Research Article Volume 5 Issue 2
Department of Mineral and Petroleum Resources Engineering, Nigeria
Correspondence: Abubakar Tanko, Mineral and Petroleum Resources Engineering Department, Kaduna Polytechnic, Nigeria, Tel +234803458 0686
Received: September 23, 2020  Published: December 22, 2020
Citation: Tanko ID, Tanko A, Bello A. Rate of penetration optimization using burgoyne and young model (a case study of Niger delta formation). Int J Petrochem Sci Eng 2020;5(2):6771. DOI: 10.15406/ipcse.2020.05.00124
Drilling optimization models provide a technique for predicting and controlling drilling processes. Rate of penetration (ROP) prediction before drilling provides a means of improving overall drilling efficiency, minimization of drilling time and by extension reduction of drilling cost. Several ROP models are available in the oil and gas industry today, however most of these models are inadequate leading to inaccurate predictions. This work employs a different technique for ROP prediction by modifying original Burgoyne and Young’s (B&Y) model using data from Niger Delta. The ROP prediction and percentage error were determined at each of the selected well depth intervals The results obtained showed that the Burgoyne &Young model performed well by error of about 0.03%. The model was further optimized to minimize the error and the overall result shows that the error was minimized from 0.03% to 0.003%. Results obtained from the optimized Burgoyne and Young model imply that the model is suitable for ROP prediction in the Niger Delta.
Keywords: drilling operation, optimization, rate of penetration, burgoyne, young model
The major goal of every drilling operation is to make holes in the ground from surface to a reference depth mainly for oil or gas exploitation. Petroleum industry is a capital intensive industry. There is a need to save time, cost and increases efficiency. One of the most costly aspects of the industry is exploration and drilling and therefore has lot of potential for optimization and reducing cost. Planning and predicting future drilling operation base on controllable variables will be essential in order to realize these efficiency gains.^{1–3} This may aid ROP prediction using mathematical models.^{4–12} The study area is located in the onshore part of Niger Delta sedimentary basin. The subarea covered by the Niger Delta basin is about 7500km^{2} a total area of 300,000km^{2} and sediment fill has a depth between 9–12km.^{13} It is composed of several different geological formations that indicate how this basin was formed, as well as the regional and large scale tectonics of the area. In addition this basin is an extensional basin surrounded by many other basin in the area that all formed from similar process. The Niger Delta basin is bounded by the Cameroon volcanic line and the transform passive continental margin.^{13}
The stratigraphic structure of the Niger Delta basin is divided into three (3) unit Benin formation, Agbada formation and Akata formation. Benin formation is the topmost formation followed by Agbada formation at the middle then the Akata formation which is lowest. The Benin formation is made up continental sand deposit with shale intercalation covered with topmost low velocity layer, which in most cases is weathered within which surface wave are excited and generated. The Agbada formation is below the Benin formation. It contains reservoir sand which traps the hydrocarbon resources of the Niger Delta Basin. The Akata formation is dominated by shale it serves as the main source of hydrocarbon in the Niger Delta Basin. Economically Niger Delta basin has a very high economic value. It contains a very predictive petroleum system, it produce more than 2 million barrels of oil per day. The entire system is predicted to contain 34.5 billion barrels of oil and 95 trillion cubic feet of natural gas.^{14} These make it one of the largest oil production provinces in the world.
Rate of penetration models
Mathematical drilling models provide method to predict and control drilling process and minimize drilling cost. Drilling models also provide a means of recognizing unusual effect when the observed but performance deviate from prediction rate, some of this models are Burgoyne and Young (B&Y), Mechanical Specific Energy (M.S.E), Dexponent, modified Dexponent, Cunningham, Maurer, Bingham, Moore, Warren Motahari etc. drilling models. Drilling parameters obtained from two (2) wells (well A & B) drilled within the Niger.^{15}
Burgoyne and young (B&Y) drilling models is the most complete mathematical that has been used for rolling cutter bit. In 1973 B&Y suggested a drilling model considering the effect of several drilling variables on the rate of penetration. In this model the effect of the parameters such as WOB, RPM, Bit tooth wear and other assumed to be independent of one another.
