A QUICK APPROACH FOR QUICK ESTIMATION OF WATER INFLUX

EGU DANIEL IKECHUKWU DEPARTMENT OF PETROLEUM ENGINEERING, MADONNA UNIVERSITY, NIGERIA

ABSTRACT Water influx estimation by manual or modeling approach requires a significant amount of time and for the final result to be accurate and precise becomes so cumbersome due to the nature and stages of the existing equations or models depending on the complexities of the reservoir. Deciding on the appropriate model to use requires performing rigorous calculations for the cumulative water influx based on known models and this can be very tedious when it’s carried out manually especially when the amount of data been considered is very large. This work is aimed at developing a computer alogorithm for faster estimation of reservoir water influx models and compiling these models in the form of a usable Windows Operating Systems desktop application, storage of user input data to perform quicker calculations and to compare results of the different models based on their different calculations procedures. The programming language which computed the iterations helped to transfer the user input data and results of final computation into the database are known as Hypertext Preprocessor (PHP). Results shows that water influx volumes for different models gave error differences for manual and computer approaches of ± 0.006, ±0.013, ±0.044, and ±0.1 for 365 days, 730 days, 1095 days, and 1460 days. It is however recommended that a chart engine be integrated into the application’s environment for easy identification of the proper model to use.

Key words: water influx, Hypertext Preprocessor, errors, model, data.

INTRODUCTION Water influx models are mathematical models that simulate and predict aquifer performance. Most importantly, they predict the cumulative water influx history. When successfully integrated with a reservoir simulator, the net result is a model that effectively simulates performance of water drive reservoirs. Nearly all reservoirs are bounded on a portion or all of their peripheries by water bearing rocks called aquifers (Dake, 1994). The aquifers may be so large compared with the reservoirs they adjoin as to appear infinite for all practical purposes, and they may range down to those as small as to be negligible in their effect on reservoir performance. The aquifer itself may be entirely bounded by impermeable rock so that the reservoir and aquifer together form a closed, or volumetric, unit. On the other hand, their reservoir may outcrop at one or more places where it may be replenished by surface waters. Finally, an aquifer may be essentially horizontal with the reservoir it adjoins, or it may rise, as at the edge of structural basins, considerably above the reservoir to provide some artesian kind of flow of water to the reservoir (Allard and Chen, 1989). In response to a pressure drop in the reservoir, the aquifer reacts to offset, or retard, pressure decline by providing a source of water influx or encroachment by

a. Expansion of the water

b. Expansion of other known or unknown hydrocarbon accumulation in the aquifer rock

c. Compressibility of the aquifer rock and also either by

d. Artesian flow

In other to determine the effect an underlying or edge aquifer has on the production from a reservoir, it is necessary to be able to calculate the amount of water that has in fluxed into the reservoir from the aquifer. This calculation can be made using the material balance equation when the initial hydrocarbon amount and the production are known. The Havlena and Odeh approach to material balance calculations

1 can sometime be used to obtain an estimate for both water influx and initial hydrocarbon amount (Craft and Hawkins 1991).

For the case of a water-drive reservoir, no original gas cap, and negligible compressibility:

1

If the correct values of We are placed in this equation as a function of reservoir pressure, then the equation should plot as a straight line with intercept, N, and slope equal to unity. The procedure to solve for both W e and N in this case involves assuming a model for We as a function of pressure, calculating We making the plot of F/Eo versus We/Eo, and observing if a straight line is obtained (Coats, 1962). If a straight line is not obtained, then a new model for We is assumed and the necessary procedure repeated as shown in figure 1. The deviation labeled as being due to using the wrong geometry means that radial geometry has been assumed whereas linear geometry would probably be more appropriate. With radial geometry there is a larger body of water in close proximity to the reservoir, for the same aquifer volume, than for a linear aquifer and, as a result, response of the radial aquifer is greater causing deviation below the theoretical straight line.

The different water influx models are based on assumptions that describe the characteristics of the aquifer. The various models proposed for calculating cumulative water influx We into the reservoir are outlined below:  Pot aquifer model  Schilthuis’ steady-state model  Hurst’s modified steady-state model  Van Everdingen-Hurst unsteady-state model . Edge-water drive . Bottom-water drive . Linear-water drive

Figure 1: Trial and error method of determining the correct aquifer model (Craft et al. 1991)

 The Carter-Tracy unsteady-state model  Fetkovich’s method . Radial aquifer . Linear aquifer Due to the inherent uncertainties in the aquifer characteristics, all of the proposed models require historical reservoir performance data to evaluate constants representing aquifer property parameters that are rarely known from exploration-development drilling with sufficient accuracy for direct application.

2 Choosing an appropriate model for water influx involves many uncertainties. Some of these include the; Size and shape of the aquifer and Aquifer properties such as: porosity and permeability. Normally, little is known about these parameters largely because the coast to drill into the aquifer to obtain the necessary data is not often justified.

