ORA-01031: insufficient privileges . The invoked JCA adapter raised a resource exception.

You have created a simple BPEL process in SOA Suite 11g .YOu are using db adapter which in inserting data in to a table in your database.
You deployed the project and when you invoked it you get following issues.

Non Recoverable System Fault :
Exception occured when binding was invoked. Exception occured during invocation of JCA binding: "JCA Binding execute of Reference operation 'insert' failed due to: DBWriteInteractionSpec Execute Failed Exception. insert failed. Descriptor name: [db.Customer]. Caused by java.sql.SQLSyntaxErrorException: ORA-01031: insufficient privileges . ". The invoked JCA adapter raised a resource exception. Please examine the above error message carefully to determine a resolution.

Reason is that your datasource is not able to connect to the database.

Create a new datasource and a new connection factory(jndi)

Use this new JNDI in jdeveloper to connect to the datasource.

Again keep in mind that do mention the data source also in jdeveloper wizard while configuring adapter

Make sure that the schema user has sufficient priviledge to perform the operation.

For me grant dba to user; worked.