$R=(f1)(f2)(f3)(f4)(fn)$ (1)
$f1={e}^{2.303a1}=k$ (2)
$f2={e}^{2.303a2(10000D)}$ (3)
$f3={e}^{2.303a3{D}^{0.69(gp9.0)}}$ (4)
$f4={e}^{2.303a4D(gppc)}$ (5)
$f5={\left[\frac{(\frac{w}{db}){(\frac{w}{db})}_{t}}{4{(\frac{w}{db})}_{t}}\right]}^{a5}$ (6)
$f6={\left(\frac{N}{60}\right)}^{a6}$ (7)
$f7={e}^{a7h}$ (8)
$f8={\left(\frac{{F}_{j}}{1000}\right)}^{a8}$ (9)
D= true vertical depth (ft)
gp= Pore pressure gradient (lbm/ft)
$\rho c$ =equivalent circulating density
$\left(\frac{w}{db}\right)t=$ Threshold bit weight per inch of bit diameter at which the bit begin to drill 1000lbf/inch
h=fractional hook dullness
Fj=hydraulic impact force beneath the bit force lbf
a1 to a8 = constant that must be chosen based on local drilling conditions
f1=function represent the effect of formation strength and bit type on penetration rate.
f_{2}=Function account for the rock strength increase due to normal compaction with depth.
f_{3}=function model effect of under compaction experienced in abnormal pressure formation.
f_{4}=function model the effect of bit weight and rotary speed on penetration rate.
f_{5}&f_{6} function account for the rock strength increase due to normal compaction with depth.
f_{7}=Function models the effect of tooth wear.
f_{8}==function model the effect of bit hydraulic on rate of penetration.
h=fractional tooth dullness
F_{j}=hydraulic impact force beneath the bit (lbf)
The constant a_{1} through a_{8} can be computed using past drilling data obtained in the area when drilling data is available. The above drilling model can be use for drilling optimization calculation and for detection of changes in formation pore pressure.^{16}
Rate of penetration prediction was done using Burgoyne and Young drilling model. Well data in Niger Delta Basin was collected from Nigeria Petroleum Development Company a subsidiary of Nigeria National Petroleum Company (N.N.P.C). The name of the well was deleted from the given data for confidential purpose, the name of the well was renamed as Well A with a total depth of 9664ft. The Well data consist of drilling parameters such as well depth, rate of penetration, weight on bit, flow rate, rotation per minute, torque, bit diameter, stand pipe pressure, etc. These parameters were analyzed using B&Y models. Well depth from 1000ft to 9000ft at 200ft interval was selected for this analysis. In this model there are some unknown parameters coefficient which must be determined based on past drilling data obtained from a field in order to determine the unknown parameters, a linear regression technique will be applied which as follows.
Y = α₀+α₁β1+α₂β2+α₃β+α₄β+α₅β+αnβn (10)
Where Y is the dependent variable,α₀ is the intercept term and the regression coefficient α_{1},α_{2,}α_{3,} α_{n} are the analogues of the shape of linear regression. From the above equation Y is the ROP; relevant drilling parameters will make up the regression variable [β_{1&}β_{n}]. α₀ to α_{n} Coefficient will be determined by using a software called statistical package for social science (SPSS Software). This SPSS software will perform the regression analysis after all the relevant drilling parameters has been uploaded into it and then run. The analysis will then provide an output computed data. The generated output data are now coefficient of interest. The first value generated will be α₀ while the values after this are the coefficient i.e. (α_{1 }to α_{n}). These values are to be multiplying with regression variable according to their order which is given as follows:
$ROP={\alpha}_{o}+{\alpha}_{1}WOB+{\alpha}_{2}FR+{\alpha}_{3}RPM+{\alpha}_{4}TRQ+{\alpha}_{5}Bd+{\alpha}_{6}SPP$ (11)
After substituting the values of the generated coefficient (i.e.α_{0} to α_{6}) and drilling factors (β_{1 }to β_{6}) in the above equation using Microsoft excel software a new predicted ROP is now obtained in ft. /hrs at every selected depth.