STATEMENT OF PROBLEM Water influx estimation by manual approach requires a significant amount of time and for the final result to be accurate in order to be precise that the model which has been chosen to predict the aquifer is the appropriate model. Deciding on the appropriate model to use requires performing calculation for the cumulative water influx based on the models own method and this can be very tedious when it’s carried out manually specially when the amount of data been considered is very large.

AIMS AND OBJECTIVES  Developing a computer alogorithm for reservoir water influx models (which are already numerical in their nature)

 Compiling these models in the form of a usable Windows Operating Systems desktop application

 Storage of user input data and Perform quicker calculations

 Compare results of the different models based on their different calculations methods/procedures.

METHODOLOGY The following programming languages and software are required to build the application:

 HTML (Hyper Text Markup Language)

 Text Editor (such as Bracket, Note Pad++, Dreamweaver)

 CSS (Cascading Style Sheet)

 Web Browser (such as Chrome, IE-9, Mozilla)

 Javascript (jQuery)

 Php (Hypertext Preprocessor)

 Server (such as WAMP, XAMP, ASP)

 MySQL

 Reservoir data used for verifying the software

HYPER TEXT MARKUP LANGUAGE (HTML) HTML is a language for describing web pages, HTML stands for Hyper Text Markup Language, HTML is a markup language, a markup language is a set of markup tags, and thetags describe document content. HTML documents contain HTML tags and plain text. HTML documents are also called web pages;HTML markup tags are usually called HTML tags.HTML tags are keywords (tag names) surrounded by angle brackets like . HTML tags normally come in pairs like

and

, the first tag in a pair is the start tag, the second tag is the end tag, the end tag is written like the start tag with a slash before the tag name. Start and end tags are also called opening tags and closing tags.

CASCADING STYLE SHEET (CSS) CSS stands for Cascading Style Sheets, styles define how to display HTML elements. External Style Sheets can save a lot of work, external Style Sheets are stored in CSS files. A CSS rule set consists of a selector and a declaration block figure 2. The selector points to the HTML element you want to style.The 3 declaration block contain one or more declarations separated by semi-colons. Each declaration includes a property name and a value, separated by a colon.

JAVASCRIPT (JQUERY) JavaScript is one of three languages all web developers must learn:

1. HTML to define the content of web pages

2. CSS to specify the layout of web pages

3. JavaScript to program the behavior of web pages

Figure 2: Cascading Style Sheet (CSS) Syntax

JavaScript is the language for HTML, for the Web, for computers, servers, laptops, tablets, smart phones, and more. jQuery is a JavaScript Library. jQuery greatly simplifies JavaScript programming. The jQuery syntax is tailor made for selecting HTML elements and performing some action on the element(s). Basic syntax is: $(selector).action()

 A $ sign to define/access jQuery

 A (selector) to "query (or find)" HTML elements

 A jQuery action() to be performed on the element(s)

Examples:

$("p").hide() - hides all

elements.

$("#test").hide() - hides the element with id="test".

WEB BROWSER The purpose of a web browser (such as Google Chrome, Internet Explorer, Firefox, Safari) is to read HTML documents and display them as web pages. The browser does not display the HTML tags, but uses the tags to determine how the content of the HTML page is to be presented/displayed to the user.

SERVER The server such as WAMP reads and translates the PHP source code into HTML, servers such as WAMP are packed with free to use relational data base management systems RDBMS such as MySQL.

HYPERTEXT PREPROCESSOR (PHP) PHP is an acronym for "PHP Hypertext Pre-processor". PHP is a widely-used, open source scripting language, PHP scripts are executed on the server, PHP costs nothing, it is free to download and use. PHP files can contain text, HTML, CSS, JavaScript, and PHP code. PHP codes are executed on the server, and the result is returned to the browser as plain HTML. PHP files have extension ".php".

FUNCTIONS OF PHP  PHP can generate dynamic page content 4  PHP can create, open, read, write, delete, and close files on the server  PHP can collect form data  PHP can send and receive cookies  PHP can add, delete, modify data in your database  PHP can restrict users to access some pages on your website  PHP can encrypt data With PHP you are not limited to output HTML. You can output images, PDF files, and even flash movies. You can also output any text, such as XHTML and XML. BASIC PHP SYNTAX  A PHP script can be placed anywhere in the document.  A PHP script starts with : The default file extension for PHP files is ".php". A PHP file normally contains HTML tags, and some PHP scripting code. DATABASE (MYSQL) The database is used for storage of user input data and the calculated results. The programming language of the database is Structured Query Language (SQL). SQL is a standard language for accessing and manipulating databases. SQL lets you access and manipulate databases, SQL is an ANSI (American National Standards Institute) standard.

