4 | 3 | 3 | 0.5 | 0.5 |
x5 | 0.2:2.2 | |||
x6 | 0.2:2.2 | |||
x7 | −3:−1 | |||
x8 | −3:−1 |
Lo Het | Hi Het | Fav | Unfav | Lo Hyst | Hyst | |
---|---|---|---|---|---|---|
x1 | 0:1 | |||||
x2 | 0 | 1 | 0.8 | 0.3 | ||
x3 | 1 | 0 | 0 | 2.5 | ||
x4 | 3 | 3 | 3 | 0 | ||
x5 | 2 | 0.5 | 2 | 1.5 | ||
x6 | 2 | 0.5 | 2 | 1.5 | ||
x7 | −4:−1.5 | |||||
x8 | −4:−1.5 |
Vary | Vary | Vary | ||
---|---|---|---|---|
0:1 | ||||
0.8 | ||||
0:2.5 | 1 | 1 | 1 | |
1 | 0:3 | 1 | 1 | |
1.5 | 1.5 | 0.1:2.4 | 1.5 | |
1.5 | 1.5 | 1.5 | 0.0:2.3 | |
−2 | ||||
−2 |
Layer | 0, 0.33, 0.5, 0.67, 1 | ||||
---|---|---|---|---|---|
1 | 2170 | 0.324 | 42 | 0.73 | |
2 | 65.9 | 0.297 | 29 | 0, 2.5 | |
3 | 589 | 0.323 | 33 | 3, 0 | |
1.83, 2.40 | |||||
250 kg/m3 | m3 | 1.50, 2.06 | |||
450 kg/m3 | 20 years | −1.28, −1.84 | |||
1500 m | 0.84 | −0.96, −1.52 | |||
750 m | 7600 m3/d |
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Andersen, P.Ø.; Nygård, J.I.; Kengessova, A. Prediction of Oil Recovery Factor in Stratified Reservoirs after Immiscible Water-Alternating Gas Injection Based on PSO-, GSA-, GWO-, and GA-LSSVM. Energies 2022, 15, 656. https://doi.org/10.3390/en15020656
Andersen PØ, Nygård JI, Kengessova A. Prediction of Oil Recovery Factor in Stratified Reservoirs after Immiscible Water-Alternating Gas Injection Based on PSO-, GSA-, GWO-, and GA-LSSVM. Energies. 2022; 15(2):656. https://doi.org/10.3390/en15020656
Chicago/Turabian StyleAndersen, Pål Østebø, Jan Inge Nygård, and Aizhan Kengessova. 2022. "Prediction of Oil Recovery Factor in Stratified Reservoirs after Immiscible Water-Alternating Gas Injection Based on PSO-, GSA-, GWO-, and GA-LSSVM" Energies 15, no. 2: 656. https://doi.org/10.3390/en15020656