Error calculation
The percentage error at each selected depth was calculated using the formula below
$PercentageError=\frac{\mathrm{Pr}edictedROPActualROP}{ActualROP}*100\%$ (12)
While the average percentage error was also calculated using the formula below.
$AveragePercentageError=\frac{{\displaystyle \sum \left(\frac{\mathrm{Pr}edictedROPActualROP}{ActualROP}\right)}}{N}*100\%$ (13)
The above error calculation was carried out using Microsoft excel.
Error minimization
In order to minimize the error the B&Y linear regression model was further developed as follows
$ROP={\alpha}_{o}+{\alpha}_{1}WOB+{\alpha}_{2}FR+{\alpha}_{3}RPM+{\alpha}_{4}TRQ+{\alpha}_{5}Bd+{\alpha}_{6}SPP+{\alpha}_{7}MW$ (14)
In the above equation another drilling parameter i.e. mud weight was introduced. The analysis was carried out using the same procedure as it was done initially in the B&Y linear regression analysis and a very desirable result was obtained.
The table above shows the generated coefficient from Statistical Package for Social Sciences Software for both initial B&Y and new B&Y regression analysis. Comparison was made between the actual ROP and predicted ROP. The actual ROP was the ROP contained in the original well Data (Well A Data) while the predicted ROP was the ROP calculated using B&Y models (Table 1). The comparison was done between the well depths of 1000ft to 9000ft at 200ft depth interval. Percentage error at each depth interval was calculated and finally average percentage error was also calculated. A graph of ROP was plotted against well depth, depth on the horizontal axis in feet (ft.) and ROP on the vertical axis in feet per hour (ft./hr.) on the vertical axis. From the graph, the actual ROP was considered as the reference plot represented with blue dotted point (Table 2). The predicted ROP are represented with lines in difference colors (Table 3). B&Y line graph seem to correlate very well in many section of the well, this shows that this model performed very well (Figure 1).
Coefficients α0 
α1 
α2 
α3 
α4 
α5 
α6 
α7 

Initial B&Y 
309.5 
0.036 
0.002 
0.212 
0.017 
4.891 
0.108 
 
New B&Y 
254.235 
0.065 
0.002 
0.292 
0.017 
5.749 
0.121 
8.776 
Table 1 Output computed data from SPSS
Depth 
Actual 
Predicted ROP (ft/hr) 
%Error 
1000 
209 
160 
23% 
1200 
329 
169 
49% 
1400 
181 
168 
7% 
1600 
187 
161 
14% 
1800 
145 
150 
3% 
2000 
161 
141 
12% 
2200 
144 
142 
1% 
2400 
120 
143 
20% 
2600 
106 
148 
39% 
2800 
112 
148 
33% 
3000 
109 
140 
28% 
3200 
106 
129 
22% 
3400 
134 
157 
17% 
3600 
125 
115 
8% 
3800 
88 
116 
31% 
4000 
64 
113 
76% 
4200 
100 
114 
14% 
4400 
44 
90 
108% 
4600 
45 
82 
80% 
4800 
76 
53 
30% 
5000 
119 
96 
19% 
5200 
169 
123 
27% 
5400 
136 
109 
20% 
5600 
110 
109 
1% 
5800 
100 
102 
2% 
6000 
102 
123 
20% 
6200 
97 
120 
24% 
6400 
86 
26 
69% 
6600 
111 
103 
7% 
6800 
90 
99 
10% 
7000 
110 
96 
12% 
7200 
96 
90 
6% 
7400 
69 
87 
26% 
7600 
111 
79 
29% 
7800 
116 
86 
26% 
8000 
92 
121 
31% 
8200 
118 
169 
43% 
8400 
114 
120 
5% 
Table 2 Predicted ROP using B&Y models
Depth 
