This paper presents the numerical density derivative approach (another phase of numerical welltesting) in which each fluid&#x2019;s densities around the wellbore are measured and used to generate pressure equivalent for each phase using simplified pressure-density correlation, as well as new statistical derivative methods to determine each fluid phase&#x2019;s permeabilities, and the average effective permeability for the system with a new empirical model. Also density related radial flow equations for each fluid phase are derived and semilog specialised plot of density versus Horner time is used to estimate <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M1" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-108" d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z"/></g></svg> relative to each phase. Results from 2 examples of oil and gas condensate reservoirs show that the derivatives of the fluid phase pressure-densities equivalent display the same wellbore and reservoir fingerprint as the conventional bottom-hole pressure BPR method. It also indicates that the average effective <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.27287pt" id="M2" height="12.5612pt" version="1.1" viewBox="-0.0498162 -9.28833 18.9795 12.5612" width="18.9795pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-108"/></g><g transform="matrix(.0091,0,0,-0.0091,6.474,3.132)"><path id="g190-98" d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z"/></g><g transform="matrix(.0091,0,0,-0.0091,10.304,3.132)"><path id="g190-119" d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z"/></g><g transform="matrix(.0091,0,0,-0.0091,14.445,3.132)"><path id="g190-102" d="M380 106C343 72 306 56 265 56C195 56 116 112 115 248C235 252 361 262 377 265C396 269 400 277 400 297C400 374 333 449 250 449H249C198 449 144 421 103 376S37 269 37 201C37 88 109 -12 232 -12C263 -12 332 6 395 84L380 106ZM225 412C281 412 315 364 314 312C314 297 308 292 290 292C232 290 176 289 120 289C135 370 180 412 225 412Z"/></g></svg> ranges between 43 and 57&#x2009;mD for scenarios (a) to (d) in Example 1.0 and 404&#x2009;mD for scenarios (a) to (b) in Example 2.0 using the new fluid phase empirical model for <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.0498209pt" id="M3" height="8.68572pt" version="1.1" viewBox="-0.0498162 -8.6359 9.95144 8.68572" width="9.95144pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-76" d="M743 650H503L496 622L527 618C563 613 564 603 532 573C449 495 371 431 323 392C301 374 272 355 246 346L280 522C297 609 300 614 379 622L385 650H135L129 622C209 614 215 609 198 522L124 133C106 39 99 35 23 28L17 0H271L277 28C193 35 192 39 208 133L239 316C264 328 280 325 303 288C368 183 435 90 502 0H652L659 28C602 34 584 43 543 94C495 154 403 283 347 369L574 554C634 603 659 612 735 624L743 650Z"/></g></svg> estimation. This is within the <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M4" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-108"/></g></svg> value used in the simulation model and likewise that estimated from the conventional BPR method. Results also discovered that in all six scenarios investigated, the heavier fluid such as water and the weighted average pressure-density equivalent of all fluid gives exact effective <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M5" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-108"/></g></svg> as the conventional BPR method. This approach provides an estimate of the possible fluid phase permeabilities and the &#x25; of each phase contribution to flow at a given point. Hence, at several <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-3.4294pt" id="M6" height="14.8655pt" version="1.1" viewBox="-0.0498162 -11.4361 17.9617 14.8655" width="17.9617pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><path id="g113-101" d="M530 686C535 705 530 712 521 712C504 712 448 684 359 674L358 648H393C437 648 439 646 429 593L400 435C372 447 345 448 332 448C286 448 194 414 144 373C68 311 23 203 23 111C23 26 57 -12 91 -12C120 -12 147 3 188 29C227 54 290 102 341 170H343L322 71C308 6 320 -12 341 -12C373 -12 442 27 501 96L485 120C455 91 422 67 408 67C401 67 401 76 404 91C440 294 479 473 530 686ZM387 375L355 241C326 187 200 53 142 53C126 53 109 73 109 130C109 217 154 337 218 381C240 396 265 404 297 404S372 390 387 375Z"/></g><g transform="matrix(.013,0,0,-0.013,6.302,0)"><path id="g113-113" d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z"/></g><g transform="matrix(.0091,0,0,-0.0091,14.012,-5.741)"><path id="g50-31" d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"/></g></svg> stabilisation points, the relative <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-0.2063999pt" id="M7" height="9.49473pt" version="1.1" viewBox="-0.0498162 -9.28833 6.66314 9.49473" width="6.66314pt"><g transform="matrix(.013,0,0,-0.013,0,0)"><use xlink:href="#g113-108"/></g></svg> can be generated.

Victor Torkiowei Biu

Shi-Yi Zheng

A New Approach in Pressure Transient Analysis: Using Numerical Density Derivatives to Improve Diagnosis of Flow Regimes and Estimation of Reservoir Properties for Multiple Phase Flow

Modeling of limestone reservoirs is traditionally developed applying tectonic fractures concepts or planar discontinuities and has been simulated dynamically without considering nonplanar discontinuities as sedimentary breccias, vugs, fault breccias, and impact breccias, assuming that all these nonplanar discontinuities are tectonic fractures, causing confusion and contradictions in reservoirs characterization. The differences in geometry and connectivity in each discontinuity affect fluid flow, generating the challenge to develop specific analytical models that describe quantitatively hydrodynamic behavior in breccias, vugs, and fractures, focusing on oil flow in limestone reservoirs. This paper demonstrates the differences between types of discontinuities that affect limestone reservoirs and recommends that all discontinuities should be included in simulation and static-dynamic characterization, because they impact fluid flow. To demonstrate these differences, different analytic models are developed. Findings of this work are based on observations of cores, outcrops, and tomography and are validated with field data. The explanations and mathematical modeling developed here could be used as diagnostic tools to predict fluid velocity and fluid flow in limestone reservoirs, improving the complex reservoirs static-dynamic characterization.