FUNCTIONS OF SQL  SQL can execute queries against a database

 SQL can retrieve data from a database

 SQL can insert records in a database

 SQL can update records in a database

 SQL can delete records from a database

 SQL can create new databases

 SQL can create new tables in a database

 SQL can create stored procedures in a database

 SQL can set permissions on tables, procedures, and views

USING SQL IN A WEB SITE To build a web application that shows data from a database, you will need:  An RDBMS database program (i.e. MS Access, SQL Server, MySQL)  To use a server-side scripting language, like PHP or ASP  To use SQL to get the data you want  To use HTML / CSS for designing the web page output RDBMS  RDBMS stands for Relational Database Management System.  RDBMS is the basis for SQL, and for all modern database systems such as MS SQL Server, IBM DB2, Oracle, MySQL, and Microsoft Access. 5  The data in RDBMS is stored in database objects called tables.  A table is a collection of related data entries and it consists of columns and rows TEXT EDITORS HTML can be edited by using a professional HTML editor like:

 Adobe Dreamweaver

 Microsoft Expression Web

 CoffeeCup HTML Editor

 Bracket

However, for learning HTML I recommend a text editor like Notepad (PC) or TextEdit (Mac).

RESERVOIR DATA Table 1 is the data used for verifying the accuracy of the software. The example case study to be used for verifying the accuracy of the software was sited from Tarek (2006). The pressure history of the reservoir was given from time = 0 day to time = 1460 days and the pressure drops from an intial pressure of 2740psi to 1949psi for the entire period of 1460days.

TABLE 1: CASE STUDY OF A RESERVOIR AND AQUIFER PROPERTIES

Parameters Values Time (days) Pressure (psi) Initial reservoir pressure Pi 2740 psi 0 2740 Reservoir properties Reservoir area 40,363 acres 365 2500 Aquifer water viscosity 0.55cp 730 2290 Aquifer permeability K 200md 1095 2109 Encroachment angle 140 o 1460 1949 Aquifer area 1,000,000 acres Aquifer Properies Aquifer porosity 0.25 Aquifer thickness h 100ft Aquifer rock compressibility Cf 3 x 10 -6 psi -1 Aquifer water compressibility Cw 4 x 10 -6 psi -1 Total compressibility Ct = Cw + Cf 7 x 10-6 psi -1

NAVIGATION MENU

Accessing any of the water influx models can be done through either of the following: (The Select Model Panel and The File button) The Select Model panel is only visible on the home page, to access any of the other models while working in the software can be done through the File button.

CODING IN PHP The programming language which computes the iterations, help transfer user input data and results of final computation in to the database is known as PHP, as stated in the foregoing sections of this chapter, PHP is a server side language which outputs HTML to the client side also known as the Browser.

RESULTS AND DISCUSSION The example case study to be used for verifying the accuracy of the softwarewas sited from Tarek Ahmed’s “Advanced Reservoir Engineering” Second edition. Example 2.10b pages(2/183 – 2/184)).

RESULTS OF MANUAL APPROACH

The results obtained by solving for the cumulative water influx for a time period of 0 day to 1460days are tabulated in Table 2. Figure 3 is a plot of cumulative water influx vs the time. This chart shows increase in the cumulative water influx as the time increases.

6 RESULTS OF COMPUTER APPROACH

The results obtained by solving for the cumulative water influx for a time period of 0 day to 1460 days are tabulated in Table 2 and also a chart was plotted figure 3 which shows an inclination in the cumulative water influx as the time increases. The curve obtained on this chart is similar to the one obtained using the manual approach.

TABLE 2: RESULTS OF CUMMULATIVE WATER INFLUX FOR 1460 DAYS

Manual Approach

ܲ ܲ ܲ ܲ ሺܲതܲ ሻ ିିଵ െെሺܲതܲ ሻ ሺܲഥܲ ݎሻܲ݊ ሺܲതܲ ሻ ିିଵ n Time (days) Pr (ΔWe)n (MMbbl) (We) (MMbbl) 0 0 2740 2740 0 0 0 0 1 365 2500 2620 2740 120 3.925 3.925 2 730 2290 2395 2689 294 9.615 13.54 3 1095 2109 2199 2565 366 11.97 25.51 4 1460 1949 2029 2409 381 12.461 37.971

Computer Approach ܲ ܲ ݁ ݎݎ ݁ ݎ ݅ ݁ ݁ ܲ ݁ ܲܲ ିିଵ ܲܲ ܣݏݏݏݏݏݏܲݎ ܲݍݏݏݏݏݏ݂ܲܲܲݎ ݏ ݏݏܲܲ ݎ ݏݏ Water influx ΔWe n Cummulative water influx ሺ ݏݏሻ n Time (days) Pressure P n (psi) ʹ (bbl) We (bbl) We (MMbbl) 0 0 2740 2740 0 0 0 0 1 365 2500 2620 2740 3931438.112 3931438.112 3.931 2 730 2290 2395 2688.691219 9621907.102 13553345.21 13.553 3 1095 2109 2199.5 2563.116733 11912805.67 25466150.89 25.466 4 1460 1949 2029 2407.643972 12405127.86 37871278.75 37.871