Actual ROP (114) 
B&Y(TTRJ 
New B&Y (tiALS) 
% Error 
1000 
209 
160 
161 
23% 
1200 
329 
169 
170 
48% 
1400 
181 
168 
170 
6% 
1600 
187 
161 
161 
14% 
1800 
145 
150 
149 
3% 
2000 
161 
141 
140 
13% 
2200 
144 
142 
141 
2% 
2400 
120 
143 
142 
19% 
2600 
106 
148 
147 
38% 
2800 
112 
148 
148 
32% 
3000 
109 
140 
138 
26% 
3200 
106 
129 
126 
19% 
3400 
134 
157 
158 
18% 
3600 
125 
115 
111 
12% 
3800 
88 
116 
111 
26% 
4000 
64 
113 
108 
69% 
4200 
100 
114 
111 
11% 
4400 
44 
90 
83 
92% 
4600 
45 
82 
76 
67% 
4800 
76 
53 
44 
42% 
5000 
119 
96 
83 
30% 
5200 
169 
123 
129 
24% 
5400 
136 
109 
116 
15% 
5600 
110 
109 
115 
5% 
5800 
1(H) 
102 
107 
7% 
6000 
102 
123 
127 
24% 
6200 
97 
120 
124 
28% 
6400 
86 
26 
29 
66% 
6600 
111 
103 
105 
5% 
6800 
90 
99 
102 
13% 
7000 
110 
96 
98 
10% 
7200 
96 
90 
92 
5% 
7400 
69 
87 
88 
27% 
7600 
111 
79 
79 
29% 
7800 
116 
86 
89 
23% 
8000 
92 
121 
134 
46% 
8200 
118 
169 
169 
43% 
8400 
114 
120 
121 
6% 
8600 
102 
118 
118 
16% 
8800 
196 
174 
174 
11% 
9000 
178 
155 
155 
13% 
Sum 
5007 
4950 
102700% 




Ave .% error 
0% 
Table 3 Predicted ROP for initial B&Y and new B&Y
Predicted B&Y model was further modeled by including additional drilling parameter (i.e. mud weight) into the initial regression equation and analyzed. The result shows that the error was minimized from 0.03% to 0.0003%. Actual ROP, Predicted ROP of initial B&Y and modified B&Y in feet per hour was plotted against well depth measured in feet. From the fig, the actual ROP was considered as the reference plot represented with dotted point. The initial and modified B&Y predicted ROP are represented with lines (Figure 2). Initial and modified B&Y line graph seem to correlate very well in many section of the well, this shows that the modified B&Y model performed very well even more than the initial B&Y Model. The error difference between initial & and new predicted ROP using B&Y model can be can be clearly illustrated from the chart in Figure 3.
B&Y model has been tested with Niger Delta well data for ROP prediction, the result shows that the model performed very well by producing a little amount of error of about 0.03% and the error was further minimized to 0.0003% after inclusion of additional drilling parameter. The model can estimate ROP as function of several drilling parameters such as WOB, RPM, Mud weight, Standpipe Pressure, Torque, flow rate, mud weight etc. with a reasonable accuracy.
The result can also provide a guide for next drilling operation near the drilled well within the Niger Delta basin and the predicted values can be used as a reference to obtain optimum drilling performance and therefore reduce cost and time of drilling operation.
We want to thank the Nigerian Petroleum Development Company (NPDC) for providing us with the data we used in the work.
There are no conflicts of interest.
None.
©2020 Tanko, et al. This is an open access article distributed under the terms of the, which permits unrestricted use, distribution, and build upon your work noncommercially.