Nelson Barros-Galvis

Pedro Villase&#xf1;or

Fernando Samaniego

Analytical Modeling and Contradictions in Limestone Reservoirs: Breccias, Vugs, and Fractures

The purpose of this paper is to examine various DoE methods for uncertainty quantification of production forecast during reservoir management. Considering all uncertainties for analysis can be time consuming and expensive. Uncertainty screening using experimental design methods helps reducing number of parameters to manageable sizes. However, adoption of various methods is more often based on experimenter discretions or company practices. This is mostly done with no or little attention been paid to the risks associated with decisions that emanated from that exercise. The consequence is the underperformance of the project when compared with the actual value of the project. This study presents the analysis of the three families of designs used for screening and four DoE methods used for response surface modeling during uncertainty analysis. The screening methods (sensitivity by one factor at-a-time, fractional experiment, and Plackett-Burman design) were critically examined and analyzed using numerical flow simulation. The modeling methods (Box-Behnken, central composite, D-optima, and full factorial) were programmed and analyzed for capabilities to reproduce actual forecast figures. The best method was selected for the case study and recommendations were made as to the best practice in selecting various DoE methods for similar applications.

Akeem O. Arinkoola

David O. Ogbe

Examination of Experimental Designs and Response Surface Methods for Uncertainty Analysis of Production Forecast: A Niger Delta Case Study

This study presents a novel approach for bundle of tubes modeling of permeability impairment due to asphaltene-induced formation damage attenuated by ultrasound which has been rarely attended in the available literature. Model uses the changes of asphaltene particle size distribution (APSD) as a function of time due to ultrasound radiation, while considering surface deposition and pore throat plugging mechanisms. The proposed model predicts the experimental data of permeability reduction during coinjection of solvent and asphaltenic oil into core with reasonable agreement. Viscosity variation due to sonication of crude oil is used to determine the fluid mobility applied in the model. The results of modeling indicate that the fluid samples exposed to ultrasound may cause much less asphaltene-induced damage inside the porous medium. Sensitivity analysis of the model parameters showed that there is an optimum time period during which the best stimulation efficiency is observed.  The results of this work can be helpful to better understand the role of ultrasound prohibition in dynamic behavior of asphaltene deposition in porous media. Furthermore, the present model could be potentially utilized for modeling of other time-dependent particle induced damages.

Arash Rabbani

Mohammad Hossein Ghazanfari

Mahmood Amani

Asphaltene Formation Damage Stimulation by Ultrasound: An Analytical Approach Using Bundle of Tubes Modeling

Oil-based mud (OBM) was formulated with soybean oil extracted from soybean using the Soxhlet extraction method. The formulated soybean mud properties were compared with diesel oil mud properties. The compared properties were rheological properties, yield point and gel strength, and mud density and filtration loss properties, fluid loss and filter cake. The results obtained show that the soybean oil mud exhibited Bingham plastic rheological model with applicable (low) yield point and gel strength when compared with the diesel oil mud. The mud density measurement showed that soybean OBM was slightly higher than diesel OBM with mud density values of 8.10&#x2009;lb/gal and 7.98&#x2009;lb/gal, respectively, at barite content of 10&#x2009;g. Additionally, the filtration loss test results showed that soybean mud fluid loss volumes, water and oil, were 13&#x2009;mL and 10&#x2009;mL, respectively, compared to diesel oil mud volume of 15&#x2009;mL and 12&#x2009;mL. Furthermore, the filtration loss test indicated that the soybean oil mud with filter cake thickness of 2&#x2009;mm had a cake characteristic of thin and soft while the diesel oil mud resulted in filter cake thickness of 2.5&#x2009;mm with cake characteristic of firm and rubbery. In comparison with previous published works in the literature, the soybean oil mud exhibits superior rheological and filtration property over other vegetable oil-based muds. Therefore, the formulated soybean oil mud exhibited good drilling mud properties that would compare favourably with those of diesel oil muds. Its filter cake characteristic of thin and soft is desirable and significant to avert stuck pipe during drilling operations, meaning that an oil-based drilling mud could be formulated from soybean oil.

Okorie E. Agwu

Anietie N. Okon

Francis D. Udoh

A Comparative Study of Diesel Oil and Soybean Oil as Oil-Based Drilling Mud

The ability to optimize drilling procedures and economics involves simulation to understand the effects operational parameters and equipment design have on the ROP. An analysis applying drilling performance modeling to optimize drilling operations has been conducted to address this issue. This study shows how optimum operational parameters and equipment can be predicted by simulating drilling operations of preexisting wells in a Northwest Louisiana field. Reference well data was gathered and processed to predict the &#x201c;drillability&#x201d; of the formations encountered by inverting bit specific ROP models to solve for rock strength. The output data generated for the reference well was formatted to simulate upcoming wells. A comparative analysis was conducted between the predicted results and the actual results to show the accuracy of the simulation. A significant higher accuracy is shown between the simulated and actual drilling results. Once simulations were validated, optimum drilling parameters and equipment specifications were found by varying different combinations of weight on bit (WOB), rotary speed (RPM), hydraulics, and bit specifications until the highest drilling rate is achieved for each well. A qualitative and quantitative analysis of the optimized results was conducted to assess the potential operational and economic benefits on drilling operations.

David Hankins

Saeed Salehi

Fatemeh Karbalaei Saleh

An Integrated Approach for Drilling Optimization Using Advanced Drilling Optimizer

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Journal of Petroleum Engineering