Figure 3: A plot of Cumulative water influx VS Time for the manual approach

Figure 4: A plot of Cumulative water influx VS Time for the computer approach

RESULTS OF DEVIATION IN FINAL COMPUTATION BY BOTH METHODS

Table 3 shows the deviation of the result obtained by the computer approach from the manual approach. Figure 5 is a plot of both methods, using each individual results of cumulative water influx against the time. The chart shows a very close similarity between both methods. The deviation was plotted against the time (figure 6) and it shows an increase in the deviation as the time increases.

DISCUSSION OF RESULTS The results obtained as shown in Table 2, shows that the significant amount of time required to compute the cumulative water influx starting at 365 days is a major advantage of using the computer application when compared to the manual approach of solving the same problem which also obtained same results as shown in Table 3 with a difference of ±0.006 MMbbl. This deviation from the result obtained from the manual approach is as a result of approximated errors during calculation. Figures 3 and 4 shows a similar curve obtained for both manual and computer approaches when the cumulative water influx is plotted against the producing times. The difference between both curves can be seen because the difference are in fractions but through observation one can notice that as the producing time increases, the fractions approaches a whole number.

TABLE 3: COMPARISON OF DEVIATIONS OF MANUAL AND COMPUTER TECHNIQUES

7 Manual approach result Computer approach result Difference

Parameter We (MMbbl) We (MMbbl) 0 0 0 ±0 365 3.925 3.931 ±0.006 Time (days) 730 13.54 13.553 ±0.013 1095 25.51 25.466 ±0.044 1460 37.971 37.871 ±0.1

Figure 5: A plot of cumulative water influx VS Time for both Computer and manual approaches

Figure 6: A plot of deviation of the computer approach from the manual approach VS Time.

CONCLUSION In conclusion the set objectives of this project as stated in chapter one which are;

 Developing a computer alogorithm for reservoir water influx models (which are already numerical in their nature)

 Compiling these models in the form of a usable Windows Operating Systems desktop application

 Storage of user input data and Perform quicker calculations

 Compare results of the different models based on their different calculations methods/procedures. were achieved at the end of this project.

RECOMMENDATIONS Recommendations that can be made in order to improve the quality of this project are as follows;

 Integration of a chart engine into the application’s environment for easy identification of the proper model to use.  Replacing the method of submitting user input values with the use of jQuery load() method.  Improving the user interface for a better use of the application  Creating a general user interface that accepts user input values and computes the final result for all the models.  The inclusion of a security interface that accepts a password and username could be included in order to protect data in the database.

REFERENCES Allard, D. R., and Chen, S. M. (1988). Calculations of water influx for bottom water drive reservoirs. SPE Reservoir Engineering, May edition, pp. 369–379.

Coats, K. (1962). A mathematical model for water movement about reservoirs. SPE Journal, March edition, pp. 44–52.

8 Craft, B., Hawkins, M., and Terry, R. (1991). Applied petroleum reservoir engineering; 2nd edition. Prentice Hall publishers, United Kingdom.

Dake, L. (1994). The practice of reservoir engineering. Amsterdam: Elsevier publishers.

APPENDIX A

INSERTING DATA INTO THE SOFTWARE STEP 1: Select the Fetkovich’s “Radial Flow” model either through the Select Model panel or File button to view Figure A-1.

STEP 2: Input the Data Name (OML-20) and click the button this name will be used to save the inputed data and output result. Procceed to step 3.

Note: If the above data name (OML-20) already exists in the database then all related information to the name will be retrived else the error message in figure A-2 will be displayed

STEP 3: Input the reservoir-aquifer parameter with the boundary pressure for time = 0 days and pressure = 2740psi and click on the button. Figure A-3

If all the required data are set the success message in figure A-4 will be displayed.

STEP 4: This step requires the user to only input the boundary pressure history starting at time = 365days and pressure = 2500psi and then clicking on the button to input the data into the database.

Figure A-1: Input Reservoir-Aquifer Parameter interface

9 Figure A-2: Error Message when specified Data name does not exit in the database

Figure A-3: Inputing data for Time = 0 days

Figure A-4: Success Message

STEP 5: Repeat step 4 with time at Tn+1 (730, 1095, 1460) and Pressure at Pn+1 (2290, 2109, 1940) until all boundary pressure histrory data have been completely entered figure A-5.

STEP 6: Compute the cumulative water influx We by clicking the button. Figure A-6 shows the final result of the calculation.

10 Figure A-5: Complete pressure history data

Figure A-6: Successful computation of the We

11